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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># Copyright (c) Facebook, Inc. and its affiliates. All rights reserved.</span>
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<h1 id="Camera-position-optimization-using-differentiable-rendering">Camera position optimization using differentiable rendering<a class="anchor-link" href="#Camera-position-optimization-using-differentiable-rendering"></a></h1><p>In this tutorial we will learn the [x, y, z] position of a camera given a reference image using differentiable rendering.</p>
<p>We will first initialize a renderer with a starting position for the camera. We will then use this to generate an image, compute a loss with the reference image, and finally backpropagate through the entire pipeline to update the position of the camera.</p>
<p>This tutorial shows how to:</p>
<ul>
<li>load a mesh from an <code>.obj</code> file</li>
<li>initialize a <code>Camera</code>, <code>Shader</code> and <code>Renderer</code>,</li>
<li>render a mesh</li>
<li>set up an optimization loop with a loss function and optimizer</li>
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<h2 id="0.-Install-and-import-modules">0. Install and import modules<a class="anchor-link" href="#0.-Install-and-import-modules"></a></h2>
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<p>If <code>torch</code>, <code>torchvision</code> and <code>pytorch3d</code> are not installed, run the following cell:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="o">!</span>pip install torch torchvision
<span class="o">!</span>pip install <span class="s1">'git+https://github.com/facebookresearch/pytorch3d.git@stable'</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">os</span>
<span class="kn">import</span> <span class="nn">torch</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">tqdm</span> <span class="k">import</span> <span class="n">tqdm_notebook</span>
<span class="kn">import</span> <span class="nn">imageio</span>
<span class="kn">import</span> <span class="nn">torch.nn</span> <span class="k">as</span> <span class="nn">nn</span>
<span class="kn">import</span> <span class="nn">torch.nn.functional</span> <span class="k">as</span> <span class="nn">F</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">skimage</span> <span class="k">import</span> <span class="n">img_as_ubyte</span>
<span class="c1"># io utils</span>
<span class="kn">from</span> <span class="nn">pytorch3d.io</span> <span class="k">import</span> <span class="n">load_obj</span>
<span class="c1"># datastructures</span>
<span class="kn">from</span> <span class="nn">pytorch3d.structures</span> <span class="k">import</span> <span class="n">Meshes</span><span class="p">,</span> <span class="n">Textures</span>
<span class="c1"># 3D transformations functions</span>
<span class="kn">from</span> <span class="nn">pytorch3d.transforms</span> <span class="k">import</span> <span class="n">Rotate</span><span class="p">,</span> <span class="n">Translate</span>
<span class="c1"># rendering components</span>
<span class="kn">from</span> <span class="nn">pytorch3d.renderer</span> <span class="k">import</span> <span class="p">(</span>
<span class="n">OpenGLPerspectiveCameras</span><span class="p">,</span> <span class="n">look_at_view_transform</span><span class="p">,</span> <span class="n">look_at_rotation</span><span class="p">,</span>
<span class="n">RasterizationSettings</span><span class="p">,</span> <span class="n">MeshRenderer</span><span class="p">,</span> <span class="n">MeshRasterizer</span><span class="p">,</span> <span class="n">BlendParams</span><span class="p">,</span>
<span class="n">SoftSilhouetteShader</span><span class="p">,</span> <span class="n">HardPhongShader</span><span class="p">,</span> <span class="n">PointLights</span>
<span class="p">)</span>
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<h2 id="1.-Load-the-Obj">1. Load the Obj<a class="anchor-link" href="#1.-Load-the-Obj"></a></h2><p>We will load an obj file and create a <strong>Meshes</strong> object. <strong>Meshes</strong> is a unique datastructure provided in PyTorch3D for working with <strong>batches of meshes of different sizes</strong>. It has several useful class methods which are used in the rendering pipeline.</p>
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<p>If you are running this notebook locally after cloning the PyTorch3D repository, the mesh will already be available. <strong>If using Google Colab, fetch the mesh and save it at the path <code>data/</code></strong>:</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="o">!</span>mkdir -p data
<span class="o">!</span>wget -P data https://dl.fbaipublicfiles.com/pytorch3d/data/teapot/teapot.obj
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># Set the cuda device </span>
<span class="n">device</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">device</span><span class="p">(</span><span class="s2">"cuda:0"</span><span class="p">)</span>
<span class="n">torch</span><span class="o">.</span><span class="n">cuda</span><span class="o">.</span><span class="n">set_device</span><span class="p">(</span><span class="n">device</span><span class="p">)</span>
<span class="c1"># Load the obj and ignore the textures and materials.</span>
