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<p>In deep learning, every optimization step operates on multiple input examples for robust training. Thus, efficient batching is crucial. For image inputs, batching is straightforward; N images are resized to the same height and width and stacked as a 4 dimensional tensor of shape <code>N x 3 x H x W</code>. For meshes, batching is less straightforward.</p>
<p><img src="assets/batch_intro.png" alt="batch_intro" align="middle"/></p>
<h2><a class="anchor" aria-hidden="true" id="batch-modes-for-meshes"></a><a href="#batch-modes-for-meshes" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Batch modes for meshes</h2>
<p>Assume you want to construct a batch containing two meshes, with <code>mesh1 = (v1: V1 x 3, f1: F1 x 3)</code> containing <code>V1</code> vertices and <code>F1</code> faces, and <code>mesh2 = (v2: V2 x 3, f2: F2 x 3)</code> with <code>V2 (!= V1)</code> vertices and <code>F2 (!= F1)</code> faces. The <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/structures/meshes.py">Meshes</a> data structure provides three different ways to batch <em>heterogeneous</em> meshes. If <code>meshes = Meshes(verts = [v1, v2], faces = [f1, f2])</code> is an instantiation of the data structure, then</p>
<p>Assume you want to construct a batch containing two meshes, with <code>mesh1 = (v1: V1 x 3, f1: F1 x 3)</code> containing <code>V1</code> vertices and <code>F1</code> faces, and <code>mesh2 = (v2: V2 x 3, f2: F2 x 3)</code> with <code>V2 (!= V1)</code> vertices and <code>F2 (!= F1)</code> faces. The <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/structures/meshes.py">Meshes</a> data structure provides three different ways to batch <em>heterogeneous</em> meshes. If <code>meshes = Meshes(verts = [v1, v2], faces = [f1, f2])</code> is an instantiation of the data structure, then</p>
<ul>
<li>List: Returns the examples in the batch as a list of tensors. Specifically, <code>meshes.verts_list()</code> returns the list of vertices <code>[v1, v2]</code>. Similarly, <code>meshes.faces_list()</code> returns the list of faces <code>[f1, f2]</code>.</li>
<li>Padded: The padded representation constructs a tensor by padding the extra values. Specifically, <code>meshes.verts_padded()</code> returns a tensor of shape <code>2 x max(V1, V2) x 3</code> and pads the extra vertices with <code>0</code>s. Similarly, <code>meshes.faces_padded()</code> returns a tensor of shape <code>2 x max(F1, F2) x 3</code> and pads the extra faces with <code>-1</code>s.</li>
@ -74,6 +74,6 @@
</ul>
<p><img src="assets/batch_modes.gif" alt="batch_modes" height="450" align="middle" /></p>
<h2><a class="anchor" aria-hidden="true" id="use-cases-for-batch-modes"></a><a href="#use-cases-for-batch-modes" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Use cases for batch modes</h2>
<p>The need for different mesh batch modes is inherent to the way PyTorch operators are implemented. To fully utilize the optimized PyTorch ops, the <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/structures/meshes.py">Meshes</a> data structure allows for efficient conversion between the different batch modes. This is crucial when aiming for a fast and efficient training cycle. An example of this is <a href="https://github.com/facebookresearch/meshrcnn">Mesh R-CNN</a>. Here, in the same forward pass different parts of the network assume different inputs, which are computed by converting between the different batch modes. In particular, <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/ops/vert_align.py">vert_align</a> assumes a <em>padded</em> input tensor while immediately after <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/ops/graph_conv.py">graph_conv</a> assumes a <em>packed</em> input tensor.</p>
<p>The need for different mesh batch modes is inherent to the way PyTorch operators are implemented. To fully utilize the optimized PyTorch ops, the <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/structures/meshes.py">Meshes</a> data structure allows for efficient conversion between the different batch modes. This is crucial when aiming for a fast and efficient training cycle. An example of this is <a href="https://github.com/facebookresearch/meshrcnn">Mesh R-CNN</a>. Here, in the same forward pass different parts of the network assume different inputs, which are computed by converting between the different batch modes. In particular, <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/ops/vert_align.py">vert_align</a> assumes a <em>padded</em> input tensor while immediately after <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/ops/graph_conv.py">graph_conv</a> assumes a <em>packed</em> input tensor.</p>
<p><img src="assets/meshrcnn.png" alt="meshrcnn" width="700" align="middle" /></p>
</span></div></article></div><div class="docLastUpdate"><em>Last updated by Jeremy Reizenstein</em></div><div class="docs-prevnext"><a class="docs-prev button" href="/docs/datasets"><span class="arrow-prev"></span><span>Data loaders</span></a><a class="docs-next button" href="/docs/cubify"><span>Cubify</span><span class="arrow-next"></span></a></div></div></div><nav class="onPageNav"><ul class="toc-headings"><li><a href="#batch-modes-for-meshes">Batch modes for meshes</a></li><li><a href="#use-cases-for-batch-modes">Use cases for batch modes</a></li></ul></nav></div><footer class="nav-footer" id="footer"><section class="sitemap"><div class="footerSection"><div class="social"><a class="github-button" href="https://github.com/facebookresearch/pytorch3d" data-count-href="https://github.com/facebookresearch/pytorch3d/stargazers" data-show-count="true" data-count-aria-label="# stargazers on GitHub" aria-label="Star PyTorch3D on GitHub">pytorch3d</a></div></div></section><a href="https://opensource.facebook.com/" target="_blank" rel="noreferrer noopener" class="fbOpenSource"><img src="/img/oss_logo.png" alt="Facebook Open Source" width="170" height="45"/></a><section class="copyright">Copyright © 2021 Facebook Inc<br/>Legal:<a href="https://opensource.facebook.com/legal/privacy/" target="_blank" rel="noreferrer noopener">Privacy</a><a href="https://opensource.facebook.com/legal/terms/" target="_blank" rel="noreferrer noopener">Terms</a></section></footer></div></body></html>

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<p>In deep learning, every optimization step operates on multiple input examples for robust training. Thus, efficient batching is crucial. For image inputs, batching is straightforward; N images are resized to the same height and width and stacked as a 4 dimensional tensor of shape <code>N x 3 x H x W</code>. For meshes, batching is less straightforward.</p>
<p><img src="assets/batch_intro.png" alt="batch_intro" align="middle"/></p>
<h2><a class="anchor" aria-hidden="true" id="batch-modes-for-meshes"></a><a href="#batch-modes-for-meshes" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Batch modes for meshes</h2>
<p>Assume you want to construct a batch containing two meshes, with <code>mesh1 = (v1: V1 x 3, f1: F1 x 3)</code> containing <code>V1</code> vertices and <code>F1</code> faces, and <code>mesh2 = (v2: V2 x 3, f2: F2 x 3)</code> with <code>V2 (!= V1)</code> vertices and <code>F2 (!= F1)</code> faces. The <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/structures/meshes.py">Meshes</a> data structure provides three different ways to batch <em>heterogeneous</em> meshes. If <code>meshes = Meshes(verts = [v1, v2], faces = [f1, f2])</code> is an instantiation of the data structure, then</p>
<p>Assume you want to construct a batch containing two meshes, with <code>mesh1 = (v1: V1 x 3, f1: F1 x 3)</code> containing <code>V1</code> vertices and <code>F1</code> faces, and <code>mesh2 = (v2: V2 x 3, f2: F2 x 3)</code> with <code>V2 (!= V1)</code> vertices and <code>F2 (!= F1)</code> faces. The <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/structures/meshes.py">Meshes</a> data structure provides three different ways to batch <em>heterogeneous</em> meshes. If <code>meshes = Meshes(verts = [v1, v2], faces = [f1, f2])</code> is an instantiation of the data structure, then</p>
<ul>
<li>List: Returns the examples in the batch as a list of tensors. Specifically, <code>meshes.verts_list()</code> returns the list of vertices <code>[v1, v2]</code>. Similarly, <code>meshes.faces_list()</code> returns the list of faces <code>[f1, f2]</code>.</li>
<li>Padded: The padded representation constructs a tensor by padding the extra values. Specifically, <code>meshes.verts_padded()</code> returns a tensor of shape <code>2 x max(V1, V2) x 3</code> and pads the extra vertices with <code>0</code>s. Similarly, <code>meshes.faces_padded()</code> returns a tensor of shape <code>2 x max(F1, F2) x 3</code> and pads the extra faces with <code>-1</code>s.</li>
@ -74,6 +74,6 @@
</ul>
<p><img src="assets/batch_modes.gif" alt="batch_modes" height="450" align="middle" /></p>
<h2><a class="anchor" aria-hidden="true" id="use-cases-for-batch-modes"></a><a href="#use-cases-for-batch-modes" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Use cases for batch modes</h2>
<p>The need for different mesh batch modes is inherent to the way PyTorch operators are implemented. To fully utilize the optimized PyTorch ops, the <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/structures/meshes.py">Meshes</a> data structure allows for efficient conversion between the different batch modes. This is crucial when aiming for a fast and efficient training cycle. An example of this is <a href="https://github.com/facebookresearch/meshrcnn">Mesh R-CNN</a>. Here, in the same forward pass different parts of the network assume different inputs, which are computed by converting between the different batch modes. In particular, <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/ops/vert_align.py">vert_align</a> assumes a <em>padded</em> input tensor while immediately after <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/ops/graph_conv.py">graph_conv</a> assumes a <em>packed</em> input tensor.</p>
<p>The need for different mesh batch modes is inherent to the way PyTorch operators are implemented. To fully utilize the optimized PyTorch ops, the <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/structures/meshes.py">Meshes</a> data structure allows for efficient conversion between the different batch modes. This is crucial when aiming for a fast and efficient training cycle. An example of this is <a href="https://github.com/facebookresearch/meshrcnn">Mesh R-CNN</a>. Here, in the same forward pass different parts of the network assume different inputs, which are computed by converting between the different batch modes. In particular, <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/ops/vert_align.py">vert_align</a> assumes a <em>padded</em> input tensor while immediately after <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/ops/graph_conv.py">graph_conv</a> assumes a <em>packed</em> input tensor.</p>
<p><img src="assets/meshrcnn.png" alt="meshrcnn" width="700" align="middle" /></p>
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<p>The <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/ops/cubify.py">cubify operator</a> converts an 3D occupancy grid of shape <code>BxDxHxW</code>, where <code>B</code> is the batch size, into a mesh instantiated as a <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/structures/meshes.py">Meshes</a> data structure of <code>B</code> elements. The operator replaces every occupied voxel (if its occupancy probability is greater than a user defined threshold) with a cuboid of 12 faces and 8 vertices. Shared vertices are merged, and internal faces are removed resulting in a <strong>watertight</strong> mesh.</p>
<p>The <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/ops/cubify.py">cubify operator</a> converts an 3D occupancy grid of shape <code>BxDxHxW</code>, where <code>B</code> is the batch size, into a mesh instantiated as a <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/structures/meshes.py">Meshes</a> data structure of <code>B</code> elements. The operator replaces every occupied voxel (if its occupancy probability is greater than a user defined threshold) with a cuboid of 12 faces and 8 vertices. Shared vertices are merged, and internal faces are removed resulting in a <strong>watertight</strong> mesh.</p>
<p>The operator provides three alignment modes {<em>topleft</em>, <em>corner</em>, <em>center</em>} which define the span of the mesh vertices with respect to the voxel grid. The alignment modes are described in the figure below for a 2D grid.</p>
<p><img src="https://user-images.githubusercontent.com/4369065/81032959-af697380-8e46-11ea-91a8-fae89597f988.png" alt="input"></p>
</span></div></article></div><div class="docLastUpdate"><em>Last updated by Nikhila Ravi</em></div><div class="docs-prevnext"><a class="docs-prev button" href="/docs/batching"><span class="arrow-prev"></span><span>Batching</span></a><a class="docs-next button" href="/docs/visualization"><span>Plotly Visualization</span><span class="arrow-next"></span></a></div></div></div><nav class="onPageNav"></nav></div><footer class="nav-footer" id="footer"><section class="sitemap"><div class="footerSection"><div class="social"><a class="github-button" href="https://github.com/facebookresearch/pytorch3d" data-count-href="https://github.com/facebookresearch/pytorch3d/stargazers" data-show-count="true" data-count-aria-label="# stargazers on GitHub" aria-label="Star PyTorch3D on GitHub">pytorch3d</a></div></div></section><a href="https://opensource.facebook.com/" target="_blank" rel="noreferrer noopener" class="fbOpenSource"><img src="/img/oss_logo.png" alt="Facebook Open Source" width="170" height="45"/></a><section class="copyright">Copyright © 2021 Facebook Inc<br/>Legal:<a href="https://opensource.facebook.com/legal/privacy/" target="_blank" rel="noreferrer noopener">Privacy</a><a href="https://opensource.facebook.com/legal/terms/" target="_blank" rel="noreferrer noopener">Terms</a></section></footer></div></body></html>
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<p>The <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/ops/cubify.py">cubify operator</a> converts an 3D occupancy grid of shape <code>BxDxHxW</code>, where <code>B</code> is the batch size, into a mesh instantiated as a <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/structures/meshes.py">Meshes</a> data structure of <code>B</code> elements. The operator replaces every occupied voxel (if its occupancy probability is greater than a user defined threshold) with a cuboid of 12 faces and 8 vertices. Shared vertices are merged, and internal faces are removed resulting in a <strong>watertight</strong> mesh.</p>
<p>The <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/ops/cubify.py">cubify operator</a> converts an 3D occupancy grid of shape <code>BxDxHxW</code>, where <code>B</code> is the batch size, into a mesh instantiated as a <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/structures/meshes.py">Meshes</a> data structure of <code>B</code> elements. The operator replaces every occupied voxel (if its occupancy probability is greater than a user defined threshold) with a cuboid of 12 faces and 8 vertices. Shared vertices are merged, and internal faces are removed resulting in a <strong>watertight</strong> mesh.</p>
<p>The operator provides three alignment modes {<em>topleft</em>, <em>corner</em>, <em>center</em>} which define the span of the mesh vertices with respect to the voxel grid. The alignment modes are described in the figure below for a 2D grid.</p>
<p><img src="https://user-images.githubusercontent.com/4369065/81032959-af697380-8e46-11ea-91a8-fae89597f988.png" alt="input"></p>
</span></div></article></div><div class="docLastUpdate"><em>Last updated by Nikhila Ravi</em></div><div class="docs-prevnext"><a class="docs-prev button" href="/docs/batching"><span class="arrow-prev"></span><span>Batching</span></a><a class="docs-next button" href="/docs/visualization"><span>Plotly Visualization</span><span class="arrow-next"></span></a></div></div></div><nav class="onPageNav"></nav></div><footer class="nav-footer" id="footer"><section class="sitemap"><div class="footerSection"><div class="social"><a class="github-button" href="https://github.com/facebookresearch/pytorch3d" data-count-href="https://github.com/facebookresearch/pytorch3d/stargazers" data-show-count="true" data-count-aria-label="# stargazers on GitHub" aria-label="Star PyTorch3D on GitHub">pytorch3d</a></div></div></section><a href="https://opensource.facebook.com/" target="_blank" rel="noreferrer noopener" class="fbOpenSource"><img src="/img/oss_logo.png" alt="Facebook Open Source" width="170" height="45"/></a><section class="copyright">Copyright © 2021 Facebook Inc<br/>Legal:<a href="https://opensource.facebook.com/legal/privacy/" target="_blank" rel="noreferrer noopener">Privacy</a><a href="https://opensource.facebook.com/legal/terms/" target="_blank" rel="noreferrer noopener">Terms</a></section></footer></div></body></html>
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<h3><a class="anchor" aria-hidden="true" id="shapetnetcore"></a><a href="#shapetnetcore" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>ShapetNetCore</h3>
<p>ShapeNet is a dataset of 3D CAD models. ShapeNetCore is a subset of the ShapeNet dataset and can be downloaded from <a href="https://www.shapenet.org/">https://www.shapenet.org/</a>. There are two versions ShapeNetCore: v1 (55 categories) and v2 (57 categories).</p>
<p>The PyTorch3D <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/datasets/shapenet/shapenet_core.py">ShapeNetCore data loader</a> inherits from <code>torch.utils.data.Dataset</code>. It takes the path where the ShapeNetCore dataset is stored locally and loads models in the dataset. The ShapeNetCore class loads and returns models with their <code>categories</code>, <code>model_ids</code>, <code>vertices</code> and <code>faces</code>. The <code>ShapeNetCore</code> data loader also has a customized <code>render</code> function that renders models by the specified <code>model_ids (List[int])</code>, <code>categories (List[str])</code> or <code>indices (List[int])</code> with PyTorch3D's differentiable renderer.</p>
<p>The loaded dataset can be passed to <code>torch.utils.data.DataLoader</code> with PyTorch3D's customized collate_fn: <code>collate_batched_meshes</code> from the <code>pytorch3d.dataset.utils</code> module. The <code>vertices</code> and <code>faces</code> of the models are used to construct a <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/structures/meshes.py">Meshes</a> object representing the batched meshes. This <code>Meshes</code> representation can be easily used with other ops and rendering in PyTorch3D.</p>
<p>The PyTorch3D <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/datasets/shapenet/shapenet_core.py">ShapeNetCore data loader</a> inherits from <code>torch.utils.data.Dataset</code>. It takes the path where the ShapeNetCore dataset is stored locally and loads models in the dataset. The ShapeNetCore class loads and returns models with their <code>categories</code>, <code>model_ids</code>, <code>vertices</code> and <code>faces</code>. The <code>ShapeNetCore</code> data loader also has a customized <code>render</code> function that renders models by the specified <code>model_ids (List[int])</code>, <code>categories (List[str])</code> or <code>indices (List[int])</code> with PyTorch3D's differentiable renderer.</p>
<p>The loaded dataset can be passed to <code>torch.utils.data.DataLoader</code> with PyTorch3D's customized collate_fn: <code>collate_batched_meshes</code> from the <code>pytorch3d.dataset.utils</code> module. The <code>vertices</code> and <code>faces</code> of the models are used to construct a <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/structures/meshes.py">Meshes</a> object representing the batched meshes. This <code>Meshes</code> representation can be easily used with other ops and rendering in PyTorch3D.</p>
<h3><a class="anchor" aria-hidden="true" id="r2n2"></a><a href="#r2n2" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>R2N2</h3>
<p>The R2N2 dataset contains 13 categories that are a subset of the ShapeNetCore v.1 dataset. The R2N2 dataset also contains its own 24 renderings of each object and voxelized models. The R2N2 Dataset can be downloaded following the instructions <a href="http://3d-r2n2.stanford.edu/">here</a>.</p>
<p>The PyTorch3D <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/datasets/r2n2/r2n2.py">R2N2 data loader</a> is initialized with the paths to the ShapeNet dataset, the R2N2 dataset and the splits file for R2N2. Just like <code>ShapeNetCore</code>, it can be passed to <code>torch.utils.data.DataLoader</code> with a customized collate_fn: <code>collate_batched_R2N2</code> from the <code>pytorch3d.dataset.r2n2.utils</code> module. It returns all the data that <code>ShapeNetCore</code> returns, and in addition, it returns the R2N2 renderings (24 views for each model) along with the camera calibration matrices and a voxel representation for each model. Similar to <code>ShapeNetCore</code>, it has a customized <code>render</code> function that supports rendering specified models with the PyTorch3D differentiable renderer. In addition, it supports rendering models with the same orientations as R2N2's original renderings.</p>
</span></div></article></div><div class="docLastUpdate"><em>Last updated by Nikhila Ravi</em></div><div class="docs-prevnext"><a class="docs-prev button" href="/docs/meshes_io"><span class="arrow-prev"></span><span>Loading from file</span></a><a class="docs-next button" href="/docs/batching"><span>Batching</span><span class="arrow-next"></span></a></div></div></div><nav class="onPageNav"></nav></div><footer class="nav-footer" id="footer"><section class="sitemap"><div class="footerSection"><div class="social"><a class="github-button" href="https://github.com/facebookresearch/pytorch3d" data-count-href="https://github.com/facebookresearch/pytorch3d/stargazers" data-show-count="true" data-count-aria-label="# stargazers on GitHub" aria-label="Star PyTorch3D on GitHub">pytorch3d</a></div></div></section><a href="https://opensource.facebook.com/" target="_blank" rel="noreferrer noopener" class="fbOpenSource"><img src="/img/oss_logo.png" alt="Facebook Open Source" width="170" height="45"/></a><section class="copyright">Copyright © 2021 Facebook Inc<br/>Legal:<a href="https://opensource.facebook.com/legal/privacy/" target="_blank" rel="noreferrer noopener">Privacy</a><a href="https://opensource.facebook.com/legal/terms/" target="_blank" rel="noreferrer noopener">Terms</a></section></footer></div></body></html>
<p>The PyTorch3D <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/datasets/r2n2/r2n2.py">R2N2 data loader</a> is initialized with the paths to the ShapeNet dataset, the R2N2 dataset and the splits file for R2N2. Just like <code>ShapeNetCore</code>, it can be passed to <code>torch.utils.data.DataLoader</code> with a customized collate_fn: <code>collate_batched_R2N2</code> from the <code>pytorch3d.dataset.r2n2.utils</code> module. It returns all the data that <code>ShapeNetCore</code> returns, and in addition, it returns the R2N2 renderings (24 views for each model) along with the camera calibration matrices and a voxel representation for each model. Similar to <code>ShapeNetCore</code>, it has a customized <code>render</code> function that supports rendering specified models with the PyTorch3D differentiable renderer. In addition, it supports rendering models with the same orientations as R2N2's original renderings.</p>
</span></div></article></div><div class="docLastUpdate"><em>Last updated by Jeremy Reizenstein</em></div><div class="docs-prevnext"><a class="docs-prev button" href="/docs/meshes_io"><span class="arrow-prev"></span><span>Loading from file</span></a><a class="docs-next button" href="/docs/batching"><span>Batching</span><span class="arrow-next"></span></a></div></div></div><nav class="onPageNav"></nav></div><footer class="nav-footer" id="footer"><section class="sitemap"><div class="footerSection"><div class="social"><a class="github-button" href="https://github.com/facebookresearch/pytorch3d" data-count-href="https://github.com/facebookresearch/pytorch3d/stargazers" data-show-count="true" data-count-aria-label="# stargazers on GitHub" aria-label="Star PyTorch3D on GitHub">pytorch3d</a></div></div></section><a href="https://opensource.facebook.com/" target="_blank" rel="noreferrer noopener" class="fbOpenSource"><img src="/img/oss_logo.png" alt="Facebook Open Source" width="170" height="45"/></a><section class="copyright">Copyright © 2021 Facebook Inc<br/>Legal:<a href="https://opensource.facebook.com/legal/privacy/" target="_blank" rel="noreferrer noopener">Privacy</a><a href="https://opensource.facebook.com/legal/terms/" target="_blank" rel="noreferrer noopener">Terms</a></section></footer></div></body></html>