<span class="n">verts</span><span class="p">,</span> <span class="n">faces_idx</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">load_obj</span><span class="p">(</span><span class="s2">"./data/teapot.obj"</span><span class="p">)</span>
<span class="n">faces</span> <span class="o">=</span> <span class="n">faces_idx</span><span class="o">.</span><span class="n">verts_idx</span>
<span class="c1"># Initialize each vertex to be white in color.</span>
<span class="n">verts_rgb</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="n">verts</span><span class="p">)[</span><span class="kc">None</span><span class="p">]</span> <span class="c1"># (1, V, 3)</span>
<span class="n">textures</span> <span class="o">=</span> <span class="n">Textures</span><span class="p">(</span><span class="n">verts_rgb</span><span class="o">=</span><span class="n">verts_rgb</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">device</span><span class="p">))</span>
<span class="c1"># Create a Meshes object for the teapot. Here we have only one mesh in the batch.</span>
<span class="n">teapot_mesh</span> <span class="o">=</span> <span class="n">Meshes</span><span class="p">(</span>
<span class="n">verts</span><span class="o">=</span><span class="p">[</span><span class="n">verts</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">device</span><span class="p">)],</span>
<span class="n">faces</span><span class="o">=</span><span class="p">[</span><span class="n">faces</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">device</span><span class="p">)],</span>
<span class="n">textures</span><span class="o">=</span><span class="n">textures</span>
<span class="p">)</span>
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<h2 id="2.-Optimization-setup">2. Optimization setup<a class="anchor-link" href="#2.-Optimization-setup"></a></h2>
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<h3 id="Create-a-renderer">Create a renderer<a class="anchor-link" href="#Create-a-renderer"></a></h3><p>A <strong>renderer</strong> in PyTorch3D is composed of a <strong>rasterizer</strong> and a <strong>shader</strong> which each have a number of subcomponents such as a <strong>camera</strong> (orthgraphic/perspective). Here we initialize some of these components and use default values for the rest.</p>
<p>For optimizing the camera position we will use a renderer which produces a <strong>silhouette</strong> of the object only and does not apply any <strong>lighting</strong> or <strong>shading</strong>. We will also initialize another renderer which applies full <strong>phong shading</strong> and use this for visualizing the outputs.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># Initialize an OpenGL perspective camera.</span>
<span class="n">cameras</span> <span class="o">=</span> <span class="n">OpenGLPerspectiveCameras</span><span class="p">(</span><span class="n">device</span><span class="o">=</span><span class="n">device</span><span class="p">)</span>
<span class="c1"># To blend the 100 faces we set a few parameters which control the opacity and the sharpness of </span>
<span class="c1"># edges. Refer to blending.py for more details. </span>
<span class="n">blend_params</span> <span class="o">=</span> <span class="n">BlendParams</span><span class="p">(</span><span class="n">sigma</span><span class="o">=</span><span class="mf">1e-4</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=</span><span class="mf">1e-4</span><span class="p">)</span>
<span class="c1"># Define the settings for rasterization and shading. Here we set the output image to be of size</span>
<span class="c1"># 256x256. To form the blended image we use 100 faces for each pixel. We also set bin_size and max_faces_per_bin to None which ensure that </span>
<span class="c1"># the faster coarse-to-fine rasterization method is used. Refer to rasterize_meshes.py for </span>
<span class="c1"># explanations of these parameters. Refer to docs/notes/renderer.md for an explanation of </span>
<span class="c1"># the difference between naive and coarse-to-fine rasterization. </span>
<span class="n">raster_settings</span> <span class="o">=</span> <span class="n">RasterizationSettings</span><span class="p">(</span>
<span class="n">image_size</span><span class="o">=</span><span class="mi">256</span><span class="p">,</span>
<span class="n">blur_radius</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="mf">1.</span> <span class="o">/</span> <span class="mf">1e-4</span> <span class="o">-</span> <span class="mf">1.</span><span class="p">)</span> <span class="o">*</span> <span class="n">blend_params</span><span class="o">.</span><span class="n">sigma</span><span class="p">,</span>
<span class="n">faces_per_pixel</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
<span class="n">bin_size</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="c1"># this setting controls whether naive or coarse-to-fine rasterization is used</span>
<span class="n">max_faces_per_bin</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># this setting is for coarse rasterization</span>
<span class="p">)</span>
<span class="c1"># Create a silhouette mesh renderer by composing a rasterizer and a shader. </span>
<span class="n">silhouette_renderer</span> <span class="o">=</span> <span class="n">MeshRenderer</span><span class="p">(</span>
<span class="n">rasterizer</span><span class="o">=</span><span class="n">MeshRasterizer</span><span class="p">(</span>