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<h3><a class="anchor" aria-hidden="true" id="shapetnetcore"></a><a href="#shapetnetcore" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>ShapetNetCore</h3>
<p>ShapeNet is a dataset of 3D CAD models. ShapeNetCore is a subset of the ShapeNet dataset and can be downloaded from <a href="https://www.shapenet.org/">https://www.shapenet.org/</a>. There are two versions ShapeNetCore: v1 (55 categories) and v2 (57 categories).</p>
<p>The PyTorch3D <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/datasets/shapenet/shapenet_core.py">ShapeNetCore data loader</a> inherits from <code>torch.utils.data.Dataset</code>. It takes the path where the ShapeNetCore dataset is stored locally and loads models in the dataset. The ShapeNetCore class loads and returns models with their <code>categories</code>, <code>model_ids</code>, <code>vertices</code> and <code>faces</code>. The <code>ShapeNetCore</code> data loader also has a customized <code>render</code> function that renders models by the specified <code>model_ids (List[int])</code>, <code>categories (List[str])</code> or <code>indices (List[int])</code> with PyTorch3D's differentiable renderer.</p>
<p>The loaded dataset can be passed to <code>torch.utils.data.DataLoader</code> with PyTorch3D's customized collate_fn: <code>collate_batched_meshes</code> from the <code>pytorch3d.dataset.utils</code> module. The <code>vertices</code> and <code>faces</code> of the models are used to construct a <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/structures/meshes.py">Meshes</a> object representing the batched meshes. This <code>Meshes</code> representation can be easily used with other ops and rendering in PyTorch3D.</p>
<p>The PyTorch3D <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/datasets/shapenet/shapenet_core.py">ShapeNetCore data loader</a> inherits from <code>torch.utils.data.Dataset</code>. It takes the path where the ShapeNetCore dataset is stored locally and loads models in the dataset. The ShapeNetCore class loads and returns models with their <code>categories</code>, <code>model_ids</code>, <code>vertices</code> and <code>faces</code>. The <code>ShapeNetCore</code> data loader also has a customized <code>render</code> function that renders models by the specified <code>model_ids (List[int])</code>, <code>categories (List[str])</code> or <code>indices (List[int])</code> with PyTorch3D's differentiable renderer.</p>
<p>The loaded dataset can be passed to <code>torch.utils.data.DataLoader</code> with PyTorch3D's customized collate_fn: <code>collate_batched_meshes</code> from the <code>pytorch3d.dataset.utils</code> module. The <code>vertices</code> and <code>faces</code> of the models are used to construct a <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/structures/meshes.py">Meshes</a> object representing the batched meshes. This <code>Meshes</code> representation can be easily used with other ops and rendering in PyTorch3D.</p>
<h3><a class="anchor" aria-hidden="true" id="r2n2"></a><a href="#r2n2" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>R2N2</h3>
<p>The R2N2 dataset contains 13 categories that are a subset of the ShapeNetCore v.1 dataset. The R2N2 dataset also contains its own 24 renderings of each object and voxelized models. The R2N2 Dataset can be downloaded following the instructions <a href="http://3d-r2n2.stanford.edu/">here</a>.</p>
<p>The PyTorch3D <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/datasets/r2n2/r2n2.py">R2N2 data loader</a> is initialized with the paths to the ShapeNet dataset, the R2N2 dataset and the splits file for R2N2. Just like <code>ShapeNetCore</code>, it can be passed to <code>torch.utils.data.DataLoader</code> with a customized collate_fn: <code>collate_batched_R2N2</code> from the <code>pytorch3d.dataset.r2n2.utils</code> module. It returns all the data that <code>ShapeNetCore</code> returns, and in addition, it returns the R2N2 renderings (24 views for each model) along with the camera calibration matrices and a voxel representation for each model. Similar to <code>ShapeNetCore</code>, it has a customized <code>render</code> function that supports rendering specified models with the PyTorch3D differentiable renderer. In addition, it supports rendering models with the same orientations as R2N2's original renderings.</p>
</span></div></article></div><div class="docLastUpdate"><em>Last updated by Nikhila Ravi</em></div><div class="docs-prevnext"><a class="docs-prev button" href="/docs/meshes_io"><span class="arrow-prev"></span><span>Loading from file</span></a><a class="docs-next button" href="/docs/batching"><span>Batching</span><span class="arrow-next"></span></a></div></div></div><nav class="onPageNav"></nav></div><footer class="nav-footer" id="footer"><section class="sitemap"><div class="footerSection"><div class="social"><a class="github-button" href="https://github.com/facebookresearch/pytorch3d" data-count-href="https://github.com/facebookresearch/pytorch3d/stargazers" data-show-count="true" data-count-aria-label="# stargazers on GitHub" aria-label="Star PyTorch3D on GitHub">pytorch3d</a></div></div></section><a href="https://opensource.facebook.com/" target="_blank" rel="noreferrer noopener" class="fbOpenSource"><img src="/img/oss_logo.png" alt="Facebook Open Source" width="170" height="45"/></a><section class="copyright">Copyright © 2021 Facebook Inc<br/>Legal:<a href="https://opensource.facebook.com/legal/privacy/" target="_blank" rel="noreferrer noopener">Privacy</a><a href="https://opensource.facebook.com/legal/terms/" target="_blank" rel="noreferrer noopener">Terms</a></section></footer></div></body></html>
<p>The PyTorch3D <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/datasets/r2n2/r2n2.py">R2N2 data loader</a> is initialized with the paths to the ShapeNet dataset, the R2N2 dataset and the splits file for R2N2. Just like <code>ShapeNetCore</code>, it can be passed to <code>torch.utils.data.DataLoader</code> with a customized collate_fn: <code>collate_batched_R2N2</code> from the <code>pytorch3d.dataset.r2n2.utils</code> module. It returns all the data that <code>ShapeNetCore</code> returns, and in addition, it returns the R2N2 renderings (24 views for each model) along with the camera calibration matrices and a voxel representation for each model. Similar to <code>ShapeNetCore</code>, it has a customized <code>render</code> function that supports rendering specified models with the PyTorch3D differentiable renderer. In addition, it supports rendering models with the same orientations as R2N2's original renderings.</p>
</span></div></article></div><div class="docLastUpdate"><em>Last updated by Jeremy Reizenstein</em></div><div class="docs-prevnext"><a class="docs-prev button" href="/docs/meshes_io"><span class="arrow-prev"></span><span>Loading from file</span></a><a class="docs-next button" href="/docs/batching"><span>Batching</span><span class="arrow-next"></span></a></div></div></div><nav class="onPageNav"></nav></div><footer class="nav-footer" id="footer"><section class="sitemap"><div class="footerSection"><div class="social"><a class="github-button" href="https://github.com/facebookresearch/pytorch3d" data-count-href="https://github.com/facebookresearch/pytorch3d/stargazers" data-show-count="true" data-count-aria-label="# stargazers on GitHub" aria-label="Star PyTorch3D on GitHub">pytorch3d</a></div></div></section><a href="https://opensource.facebook.com/" target="_blank" rel="noreferrer noopener" class="fbOpenSource"><img src="/img/oss_logo.png" alt="Facebook Open Source" width="170" height="45"/></a><section class="copyright">Copyright © 2021 Facebook Inc<br/>Legal:<a href="https://opensource.facebook.com/legal/privacy/" target="_blank" rel="noreferrer noopener">Privacy</a><a href="https://opensource.facebook.com/legal/terms/" target="_blank" rel="noreferrer noopener">Terms</a></section></footer></div></body></html>

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</script></nav></div><div class="container mainContainer docsContainer"><div class="wrapper"><div class="post"><header class="postHeader"></header><article><div><span><h1><a class="anchor" aria-hidden="true" id="intersection-over-union-of-oriented-3d-boxes-a-new-algorithm"></a><a href="#intersection-over-union-of-oriented-3d-boxes-a-new-algorithm" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Intersection Over Union of Oriented 3D Boxes: A New Algorithm</h1>
<p>Author: Georgia Gkioxari</p>
<p>Implementation: Georgia Gkioxari and Nikhila Ravi</p>
<h2><a class="anchor" aria-hidden="true" id="description"></a><a href="#description" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Description</h2>
<p>Intersection over union (IoU) of boxes is widely used as an evaluation metric in object detection (<a href="http://host.robots.ox.ac.uk/pascal/VOC/">1</a>, <a href="https://cocodataset.org/">2</a>).
In 2D, IoU is commonly applied to axis-aligned boxes, namely boxes with edges parallel to the image axis.
In 3D, boxes are usually not axis aligned and can be oriented in any way in the world.
We introduce a new algorithm which computes the <em>exact</em> IoU of two <em>oriented 3D boxes</em>.</p>
<p>Our algorithm is based on the simple observation that the intersection of two oriented 3D boxes, <code>box1</code> and <code>box2</code>, is a convex polyhedron (convex n-gon in 2D) with <code>n &gt; 2</code> comprised of connected <em>planar units</em>.
In 3D, these planar units are 3D triangular faces.
In 2D, they are 2D edges.
Each planar unit belongs strictly to either <code>box1</code> or <code>box2</code>.
Our algorithm finds these units by iterating through the sides of each box.</p>
<ol>
<li>For each 3D triangular face <code>e</code> in <code>box1</code> we check wether <code>e</code> is <em>inside</em> <code>box2</code>.</li>
<li>If <code>e</code> is not <em>inside</em>, then we discard it.</li>
<li>If <code>e</code> is <em>inside</em> or <em>partially inside</em>, then the part of <code>e</code> <em>inside</em> <code>box2</code> is added to the units that comprise the final intersection shape.</li>
<li>We repeat for <code>box2</code>.</li>
</ol>
<p>Below, we show a visualization of our algorithm for the case of 2D oriented boxes.</p>
<p align="center">
<img src="assets/iou3d.gif" alt="drawing" width="400"/>
</p>
<p>Note that when a box's unit <code>e</code> is <em>partially inside</em> a <code>box</code> then <code>e</code> breaks into smaller units. In 2D, <code>e</code> is an edge and breaks into smaller edges. In 3D, <code>e</code> is a 3D triangular face and is clipped to more and smaller faces by the plane of the <code>box</code> it intersects with.
This is the sole fundamental difference between the algorithms for 2D and 3D.</p>
<h2><a class="anchor" aria-hidden="true" id="comparison-with-other-algorithms"></a><a href="#comparison-with-other-algorithms" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Comparison With Other Algorithms</h2>
<p>Current algorithms for 3D box IoU rely on crude approximations or make box assumptions, for example they restrict the orientation of the 3D boxes.
<a href="https://arxiv.org/abs/2012.09988">Objectron</a> provides a nice discussion on the limitations of prior works.
<a href="https://arxiv.org/abs/2012.09988">Objectron</a> introduces a great algorithm for exact IoU computation of oriented 3D boxes.
Objectron's algorithm computes the intersection points of two boxes using the <a href="https://en.wikipedia.org/wiki/Sutherland%E2%80%93Hodgman_algorithm">Sutherland-Hodgman algorithm</a>.
The intersection shape is formed by the convex hull from the intersection points, using the <a href="http://www.qhull.org/">Qhull library</a>.</p>
<p>Our algorithm has several advantages over Objectron's:</p>
<ul>
<li>Our algorithm also computes the points of intersection, similar to Objectron, but in addition stores the <em>planar units</em> the points belong to. This eliminates the need for convex hull computation which is <code>O(nlogn)</code> and relies on a third party library which often crashes with nondescript error messages.</li>
<li>Objectron's implementation assumes that boxes are a rotation away from axis aligned. Our algorithm and implementation make no such assumption and work for any 3D boxes.</li>
<li>Our implementation supports batching, unlike Objectron which assumes single element inputs for <code>box1</code> and <code>box2</code>.</li>
<li>Our implementation is easily parallelizable and in fact we provide a custom C++/CUDA implementation which is <strong>450 times faster than Objectron</strong>.</li>
</ul>
<p>Below we compare the performance for Objectron (in C++) and our algorithm, in C++ and CUDA. We benchmark for a common use case in object detection where <code>boxes1</code> hold M predictions and <code>boxes2</code> hold N ground truth 3D boxes in an image and compute the <code>MxN</code> IoU matrix. We report the time in ms for <code>M=N=16</code>.</p>
<p align="center">
<img src="assets/iou3d_comp.png" alt="drawing" width="400"/>
</p>
<h2><a class="anchor" aria-hidden="true" id="usage-and-code"></a><a href="#usage-and-code" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Usage and Code</h2>
<pre><code class="hljs css language-python"><span class="hljs-keyword">from</span> pytorch3d.ops <span class="hljs-keyword">import</span> box3d_overlap
<span class="hljs-comment"># Assume inputs: boxes1 (M, 8, 3) and boxes2 (N, 8, 3)</span>
intersection_vol, iou_3d = box3d_overal(boxes1, boxes2)
</code></pre>
<p>For more details, read <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/ops/iou_box3d.py">iou_box3d.py</a>.</p>
<p>Note that our implementation is not differentiable as of now. We plan to add gradient support soon.</p>
<p>We also include have extensive <a href="https://github.com/facebookresearch/pytorch3d/blob/main/tests/test_iou_box3d.py">tests</a> comparing our implementation with Objectron and MeshLab.</p>
<h2><a class="anchor" aria-hidden="true" id="cite"></a><a href="#cite" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Cite</h2>
<p>If you use our 3D IoU algorithm, please cite PyTorch3D</p>
<pre><code class="hljs css language-bibtex">@article{ravi2020pytorch3d,
author = {Nikhila Ravi <span class="hljs-keyword">and </span><span class="hljs-keyword">Jeremy </span>Reizenstein <span class="hljs-keyword">and </span>David Novotny <span class="hljs-keyword">and </span>Taylor Gordon
<span class="hljs-keyword">and </span>Wan-Yen Lo <span class="hljs-keyword">and </span><span class="hljs-keyword">Justin </span><span class="hljs-keyword">Johnson </span><span class="hljs-keyword">and </span>Georgia Gkioxari},
title = {Accelerating <span class="hljs-number">3</span>D Deep Learning with PyTorch3D},
<span class="hljs-keyword">journal </span>= {arXiv:<span class="hljs-number">2007</span>.<span class="hljs-number">08501</span>},
year = {<span class="hljs-number">2020</span>},
}
</code></pre>
</span></div></article></div><div class="docLastUpdate"><em>Last updated by Georgia Gkioxari</em></div><div class="docs-prevnext"><a class="docs-prev button" href="/docs/cubify"><span class="arrow-prev"></span><span>Cubify</span></a><a class="docs-next button" href="/docs/visualization"><span>Plotly Visualization</span><span class="arrow-next"></span></a></div></div></div><nav class="onPageNav"><ul class="toc-headings"><li><a href="#description">Description</a></li><li><a href="#comparison-with-other-algorithms">Comparison With Other Algorithms</a></li><li><a href="#usage-and-code">Usage and Code</a></li><li><a href="#cite">Cite</a></li></ul></nav></div><footer class="nav-footer" id="footer"><section class="sitemap"><div class="footerSection"><div class="social"><a class="github-button" href="https://github.com/facebookresearch/pytorch3d" data-count-href="https://github.com/facebookresearch/pytorch3d/stargazers" data-show-count="true" data-count-aria-label="# stargazers on GitHub" aria-label="Star PyTorch3D on GitHub">pytorch3d</a></div></div></section><a href="https://opensource.facebook.com/" target="_blank" rel="noreferrer noopener" class="fbOpenSource"><img src="/img/oss_logo.png" alt="Facebook Open Source" width="170" height="45"/></a><section class="copyright">Copyright © 2021 Facebook Inc<br/>Legal:<a href="https://opensource.facebook.com/legal/privacy/" target="_blank" rel="noreferrer noopener">Privacy</a><a href="https://opensource.facebook.com/legal/terms/" target="_blank" rel="noreferrer noopener">Terms</a></section></footer></div></body></html>

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</script></nav></div><div class="container mainContainer docsContainer"><div class="wrapper"><div class="post"><header class="postHeader"></header><article><div><span><h1><a class="anchor" aria-hidden="true" id="intersection-over-union-of-oriented-3d-boxes-a-new-algorithm"></a><a href="#intersection-over-union-of-oriented-3d-boxes-a-new-algorithm" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Intersection Over Union of Oriented 3D Boxes: A New Algorithm</h1>
<p>Author: Georgia Gkioxari</p>
<p>Implementation: Georgia Gkioxari and Nikhila Ravi</p>
<h2><a class="anchor" aria-hidden="true" id="description"></a><a href="#description" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Description</h2>
<p>Intersection over union (IoU) of boxes is widely used as an evaluation metric in object detection (<a href="http://host.robots.ox.ac.uk/pascal/VOC/">1</a>, <a href="https://cocodataset.org/">2</a>).
In 2D, IoU is commonly applied to axis-aligned boxes, namely boxes with edges parallel to the image axis.
In 3D, boxes are usually not axis aligned and can be oriented in any way in the world.
We introduce a new algorithm which computes the <em>exact</em> IoU of two <em>oriented 3D boxes</em>.</p>
<p>Our algorithm is based on the simple observation that the intersection of two oriented 3D boxes, <code>box1</code> and <code>box2</code>, is a convex polyhedron (convex n-gon in 2D) with <code>n &gt; 2</code> comprised of connected <em>planar units</em>.
In 3D, these planar units are 3D triangular faces.
In 2D, they are 2D edges.
Each planar unit belongs strictly to either <code>box1</code> or <code>box2</code>.
Our algorithm finds these units by iterating through the sides of each box.</p>
<ol>
<li>For each 3D triangular face <code>e</code> in <code>box1</code> we check wether <code>e</code> is <em>inside</em> <code>box2</code>.</li>
<li>If <code>e</code> is not <em>inside</em>, then we discard it.</li>
<li>If <code>e</code> is <em>inside</em> or <em>partially inside</em>, then the part of <code>e</code> <em>inside</em> <code>box2</code> is added to the units that comprise the final intersection shape.</li>
<li>We repeat for <code>box2</code>.</li>
</ol>
<p>Below, we show a visualization of our algorithm for the case of 2D oriented boxes.</p>
<p align="center">
<img src="assets/iou3d.gif" alt="drawing" width="400"/>
</p>
<p>Note that when a box's unit <code>e</code> is <em>partially inside</em> a <code>box</code> then <code>e</code> breaks into smaller units. In 2D, <code>e</code> is an edge and breaks into smaller edges. In 3D, <code>e</code> is a 3D triangular face and is clipped to more and smaller faces by the plane of the <code>box</code> it intersects with.
This is the sole fundamental difference between the algorithms for 2D and 3D.</p>
<h2><a class="anchor" aria-hidden="true" id="comparison-with-other-algorithms"></a><a href="#comparison-with-other-algorithms" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Comparison With Other Algorithms</h2>
<p>Current algorithms for 3D box IoU rely on crude approximations or make box assumptions, for example they restrict the orientation of the 3D boxes.
<a href="https://arxiv.org/abs/2012.09988">Objectron</a> provides a nice discussion on the limitations of prior works.
<a href="https://arxiv.org/abs/2012.09988">Objectron</a> introduces a great algorithm for exact IoU computation of oriented 3D boxes.
Objectron's algorithm computes the intersection points of two boxes using the <a href="https://en.wikipedia.org/wiki/Sutherland%E2%80%93Hodgman_algorithm">Sutherland-Hodgman algorithm</a>.
The intersection shape is formed by the convex hull from the intersection points, using the <a href="http://www.qhull.org/">Qhull library</a>.</p>
<p>Our algorithm has several advantages over Objectron's:</p>
<ul>
<li>Our algorithm also computes the points of intersection, similar to Objectron, but in addition stores the <em>planar units</em> the points belong to. This eliminates the need for convex hull computation which is <code>O(nlogn)</code> and relies on a third party library which often crashes with nondescript error messages.</li>
<li>Objectron's implementation assumes that boxes are a rotation away from axis aligned. Our algorithm and implementation make no such assumption and work for any 3D boxes.</li>
<li>Our implementation supports batching, unlike Objectron which assumes single element inputs for <code>box1</code> and <code>box2</code>.</li>
<li>Our implementation is easily parallelizable and in fact we provide a custom C++/CUDA implementation which is <strong>450 times faster than Objectron</strong>.</li>
</ul>
<p>Below we compare the performance for Objectron (in C++) and our algorithm, in C++ and CUDA. We benchmark for a common use case in object detection where <code>boxes1</code> hold M predictions and <code>boxes2</code> hold N ground truth 3D boxes in an image and compute the <code>MxN</code> IoU matrix. We report the time in ms for <code>M=N=16</code>.</p>
<p align="center">
<img src="assets/iou3d_comp.png" alt="drawing" width="400"/>
</p>
<h2><a class="anchor" aria-hidden="true" id="usage-and-code"></a><a href="#usage-and-code" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Usage and Code</h2>
<pre><code class="hljs css language-python"><span class="hljs-keyword">from</span> pytorch3d.ops <span class="hljs-keyword">import</span> box3d_overlap
<span class="hljs-comment"># Assume inputs: boxes1 (M, 8, 3) and boxes2 (N, 8, 3)</span>
intersection_vol, iou_3d = box3d_overal(boxes1, boxes2)
</code></pre>
<p>For more details, read <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/ops/iou_box3d.py">iou_box3d.py</a>.</p>
<p>Note that our implementation is not differentiable as of now. We plan to add gradient support soon.</p>
<p>We also include have extensive <a href="https://github.com/facebookresearch/pytorch3d/blob/main/tests/test_iou_box3d.py">tests</a> comparing our implementation with Objectron and MeshLab.</p>
<h2><a class="anchor" aria-hidden="true" id="cite"></a><a href="#cite" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Cite</h2>
<p>If you use our 3D IoU algorithm, please cite PyTorch3D</p>
<pre><code class="hljs css language-bibtex">@article{ravi2020pytorch3d,
author = {Nikhila Ravi <span class="hljs-keyword">and </span><span class="hljs-keyword">Jeremy </span>Reizenstein <span class="hljs-keyword">and </span>David Novotny <span class="hljs-keyword">and </span>Taylor Gordon
<span class="hljs-keyword">and </span>Wan-Yen Lo <span class="hljs-keyword">and </span><span class="hljs-keyword">Justin </span><span class="hljs-keyword">Johnson </span><span class="hljs-keyword">and </span>Georgia Gkioxari},
title = {Accelerating <span class="hljs-number">3</span>D Deep Learning with PyTorch3D},
<span class="hljs-keyword">journal </span>= {arXiv:<span class="hljs-number">2007</span>.<span class="hljs-number">08501</span>},
year = {<span class="hljs-number">2020</span>},
}
</code></pre>
</span></div></article></div><div class="docLastUpdate"><em>Last updated by Georgia Gkioxari</em></div><div class="docs-prevnext"><a class="docs-prev button" href="/docs/cubify"><span class="arrow-prev"></span><span>Cubify</span></a><a class="docs-next button" href="/docs/visualization"><span>Plotly Visualization</span><span class="arrow-next"></span></a></div></div></div><nav class="onPageNav"><ul class="toc-headings"><li><a href="#description">Description</a></li><li><a href="#comparison-with-other-algorithms">Comparison With Other Algorithms</a></li><li><a href="#usage-and-code">Usage and Code</a></li><li><a href="#cite">Cite</a></li></ul></nav></div><footer class="nav-footer" id="footer"><section class="sitemap"><div class="footerSection"><div class="social"><a class="github-button" href="https://github.com/facebookresearch/pytorch3d" data-count-href="https://github.com/facebookresearch/pytorch3d/stargazers" data-show-count="true" data-count-aria-label="# stargazers on GitHub" aria-label="Star PyTorch3D on GitHub">pytorch3d</a></div></div></section><a href="https://opensource.facebook.com/" target="_blank" rel="noreferrer noopener" class="fbOpenSource"><img src="/img/oss_logo.png" alt="Facebook Open Source" width="170" height="45"/></a><section class="copyright">Copyright © 2021 Facebook Inc<br/>Legal:<a href="https://opensource.facebook.com/legal/privacy/" target="_blank" rel="noreferrer noopener">Privacy</a><a href="https://opensource.facebook.com/legal/terms/" target="_blank" rel="noreferrer noopener">Terms</a></section></footer></div></body></html>