<span class="n">cameras</span><span class="o">=</span><span class="n">cameras</span><span class="p">,</span>
<span class="n">raster_settings</span><span class="o">=</span><span class="n">raster_settings</span>
<span class="p">),</span>
<span class="n">shader</span><span class="o">=</span><span class="n">SoftSilhouetteShader</span><span class="p">(</span><span class="n">blend_params</span><span class="o">=</span><span class="n">blend_params</span><span class="p">)</span>
<span class="p">)</span>
<span class="c1"># We will also create a phong renderer. This is simpler and only needs to render one face per pixel.</span>
<span class="n">raster_settings</span> <span class="o">=</span> <span class="n">RasterizationSettings</span><span class="p">(</span>
<span class="n">image_size</span><span class="o">=</span><span class="mi">256</span><span class="p">,</span>
<span class="n">blur_radius</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span>
<span class="n">faces_per_pixel</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
<span class="n">bin_size</span><span class="o">=</span><span class="mi">0</span>
<span class="p">)</span>
<span class="c1"># We can add a point light in front of the object. </span>
<span class="n">lights</span> <span class="o">=</span> <span class="n">PointLights</span><span class="p">(</span><span class="n">device</span><span class="o">=</span><span class="n">device</span><span class="p">,</span> <span class="n">location</span><span class="o">=</span><span class="p">((</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.0</span><span class="p">),))</span>
<span class="n">phong_renderer</span> <span class="o">=</span> <span class="n">MeshRenderer</span><span class="p">(</span>
<span class="n">rasterizer</span><span class="o">=</span><span class="n">MeshRasterizer</span><span class="p">(</span>
<span class="n">cameras</span><span class="o">=</span><span class="n">cameras</span><span class="p">,</span>
<span class="n">raster_settings</span><span class="o">=</span><span class="n">raster_settings</span>
<span class="p">),</span>
<span class="n">shader</span><span class="o">=</span><span class="n">HardPhongShader</span><span class="p">(</span><span class="n">device</span><span class="o">=</span><span class="n">device</span><span class="p">,</span> <span class="n">lights</span><span class="o">=</span><span class="n">lights</span><span class="p">)</span>
<span class="p">)</span>
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<h3 id="Create-a-reference-image">Create a reference image<a class="anchor-link" href="#Create-a-reference-image"></a></h3><p>We will first position the teapot and generate an image. We use helper functions to rotate the teapot to a desired viewpoint. Then we can use the renderers to produce an image. Here we will use both renderers and visualize the silhouette and full shaded image.</p>
<p>The world coordinate system is defined as +Y up, +X left and +Z in. The teapot in world coordinates has the spout pointing to the left.</p>
<p>We defined a camera which is positioned on the positive z axis hence sees the spout to the right.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># Select the viewpoint using spherical angles </span>
<span class="n">distance</span> <span class="o">=</span> <span class="mi">3</span> <span class="c1"># distance from camera to the object</span>
<span class="n">elevation</span> <span class="o">=</span> <span class="mf">50.0</span> <span class="c1"># angle of elevation in degrees</span>
<span class="n">azimuth</span> <span class="o">=</span> <span class="mf">0.0</span> <span class="c1"># No rotation so the camera is positioned on the +Z axis. </span>
<span class="c1"># Get the position of the camera based on the spherical angles</span>
<span class="n">R</span><span class="p">,</span> <span class="n">T</span> <span class="o">=</span> <span class="n">look_at_view_transform</span><span class="p">(</span><span class="n">distance</span><span class="p">,</span> <span class="n">elevation</span><span class="p">,</span> <span class="n">azimuth</span><span class="p">,</span> <span class="n">device</span><span class="o">=</span><span class="n">device</span><span class="p">)</span>
<span class="c1"># Render the teapot providing the values of R and T. </span>
<span class="n">silhouete</span> <span class="o">=</span> <span class="n">silhouette_renderer</span><span class="p">(</span><span class="n">meshes_world</span><span class="o">=</span><span class="n">teapot_mesh</span><span class="p">,</span> <span class="n">R</span><span class="o">=</span><span class="n">R</span><span class="p">,</span> <span class="n">T</span><span class="o">=</span><span class="n">T</span><span class="p">)</span>
<span class="n">image_ref</span> <span class="o">=</span> <span class="n">phong_renderer</span><span class="p">(</span><span class="n">meshes_world</span><span class="o">=</span><span class="n">teapot_mesh</span><span class="p">,</span> <span class="n">R</span><span class="o">=</span><span class="n">R</span><span class="p">,</span> <span class="n">T</span><span class="o">=</span><span class="n">T</span><span class="p">)</span>
<span class="n">silhouete</span> <span class="o">=</span> <span class="n">silhouete</span><span class="o">.</span><span class="n">cpu</span><span class="p">()</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span>