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@ -105,14 +105,14 @@ In the cameras e.g. <code>FoVPerspectiveCameras</code>, the <code>aspect_ratio</
<h3><a class="anchor" aria-hidden="true" id="the-pulsar-backend"></a><a href="#the-pulsar-backend" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>The pulsar backend</h3>
<p>Since v0.3, <a href="https://arxiv.org/abs/2004.07484">pulsar</a> can be used as a backend for point-rendering. It has a focus on efficiency, which comes with pros and cons: it is highly optimized and all rendering stages are integrated in the CUDA kernels. This leads to significantly higher speed and better scaling behavior. We use it at Facebook Reality Labs to render and optimize scenes with millions of spheres in resolutions up to 4K. You can find a runtime comparison plot below (settings: <code>bin_size=None</code>, <code>points_per_pixel=5</code>, <code>image_size=1024</code>, <code>radius=1e-2</code>, <code>composite_params.radius=1e-4</code>; benchmarked on an RTX 2070 GPU).</p>
<p><img align="center" src="assets/pulsar_bm.png" width="300"></p>
<p>Pulsar's processing steps are tightly integrated CUDA kernels and do not work with custom <code>rasterizer</code> and <code>compositor</code> components. We provide two ways to use Pulsar: (1) there is a unified interface to match the PyTorch3D calling convention seamlessly. This is, for example, illustrated in the <a href="https://github.com/facebookresearch/pytorch3d/blob/master/docs/tutorials/render_colored_points.ipynb">point cloud tutorial</a>. (2) There is a direct interface available to the pulsar backend, which exposes the full functionality of the backend (including opacity, which is not yet available in PyTorch3D). Examples showing its use as well as the matching PyTorch3D interface code are available in <a href="https://github.com/facebookresearch/pytorch3d/tree/master/docs/examples">this folder</a>.</p>
<p>Pulsar's processing steps are tightly integrated CUDA kernels and do not work with custom <code>rasterizer</code> and <code>compositor</code> components. We provide two ways to use Pulsar: (1) there is a unified interface to match the PyTorch3D calling convention seamlessly. This is, for example, illustrated in the <a href="https://github.com/facebookresearch/pytorch3d/blob/main/docs/tutorials/render_colored_points.ipynb">point cloud tutorial</a>. (2) There is a direct interface available to the pulsar backend, which exposes the full functionality of the backend (including opacity, which is not yet available in PyTorch3D). Examples showing its use as well as the matching PyTorch3D interface code are available in <a href="https://github.com/facebookresearch/pytorch3d/tree/master/docs/examples">this folder</a>.</p>
<hr>
<h3><a class="anchor" aria-hidden="true" id="texturing-options"></a><a href="#texturing-options" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Texturing options</h3>
<p>For mesh texturing we offer several options (in <code>pytorch3d/renderer/mesh/texturing.py</code>):</p>
<ol>
<li><strong>Vertex Textures</strong>: D dimensional textures for each vertex (for example an RGB color) which can be interpolated across the face. This can be represented as an <code>(N, V, D)</code> tensor. This is a fairly simple representation though and cannot model complex textures if the mesh faces are large.</li>
<li><strong>UV Textures</strong>: vertex UV coordinates and <strong>one</strong> texture map for the whole mesh. For a point on a face with given barycentric coordinates, the face color can be computed by interpolating the vertex uv coordinates and then sampling from the texture map. This representation requires two tensors (UVs: <code>(N, V, 2), Texture map:</code>(N, H, W, 3)`), and is limited to only support one texture map per mesh.</li>
<li><strong>Face Textures</strong>: In more complex cases such as ShapeNet meshes, there are multiple texture maps per mesh and some faces have texture while other do not. For these cases, a more flexible representation is a texture atlas, where each face is represented as an <code>(RxR)</code> texture map where R is the texture resolution. For a given point on the face, the texture value can be sampled from the per face texture map using the barycentric coordinates of the point. This representation requires one tensor of shape <code>(N, F, R, R, 3)</code>. This texturing method is inspired by the SoftRasterizer implementation. For more details refer to the <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/io/mtl_io.py#L123"><code>make_material_atlas</code></a> and <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/renderer/mesh/textures.py#L452"><code>sample_textures</code></a> functions. <strong>NOTE:</strong>: The <code>TexturesAtlas</code> texture sampling is only differentiable with respect to the texture atlas but not differentiable with respect to the barycentric coordinates.</li>
<li><strong>Face Textures</strong>: In more complex cases such as ShapeNet meshes, there are multiple texture maps per mesh and some faces have texture while other do not. For these cases, a more flexible representation is a texture atlas, where each face is represented as an <code>(RxR)</code> texture map where R is the texture resolution. For a given point on the face, the texture value can be sampled from the per face texture map using the barycentric coordinates of the point. This representation requires one tensor of shape <code>(N, F, R, R, 3)</code>. This texturing method is inspired by the SoftRasterizer implementation. For more details refer to the <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/io/mtl_io.py#L123"><code>make_material_atlas</code></a> and <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/renderer/mesh/textures.py#L452"><code>sample_textures</code></a> functions. <strong>NOTE:</strong>: The <code>TexturesAtlas</code> texture sampling is only differentiable with respect to the texture atlas but not differentiable with respect to the barycentric coordinates.</li>
</ol>
<p><img src="assets/texturing.jpg" width="1000"></p>
<hr>

View File

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@ -105,14 +105,14 @@ In the cameras e.g. <code>FoVPerspectiveCameras</code>, the <code>aspect_ratio</
<h3><a class="anchor" aria-hidden="true" id="the-pulsar-backend"></a><a href="#the-pulsar-backend" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>The pulsar backend</h3>
<p>Since v0.3, <a href="https://arxiv.org/abs/2004.07484">pulsar</a> can be used as a backend for point-rendering. It has a focus on efficiency, which comes with pros and cons: it is highly optimized and all rendering stages are integrated in the CUDA kernels. This leads to significantly higher speed and better scaling behavior. We use it at Facebook Reality Labs to render and optimize scenes with millions of spheres in resolutions up to 4K. You can find a runtime comparison plot below (settings: <code>bin_size=None</code>, <code>points_per_pixel=5</code>, <code>image_size=1024</code>, <code>radius=1e-2</code>, <code>composite_params.radius=1e-4</code>; benchmarked on an RTX 2070 GPU).</p>
<p><img align="center" src="assets/pulsar_bm.png" width="300"></p>
<p>Pulsar's processing steps are tightly integrated CUDA kernels and do not work with custom <code>rasterizer</code> and <code>compositor</code> components. We provide two ways to use Pulsar: (1) there is a unified interface to match the PyTorch3D calling convention seamlessly. This is, for example, illustrated in the <a href="https://github.com/facebookresearch/pytorch3d/blob/master/docs/tutorials/render_colored_points.ipynb">point cloud tutorial</a>. (2) There is a direct interface available to the pulsar backend, which exposes the full functionality of the backend (including opacity, which is not yet available in PyTorch3D). Examples showing its use as well as the matching PyTorch3D interface code are available in <a href="https://github.com/facebookresearch/pytorch3d/tree/master/docs/examples">this folder</a>.</p>
<p>Pulsar's processing steps are tightly integrated CUDA kernels and do not work with custom <code>rasterizer</code> and <code>compositor</code> components. We provide two ways to use Pulsar: (1) there is a unified interface to match the PyTorch3D calling convention seamlessly. This is, for example, illustrated in the <a href="https://github.com/facebookresearch/pytorch3d/blob/main/docs/tutorials/render_colored_points.ipynb">point cloud tutorial</a>. (2) There is a direct interface available to the pulsar backend, which exposes the full functionality of the backend (including opacity, which is not yet available in PyTorch3D). Examples showing its use as well as the matching PyTorch3D interface code are available in <a href="https://github.com/facebookresearch/pytorch3d/tree/master/docs/examples">this folder</a>.</p>
<hr>
<h3><a class="anchor" aria-hidden="true" id="texturing-options"></a><a href="#texturing-options" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Texturing options</h3>
<p>For mesh texturing we offer several options (in <code>pytorch3d/renderer/mesh/texturing.py</code>):</p>
<ol>
<li><strong>Vertex Textures</strong>: D dimensional textures for each vertex (for example an RGB color) which can be interpolated across the face. This can be represented as an <code>(N, V, D)</code> tensor. This is a fairly simple representation though and cannot model complex textures if the mesh faces are large.</li>
<li><strong>UV Textures</strong>: vertex UV coordinates and <strong>one</strong> texture map for the whole mesh. For a point on a face with given barycentric coordinates, the face color can be computed by interpolating the vertex uv coordinates and then sampling from the texture map. This representation requires two tensors (UVs: <code>(N, V, 2), Texture map:</code>(N, H, W, 3)`), and is limited to only support one texture map per mesh.</li>
<li><strong>Face Textures</strong>: In more complex cases such as ShapeNet meshes, there are multiple texture maps per mesh and some faces have texture while other do not. For these cases, a more flexible representation is a texture atlas, where each face is represented as an <code>(RxR)</code> texture map where R is the texture resolution. For a given point on the face, the texture value can be sampled from the per face texture map using the barycentric coordinates of the point. This representation requires one tensor of shape <code>(N, F, R, R, 3)</code>. This texturing method is inspired by the SoftRasterizer implementation. For more details refer to the <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/io/mtl_io.py#L123"><code>make_material_atlas</code></a> and <a href="https://github.com/facebookresearch/pytorch3d/blob/master/pytorch3d/renderer/mesh/textures.py#L452"><code>sample_textures</code></a> functions. <strong>NOTE:</strong>: The <code>TexturesAtlas</code> texture sampling is only differentiable with respect to the texture atlas but not differentiable with respect to the barycentric coordinates.</li>
<li><strong>Face Textures</strong>: In more complex cases such as ShapeNet meshes, there are multiple texture maps per mesh and some faces have texture while other do not. For these cases, a more flexible representation is a texture atlas, where each face is represented as an <code>(RxR)</code> texture map where R is the texture resolution. For a given point on the face, the texture value can be sampled from the per face texture map using the barycentric coordinates of the point. This representation requires one tensor of shape <code>(N, F, R, R, 3)</code>. This texturing method is inspired by the SoftRasterizer implementation. For more details refer to the <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/io/mtl_io.py#L123"><code>make_material_atlas</code></a> and <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/renderer/mesh/textures.py#L452"><code>sample_textures</code></a> functions. <strong>NOTE:</strong>: The <code>TexturesAtlas</code> texture sampling is only differentiable with respect to the texture atlas but not differentiable with respect to the barycentric coordinates.</li>
</ol>
<p><img src="assets/texturing.jpg" width="1000"></p>
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<p>PyTorch3D provides a modular differentiable renderer, but for instances where we want interactive plots or are not concerned with the differentiability of the rendering process, we provide <a href="../../pytorch3d/vis/plotly_vis.py">functions to render meshes and pointclouds in plotly</a>. These plotly figures allow you to rotate and zoom the rendered images and support plotting batched data as multiple traces in a singular plot or divided into individual subplots.</p>
<p>PyTorch3D provides a modular differentiable renderer, but for instances where we want interactive plots or are not concerned with the differentiability of the rendering process, we provide <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/vis/plotly_vis.py">functions to render meshes and pointclouds in plotly</a>. These plotly figures allow you to rotate and zoom the rendered images and support plotting batched data as multiple traces in a singular plot or divided into individual subplots.</p>
<h1><a class="anchor" aria-hidden="true" id="examples"></a><a href="#examples" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Examples</h1>
<p>These rendering functions accept plotly x,y, and z axis arguments as <code>kwargs</code>, allowing us to customize the plots. Here are two plots with colored axes, a <a href="/docs/assets/plotly_pointclouds.png">Pointclouds plot</a>, a <a href="/docs/assets/plotly_meshes_batch.png">batched Meshes plot in subplots</a>, and a <a href="/docs/assets/plotly_meshes_trace.png">batched Meshes plot with multiple traces</a>. Refer to the <a href="../tutorials/render_textured_meshes.ipynb">render textured meshes</a> and <a href="../tutorials/render_colored_points">render colored pointclouds</a> tutorials for code examples.</p>
<p>These rendering functions accept plotly x,y, and z axis arguments as <code>kwargs</code>, allowing us to customize the plots. Here are two plots with colored axes, a <a href="/docs/assets/plotly_pointclouds.png">Pointclouds plot</a>, a <a href="/docs/assets/plotly_meshes_batch.png">batched Meshes plot in subplots</a>, and a <a href="/docs/assets/plotly_meshes_trace.png">batched Meshes plot with multiple traces</a>. Refer to the <a href="https://pytorch3d.org/tutorials/render_textured_meshes">render textured meshes</a> and <a href="https://pytorch3d.org/tutorials/render_colored_points">render colored pointclouds</a> tutorials for code examples.</p>
<h1><a class="anchor" aria-hidden="true" id="saving-plots-to-images"></a><a href="#saving-plots-to-images" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Saving plots to images</h1>
<p>If you want to save these plotly plots, you will need to install a separate library such as <a href="https://plotly.com/python/static-image-export/">Kaleido</a>.</p>
<p>Install Kaleido</p>
@ -75,4 +75,4 @@
<pre><code class="hljs"><span class="hljs-attribute">fig</span> = ...
fig.write_image(<span class="hljs-string">"image_name.png"</span>)
</code></pre>
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<p>PyTorch3D provides a modular differentiable renderer, but for instances where we want interactive plots or are not concerned with the differentiability of the rendering process, we provide <a href="../../pytorch3d/vis/plotly_vis.py">functions to render meshes and pointclouds in plotly</a>. These plotly figures allow you to rotate and zoom the rendered images and support plotting batched data as multiple traces in a singular plot or divided into individual subplots.</p>
<p>PyTorch3D provides a modular differentiable renderer, but for instances where we want interactive plots or are not concerned with the differentiability of the rendering process, we provide <a href="https://github.com/facebookresearch/pytorch3d/blob/main/pytorch3d/vis/plotly_vis.py">functions to render meshes and pointclouds in plotly</a>. These plotly figures allow you to rotate and zoom the rendered images and support plotting batched data as multiple traces in a singular plot or divided into individual subplots.</p>
<h1><a class="anchor" aria-hidden="true" id="examples"></a><a href="#examples" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Examples</h1>
<p>These rendering functions accept plotly x,y, and z axis arguments as <code>kwargs</code>, allowing us to customize the plots. Here are two plots with colored axes, a <a href="/docs/assets/plotly_pointclouds.png">Pointclouds plot</a>, a <a href="/docs/assets/plotly_meshes_batch.png">batched Meshes plot in subplots</a>, and a <a href="/docs/assets/plotly_meshes_trace.png">batched Meshes plot with multiple traces</a>. Refer to the <a href="../tutorials/render_textured_meshes.ipynb">render textured meshes</a> and <a href="../tutorials/render_colored_points">render colored pointclouds</a> tutorials for code examples.</p>
<p>These rendering functions accept plotly x,y, and z axis arguments as <code>kwargs</code>, allowing us to customize the plots. Here are two plots with colored axes, a <a href="/docs/assets/plotly_pointclouds.png">Pointclouds plot</a>, a <a href="/docs/assets/plotly_meshes_batch.png">batched Meshes plot in subplots</a>, and a <a href="/docs/assets/plotly_meshes_trace.png">batched Meshes plot with multiple traces</a>. Refer to the <a href="https://pytorch3d.org/tutorials/render_textured_meshes">render textured meshes</a> and <a href="https://pytorch3d.org/tutorials/render_colored_points">render colored pointclouds</a> tutorials for code examples.</p>
<h1><a class="anchor" aria-hidden="true" id="saving-plots-to-images"></a><a href="#saving-plots-to-images" aria-hidden="true" class="hash-link"><svg class="hash-link-icon" aria-hidden="true" height="16" version="1.1" viewBox="0 0 16 16" width="16"><path fill-rule="evenodd" d="M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z"></path></svg></a>Saving plots to images</h1>
<p>If you want to save these plotly plots, you will need to install a separate library such as <a href="https://plotly.com/python/static-image-export/">Kaleido</a>.</p>
<p>Install Kaleido</p>
@ -75,4 +75,4 @@
<pre><code class="hljs"><span class="hljs-attribute">fig</span> = ...
fig.write_image(<span class="hljs-string">"image_name.png"</span>)
</code></pre>
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</span></div></h2><div><span><p>Supports optimized implementations of several common functions for 3D data</p>
</span></div></div></div><div class="blockElement alignCenter fourByGridBlock imageAlignTop"><div class="blockImage"><img src="/img/rendering.svg"/></div><div class="blockContent"><h2><div><span><p>Differentiable Rendering</p>
</span></div></h2><div><span><p>Modular differentiable rendering API with parallel implementations in PyTorch, C++ and CUDA</p>
</span></div></div></div></div></div></div></div><div class="productShowcaseSection" id="quickstart" style="text-align:center"><h2>Get Started</h2><div class="container"><div class="wrapper"><ol><li><strong>Install PyTorch3D </strong> (following the instructions <a href="https://github.com/facebookresearch/pytorch3d/blob/master/INSTALL.md">here</a>)</li><li><strong>Try a few 3D operators </strong>e.g. compute the chamfer loss between two meshes:<div><span><pre><code class="hljs css language-python"><span class="hljs-keyword">from</span> pytorch3d.utils <span class="hljs-keyword">import</span> ico_sphere
</span></div></div></div></div></div></div></div><div class="productShowcaseSection" id="quickstart" style="text-align:center"><h2>Get Started</h2><div class="container"><div class="wrapper"><ol><li><strong>Install PyTorch3D </strong> (following the instructions <a href="https://github.com/facebookresearch/pytorch3d/blob/main/INSTALL.md">here</a>)</li><li><strong>Try a few 3D operators </strong>e.g. compute the chamfer loss between two meshes:<div><span><pre><code class="hljs css language-python"><span class="hljs-keyword">from</span> pytorch3d.utils <span class="hljs-keyword">import</span> ico_sphere
<span class="hljs-keyword">from</span> pytorch3d.io <span class="hljs-keyword">import</span> load_obj
<span class="hljs-keyword">from</span> pytorch3d.structures <span class="hljs-keyword">import</span> Meshes
<span class="hljs-keyword">from</span> pytorch3d.ops <span class="hljs-keyword">import</span> sample_points_from_meshes