<span class="n">image_ref</span> <span class="o">=</span> <span class="n">image_ref</span><span class="o">.</span><span class="n">cpu</span><span class="p">()</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">silhouete</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()[</span><span class="o">...</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span> <span class="c1"># only plot the alpha channel of the RGBA image</span>
<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">image_ref</span><span class="o">.</span><span class="n">squeeze</span><span class="p">())</span>
<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
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<h3 id="Set-up-a-basic-model">Set up a basic model<a class="anchor-link" href="#Set-up-a-basic-model"></a></h3><p>Here we create a simple model class and initialize a parameter for the camera position.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="k">class</span> <span class="nc">Model</span><span class="p">(</span><span class="n">nn</span><span class="o">.</span><span class="n">Module</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">meshes</span><span class="p">,</span> <span class="n">renderer</span><span class="p">,</span> <span class="n">image_ref</span><span class="p">):</span>
<span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
<span class="bp">self</span><span class="o">.</span><span class="n">meshes</span> <span class="o">=</span> <span class="n">meshes</span>
<span class="bp">self</span><span class="o">.</span><span class="n">device</span> <span class="o">=</span> <span class="n">meshes</span><span class="o">.</span><span class="n">device</span>
<span class="bp">self</span><span class="o">.</span><span class="n">renderer</span> <span class="o">=</span> <span class="n">renderer</span>
<span class="c1"># Get the silhouette of the reference RGB image by finding all the non zero values. </span>
<span class="n">image_ref</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">from_numpy</span><span class="p">((</span><span class="n">image_ref</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="p">:</span><span class="mi">3</span><span class="p">]</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">))</span>
<span class="bp">self</span><span class="o">.</span><span class="n">register_buffer</span><span class="p">(</span><span class="s1">'image_ref'</span><span class="p">,</span> <span class="n">image_ref</span><span class="p">)</span>
<span class="c1"># Create an optimizable parameter for the x, y, z position of the camera. </span>
<span class="bp">self</span><span class="o">.</span><span class="n">camera_position</span> <span class="o">=</span> <span class="n">nn</span><span class="o">.</span><span class="n">Parameter</span><span class="p">(</span>
<span class="n">torch</span><span class="o">.</span><span class="n">from_numpy</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">3.0</span><span class="p">,</span> <span class="mf">6.9</span><span class="p">,</span> <span class="o">+</span><span class="mf">2.5</span><span class="p">],</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">))</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">meshes</span><span class="o">.</span><span class="n">device</span><span class="p">))</span>
<span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="c1"># Render the image using the updated camera position. Based on the new position of the </span>
<span class="c1"># camer we calculate the rotation and translation matrices</span>
<span class="n">R</span> <span class="o">=</span> <span class="n">look_at_rotation</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">camera_position</span><span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="p">:],</span> <span class="n">device</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">device</span><span class="p">)</span> <span class="c1"># (1, 3, 3)</span>
<span class="n">T</span> <span class="o">=</span> <span class="o">-</span><span class="n">torch</span><span class="o">.</span><span class="n">bmm</span><span class="p">(</span><span class="n">R</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">camera_position</span><span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="p">:,</span> <span class="kc">None</span><span class="p">])[:,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">]</span> <span class="c1"># (1, 3)</span>
<span class="n">image</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">renderer</span><span class="p">(</span><span class="n">meshes_world</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">meshes</span><span class="o">.</span><span class="n">clone</span><span class="p">(),</span> <span class="n">R</span><span class="o">=</span><span class="n">R</span><span class="p">,</span> <span class="n">T</span><span class="o">=</span><span class="n">T</span><span class="p">)</span>
<span class="c1"># Calculate the silhouette loss</span>
<span class="n">loss</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">image</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">image_ref</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
<span class="k">return</span> <span class="n">loss</span><span class="p">,</span> <span class="n">image</span>