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@ -6,4 +6,4 @@
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ga('send', 'pageview');
</script><script type="text/javascript" src="https://buttons.github.io/buttons.js"></script><script src="/js/scrollSpy.js"></script><link rel="stylesheet" href="/css/main.css"/><script src="/js/codetabs.js"></script></head><body><div class="fixedHeaderContainer"><div class="headerWrapper wrapper"><header><a href="/"><img class="logo" src="/img/pytorch3dfavicon.png" alt="PyTorch3D"/><h2 class="headerTitleWithLogo">PyTorch3D</h2></a><div class="navigationWrapper navigationSlider"><nav class="slidingNav"><ul class="nav-site nav-site-internal"><li class=""><a href="/docs/why_pytorch3d" target="_self">Docs</a></li><li class=""><a href="/tutorials" target="_self">Tutorials</a></li><li class=""><a href="https://pytorch3d.readthedocs.io/" target="_self">API</a></li><li class=""><a href="https://github.com/facebookresearch/pytorch3d" target="_self">GitHub</a></li></ul></nav></div></header></div></div><div class="navPusher"><div class="mainContainer"><div class="container paddingBottom paddingTop"><div class="wrapper"><div class="showcaseSection"><div class="prose"><h1>Who is Using This?</h1><p>This project is used by many folks</p></div><div class="logos"><a href="https://www.facebook.com"><img src="/img/undraw_open_source.svg" alt="User1" title="User1"/></a></div><p>Are you using this project?</p><a href="undefined/edit/master/website/siteConfig.js" class="button">Add your company</a></div></div></div></div><footer class="nav-footer" id="footer"><section class="sitemap"><div class="footerSection"><div class="social"><a class="github-button" href="https://github.com/facebookresearch/pytorch3d" data-count-href="https://github.com/facebookresearch/pytorch3d/stargazers" data-show-count="true" data-count-aria-label="# stargazers on GitHub" aria-label="Star PyTorch3D on GitHub">pytorch3d</a></div></div></section><a href="https://opensource.facebook.com/" target="_blank" rel="noreferrer noopener" class="fbOpenSource"><img src="/img/oss_logo.png" alt="Facebook Open Source" width="170" height="45"/></a><section class="copyright">Copyright © 2021 Facebook Inc<br/>Legal:<a href="https://opensource.facebook.com/legal/privacy/" target="_blank" rel="noreferrer noopener">Privacy</a><a href="https://opensource.facebook.com/legal/terms/" target="_blank" rel="noreferrer noopener">Terms</a></section></footer></div></body></html>
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View File

@ -36,10 +36,10 @@
"where $d(g_i, g_j)$ is a suitable metric that compares the extrinsics of cameras $g_i$ and $g_j$. \n",
"\n",
"Visually, the problem can be described as follows. The picture below depicts the situation at the beginning of our optimization. The ground truth cameras are plotted in purple while the randomly initialized estimated cameras are plotted in orange:\n",
"![Initialization](https://github.com/facebookresearch/pytorch3d/blob/master/docs/tutorials/data/bundle_adjustment_initialization.png?raw=1)\n",
"![Initialization](https://github.com/facebookresearch/pytorch3d/blob/main/docs/tutorials/data/bundle_adjustment_initialization.png?raw=1)\n",
"\n",
"Our optimization seeks to align the estimated (orange) cameras with the ground truth (purple) cameras, by minimizing the discrepancies between pairs of relative cameras. Thus, the solution to the problem should look as follows:\n",
"![Solution](https://github.com/facebookresearch/pytorch3d/blob/master/docs/tutorials/data/bundle_adjustment_final.png?raw=1)\n",
"![Solution](https://github.com/facebookresearch/pytorch3d/blob/main/docs/tutorials/data/bundle_adjustment_final.png?raw=1)\n",
"\n",
"In practice, the camera extrinsics $g_{ij}$ and $g_i$ are represented using objects from the `SfMPerspectiveCameras` class initialized with the corresponding rotation and translation matrices `R_absolute` and `T_absolute` that define the extrinsic parameters $g = (R, T); R \\in SO(3); T \\in \\mathbb{R}^3$. In order to ensure that `R_absolute` is a valid rotation matrix, we represent it using an exponential map (implemented with `so3_exp_map`) of the axis-angle representation of the rotation `log_R_absolute`.\n",
"\n",
@ -167,11 +167,11 @@
},
"outputs": [],
"source": [
"!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/camera_visualization.py\n",
"!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/camera_visualization.py\n",
"from camera_visualization import plot_camera_scene\n",
"\n",
"!mkdir data\n",
"!wget -P data https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/data/camera_graph.pth"
"!wget -P data https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/data/camera_graph.pth"
]
},
{

View File

@ -23,10 +23,10 @@
# where $d(g_i, g_j)$ is a suitable metric that compares the extrinsics of cameras $g_i$ and $g_j$.
#
# Visually, the problem can be described as follows. The picture below depicts the situation at the beginning of our optimization. The ground truth cameras are plotted in purple while the randomly initialized estimated cameras are plotted in orange:
# ![Initialization](https://github.com/facebookresearch/pytorch3d/blob/master/docs/tutorials/data/bundle_adjustment_initialization.png?raw=1)
# ![Initialization](https://github.com/facebookresearch/pytorch3d/blob/main/docs/tutorials/data/bundle_adjustment_initialization.png?raw=1)
#
# Our optimization seeks to align the estimated (orange) cameras with the ground truth (purple) cameras, by minimizing the discrepancies between pairs of relative cameras. Thus, the solution to the problem should look as follows:
# ![Solution](https://github.com/facebookresearch/pytorch3d/blob/master/docs/tutorials/data/bundle_adjustment_final.png?raw=1)
# ![Solution](https://github.com/facebookresearch/pytorch3d/blob/main/docs/tutorials/data/bundle_adjustment_final.png?raw=1)
#
# In practice, the camera extrinsics $g_{ij}$ and $g_i$ are represented using objects from the `SfMPerspectiveCameras` class initialized with the corresponding rotation and translation matrices `R_absolute` and `T_absolute` that define the extrinsic parameters $g = (R, T); R \in SO(3); T \in \mathbb{R}^3$. In order to ensure that `R_absolute` is a valid rotation matrix, we represent it using an exponential map (implemented with `so3_exp_map`) of the axis-angle representation of the rotation `log_R_absolute`.
#
@ -97,11 +97,11 @@ else:
# In[ ]:
get_ipython().system('wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/camera_visualization.py')
get_ipython().system('wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/camera_visualization.py')
from camera_visualization import plot_camera_scene
get_ipython().system('mkdir data')
get_ipython().system('wget -P data https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/data/camera_graph.pth')
get_ipython().system('wget -P data https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/data/camera_graph.pth')
# OR if running **locally** uncomment and run the following cell:

View File

@ -112,7 +112,7 @@
"metadata": {},
"outputs": [],
"source": [
"!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py\n",
"!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py\n",
"from plot_image_grid import image_grid"
]
},

View File

@ -81,7 +81,7 @@ sys.path.append(os.path.abspath(''))
# In[ ]:
get_ipython().system('wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py')
get_ipython().system('wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py')
from plot_image_grid import image_grid

View File

@ -126,8 +126,8 @@
"metadata": {},
"outputs": [],
"source": [
"!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py\n",
"!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/generate_cow_renders.py\n",
"!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py\n",
"!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/generate_cow_renders.py\n",
"from plot_image_grid import image_grid\n",
"from generate_cow_renders import generate_cow_renders"
]

View File

@ -106,8 +106,8 @@ else:
# In[ ]:
get_ipython().system('wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py')
get_ipython().system('wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/generate_cow_renders.py')
get_ipython().system('wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py')
get_ipython().system('wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/generate_cow_renders.py')
from plot_image_grid import image_grid
from generate_cow_renders import generate_cow_renders

View File

@ -155,7 +155,7 @@
},
"outputs": [],
"source": [
"!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py\n",
"!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py\n",
"from plot_image_grid import image_grid"
]
},

View File

@ -96,7 +96,7 @@ sys.path.append(os.path.abspath(''))
# In[ ]:
get_ipython().system('wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py')
get_ipython().system('wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py')
from plot_image_grid import image_grid

View File

@ -106,8 +106,8 @@
"metadata": {},
"outputs": [],
"source": [
"!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py\n",
"!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/generate_cow_renders.py\n",
"!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py\n",
"!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/generate_cow_renders.py\n",
"from plot_image_grid import image_grid\n",
"from generate_cow_renders import generate_cow_renders"
]

View File

@ -85,8 +85,8 @@ else:
# In[ ]:
get_ipython().system('wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py')
get_ipython().system('wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/generate_cow_renders.py')
get_ipython().system('wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py')
get_ipython().system('wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/generate_cow_renders.py')
from plot_image_grid import image_grid
from generate_cow_renders import generate_cow_renders

View File

@ -154,7 +154,7 @@
},
"outputs": [],
"source": [
"!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py\n",
"!wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py\n",
"from plot_image_grid import image_grid"
]
},

View File

@ -87,7 +87,7 @@ sys.path.append(os.path.abspath(''))
# In[ ]:
get_ipython().system('wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py')
get_ipython().system('wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py')
from plot_image_grid import image_grid

View File

@ -12,7 +12,7 @@
</span></div></h2><div><span><p>Supports optimized implementations of several common functions for 3D data</p>
</span></div></div></div><div class="blockElement alignCenter fourByGridBlock imageAlignTop"><div class="blockImage"><img src="/img/rendering.svg"/></div><div class="blockContent"><h2><div><span><p>Differentiable Rendering</p>
</span></div></h2><div><span><p>Modular differentiable rendering API with parallel implementations in PyTorch, C++ and CUDA</p>
</span></div></div></div></div></div></div></div><div class="productShowcaseSection" id="quickstart" style="text-align:center"><h2>Get Started</h2><div class="container"><div class="wrapper"><ol><li><strong>Install PyTorch3D </strong> (following the instructions <a href="https://github.com/facebookresearch/pytorch3d/blob/master/INSTALL.md">here</a>)</li><li><strong>Try a few 3D operators </strong>e.g. compute the chamfer loss between two meshes:<div><span><pre><code class="hljs css language-python"><span class="hljs-keyword">from</span> pytorch3d.utils <span class="hljs-keyword">import</span> ico_sphere
</span></div></div></div></div></div></div></div><div class="productShowcaseSection" id="quickstart" style="text-align:center"><h2>Get Started</h2><div class="container"><div class="wrapper"><ol><li><strong>Install PyTorch3D </strong> (following the instructions <a href="https://github.com/facebookresearch/pytorch3d/blob/main/INSTALL.md">here</a>)</li><li><strong>Try a few 3D operators </strong>e.g. compute the chamfer loss between two meshes:<div><span><pre><code class="hljs css language-python"><span class="hljs-keyword">from</span> pytorch3d.utils <span class="hljs-keyword">import</span> ico_sphere
<span class="hljs-keyword">from</span> pytorch3d.io <span class="hljs-keyword">import</span> load_obj
<span class="hljs-keyword">from</span> pytorch3d.structures <span class="hljs-keyword">import</span> Meshes
<span class="hljs-keyword">from</span> pytorch3d.ops <span class="hljs-keyword">import</span> sample_points_from_meshes

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@ -1 +1 @@
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@ -95,9 +95,9 @@ g_1, ..., g_N =
$$,
where $d(g_i, g_j)$ is a suitable metric that compares the extrinsics of cameras $g_i$ and $g_j$.</p>
<p>Visually, the problem can be described as follows. The picture below depicts the situation at the beginning of our optimization. The ground truth cameras are plotted in purple while the randomly initialized estimated cameras are plotted in orange:
<img alt="Initialization" src="https://github.com/facebookresearch/pytorch3d/blob/master/docs/tutorials/data/bundle_adjustment_initialization.png?raw=1"/></p>
<img alt="Initialization" src="https://github.com/facebookresearch/pytorch3d/blob/main/docs/tutorials/data/bundle_adjustment_initialization.png?raw=1"/></p>
<p>Our optimization seeks to align the estimated (orange) cameras with the ground truth (purple) cameras, by minimizing the discrepancies between pairs of relative cameras. Thus, the solution to the problem should look as follows:
<img alt="Solution" src="https://github.com/facebookresearch/pytorch3d/blob/master/docs/tutorials/data/bundle_adjustment_final.png?raw=1"/></p>
<img alt="Solution" src="https://github.com/facebookresearch/pytorch3d/blob/main/docs/tutorials/data/bundle_adjustment_final.png?raw=1"/></p>
<p>In practice, the camera extrinsics $g_{ij}$ and $g_i$ are represented using objects from the <code>SfMPerspectiveCameras</code> class initialized with the corresponding rotation and translation matrices <code>R_absolute</code> and <code>T_absolute</code> that define the extrinsic parameters $g = (R, T); R \in SO(3); T \in \mathbb{R}^3$. In order to ensure that <code>R_absolute</code> is a valid rotation matrix, we represent it using an exponential map (implemented with <code>so3_exp_map</code>) of the axis-angle representation of the rotation <code>log_R_absolute</code>.</p>
<p>Note that the solution to this problem could only be recovered up to an unknown global rigid transformation $g_{glob} \in SE(3)$. Thus, for simplicity, we assume knowledge of the absolute extrinsics of the first camera $g_0$. We set $g_0$ as a trivial camera $g_0 = (I, \vec{0})$.</p>
</div>
@ -197,11 +197,11 @@ where $d(g_i, g_j)$ is a suitable metric that compares the extrinsics of cameras
<div class="prompt input_prompt">In [ ]:</div>
<div class="inner_cell">
<div class="input_area">
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/camera_visualization.py
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/camera_visualization.py
<span class="kn">from</span> <span class="nn">camera_visualization</span> <span class="kn">import</span> <span class="n">plot_camera_scene</span>
<span class="o">!</span>mkdir data
<span class="o">!</span>wget -P data https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/data/camera_graph.pth
<span class="o">!</span>wget -P data https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/data/camera_graph.pth
</pre></div>
</div>
</div>

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@ -95,9 +95,9 @@ g_1, ..., g_N =
$$,
where $d(g_i, g_j)$ is a suitable metric that compares the extrinsics of cameras $g_i$ and $g_j$.</p>
<p>Visually, the problem can be described as follows. The picture below depicts the situation at the beginning of our optimization. The ground truth cameras are plotted in purple while the randomly initialized estimated cameras are plotted in orange:
<img alt="Initialization" src="https://github.com/facebookresearch/pytorch3d/blob/master/docs/tutorials/data/bundle_adjustment_initialization.png?raw=1"/></p>
<img alt="Initialization" src="https://github.com/facebookresearch/pytorch3d/blob/main/docs/tutorials/data/bundle_adjustment_initialization.png?raw=1"/></p>
<p>Our optimization seeks to align the estimated (orange) cameras with the ground truth (purple) cameras, by minimizing the discrepancies between pairs of relative cameras. Thus, the solution to the problem should look as follows:
<img alt="Solution" src="https://github.com/facebookresearch/pytorch3d/blob/master/docs/tutorials/data/bundle_adjustment_final.png?raw=1"/></p>
<img alt="Solution" src="https://github.com/facebookresearch/pytorch3d/blob/main/docs/tutorials/data/bundle_adjustment_final.png?raw=1"/></p>
<p>In practice, the camera extrinsics $g_{ij}$ and $g_i$ are represented using objects from the <code>SfMPerspectiveCameras</code> class initialized with the corresponding rotation and translation matrices <code>R_absolute</code> and <code>T_absolute</code> that define the extrinsic parameters $g = (R, T); R \in SO(3); T \in \mathbb{R}^3$. In order to ensure that <code>R_absolute</code> is a valid rotation matrix, we represent it using an exponential map (implemented with <code>so3_exp_map</code>) of the axis-angle representation of the rotation <code>log_R_absolute</code>.</p>
<p>Note that the solution to this problem could only be recovered up to an unknown global rigid transformation $g_{glob} \in SE(3)$. Thus, for simplicity, we assume knowledge of the absolute extrinsics of the first camera $g_0$. We set $g_0$ as a trivial camera $g_0 = (I, \vec{0})$.</p>
</div>
@ -197,11 +197,11 @@ where $d(g_i, g_j)$ is a suitable metric that compares the extrinsics of cameras
<div class="prompt input_prompt">In [ ]:</div>
<div class="inner_cell">
<div class="input_area">
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/camera_visualization.py
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/camera_visualization.py
<span class="kn">from</span> <span class="nn">camera_visualization</span> <span class="kn">import</span> <span class="n">plot_camera_scene</span>
<span class="o">!</span>mkdir data
<span class="o">!</span>wget -P data https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/data/camera_graph.pth
<span class="o">!</span>wget -P data https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/data/camera_graph.pth
</pre></div>
</div>
</div>

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@ -192,7 +192,7 @@
<div class="prompt input_prompt">In [ ]:</div>
<div class="inner_cell">
<div class="input_area">
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py
<span class="kn">from</span> <span class="nn">plot_image_grid</span> <span class="kn">import</span> <span class="n">image_grid</span>
</pre></div>
</div>

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@ -192,7 +192,7 @@
<div class="prompt input_prompt">In [ ]:</div>
<div class="inner_cell">
<div class="input_area">
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py
<span class="kn">from</span> <span class="nn">plot_image_grid</span> <span class="kn">import</span> <span class="n">image_grid</span>
</pre></div>
</div>

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@ -201,8 +201,8 @@
<div class="prompt input_prompt">In [ ]:</div>
<div class="inner_cell">
<div class="input_area">
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py
<span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/generate_cow_renders.py
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py
<span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/generate_cow_renders.py
<span class="kn">from</span> <span class="nn">plot_image_grid</span> <span class="kn">import</span> <span class="n">image_grid</span>
<span class="kn">from</span> <span class="nn">generate_cow_renders</span> <span class="kn">import</span> <span class="n">generate_cow_renders</span>
</pre></div>

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@ -201,8 +201,8 @@
<div class="prompt input_prompt">In [ ]:</div>
<div class="inner_cell">
<div class="input_area">
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py
<span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/generate_cow_renders.py
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py
<span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/generate_cow_renders.py
<span class="kn">from</span> <span class="nn">plot_image_grid</span> <span class="kn">import</span> <span class="n">image_grid</span>
<span class="kn">from</span> <span class="nn">generate_cow_renders</span> <span class="kn">import</span> <span class="n">generate_cow_renders</span>
</pre></div>

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@ -206,7 +206,7 @@
<div class="prompt input_prompt">In [ ]:</div>
<div class="inner_cell">
<div class="input_area">
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py
<span class="kn">from</span> <span class="nn">plot_image_grid</span> <span class="kn">import</span> <span class="n">image_grid</span>
</pre></div>
</div>

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@ -206,7 +206,7 @@
<div class="prompt input_prompt">In [ ]:</div>
<div class="inner_cell">
<div class="input_area">
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py
<span class="kn">from</span> <span class="nn">plot_image_grid</span> <span class="kn">import</span> <span class="n">image_grid</span>
</pre></div>
</div>

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@ -181,8 +181,8 @@
<div class="prompt input_prompt">In [ ]:</div>
<div class="inner_cell">
<div class="input_area">
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py
<span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/generate_cow_renders.py
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py
<span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/generate_cow_renders.py
<span class="kn">from</span> <span class="nn">plot_image_grid</span> <span class="kn">import</span> <span class="n">image_grid</span>
<span class="kn">from</span> <span class="nn">generate_cow_renders</span> <span class="kn">import</span> <span class="n">generate_cow_renders</span>
</pre></div>

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@ -181,8 +181,8 @@
<div class="prompt input_prompt">In [ ]:</div>
<div class="inner_cell">
<div class="input_area">
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py
<span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/generate_cow_renders.py
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py
<span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/generate_cow_renders.py
<span class="kn">from</span> <span class="nn">plot_image_grid</span> <span class="kn">import</span> <span class="n">image_grid</span>
<span class="kn">from</span> <span class="nn">generate_cow_renders</span> <span class="kn">import</span> <span class="n">generate_cow_renders</span>
</pre></div>

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@ -197,7 +197,7 @@
<div class="prompt input_prompt">In [ ]:</div>
<div class="inner_cell">
<div class="input_area">
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py
<span class="kn">from</span> <span class="nn">plot_image_grid</span> <span class="kn">import</span> <span class="n">image_grid</span>
</pre></div>
</div>

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@ -197,7 +197,7 @@
<div class="prompt input_prompt">In [ ]:</div>
<div class="inner_cell">
<div class="input_area">
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/master/docs/tutorials/utils/plot_image_grid.py
<div class="highlight hl-ipython3"><pre><span></span><span class="o">!</span>wget https://raw.githubusercontent.com/facebookresearch/pytorch3d/main/docs/tutorials/utils/plot_image_grid.py
<span class="kn">from</span> <span class="nn">plot_image_grid</span> <span class="kn">import</span> <span class="n">image_grid</span>
</pre></div>
</div>

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@ -6,4 +6,4 @@
ga('create', 'UA-157376881-1', 'auto');
ga('send', 'pageview');
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