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<h2 id="3.-Initialize-the-model-and-optimizer">3. Initialize the model and optimizer<a class="anchor-link" href="#3.-Initialize-the-model-and-optimizer"></a></h2><p>Now we can create an instance of the <strong>model</strong> above and set up an <strong>optimizer</strong> for the camera position parameter.</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># We will save images periodically and compose them into a GIF.</span>
<span class="n">filename_output</span> <span class="o">=</span> <span class="s2">"./teapot_optimization_demo.gif"</span>
<span class="n">writer</span> <span class="o">=</span> <span class="n">imageio</span><span class="o">.</span><span class="n">get_writer</span><span class="p">(</span><span class="n">filename_output</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">'I'</span><span class="p">,</span> <span class="n">duration</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span>
<span class="c1"># Initialize a model using the renderer, mesh and reference image</span>
<span class="n">model</span> <span class="o">=</span> <span class="n">Model</span><span class="p">(</span><span class="n">meshes</span><span class="o">=</span><span class="n">teapot_mesh</span><span class="p">,</span> <span class="n">renderer</span><span class="o">=</span><span class="n">silhouette_renderer</span><span class="p">,</span> <span class="n">image_ref</span><span class="o">=</span><span class="n">image_ref</span><span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">device</span><span class="p">)</span>
<span class="c1"># Create an optimizer. Here we are using Adam and we pass in the parameters of the model</span>
<span class="n">optimizer</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">optim</span><span class="o">.</span><span class="n">Adam</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">parameters</span><span class="p">(),</span> <span class="n">lr</span><span class="o">=</span><span class="mf">0.05</span><span class="p">)</span>
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<h3 id="Visualize-the-starting-position-and-the-reference-position">Visualize the starting position and the reference position<a class="anchor-link" href="#Visualize-the-starting-position-and-the-reference-position"></a></h3>
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<div class="prompt input_prompt">In [19]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">))</span>
<span class="n">_</span><span class="p">,</span> <span class="n">image_init</span> <span class="o">=</span> <span class="n">model</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">image_init</span><span class="o">.</span><span class="n">detach</span><span class="p">()</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span><span class="o">.</span><span class="n">cpu</span><span class="p">()</span><span class="o">.</span><span class="n">numpy</span><span class="p">()[</span><span class="o">...</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Starting position"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">image_ref</span><span class="o">.</span><span class="n">cpu</span><span class="p">()</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span><span class="o">.</span><span class="n">squeeze</span><span class="p">())</span>
<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"Reference silhouette"</span><span class="p">)</span>
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<pre>Text(0.5, 1.0, 'Reference silhouette')</pre>
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<h2 id="4.-Run-the-optimization">4. Run the optimization<a class="anchor-link" href="#4.-Run-the-optimization"></a></h2><p>We run several iterations of the forward and backward pass and save outputs every 10 iterations. When this has finished take a look at <code>./teapot_optimization_demo.gif</code> for a cool gif of the optimization process!</p>
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<div class="prompt input_prompt">In [20]:</div>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">loop</span> <span class="o">=</span> <span class="n">tqdm_notebook</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">200</span><span class="p">))</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">loop</span><span class="p">:</span>
<span class="n">optimizer</span><span class="o">.</span><span class="n">zero_grad</span><span class="p">()</span>
<span class="n">loss</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">model</span><span class="p">()</span>
<span class="n">loss</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
<span class="n">optimizer</span><span class="o">.</span><span class="n">step</span><span class="p">()</span>
<span class="n">loop</span><span class="o">.</span><span class="n">set_description</span><span class="p">(</span><span class="s1">'Optimizing (loss </span><span class="si">%.4f</span><span class="s1">)'</span> <span class="o">%</span> <span class="n">loss</span><span class="o">.</span><span class="n">data</span><span class="p">)</span>
<span class="k">if</span> <span class="n">loss</span><span class="o">.</span><span class="n">item</span><span class="p">()</span> <span class="o">&lt;</span> <span class="mi">200</span><span class="p">:</span>
<span class="k">break</span>
<span class="c1"># Save outputs to create a GIF. </span>
<span class="k">if</span> <span class="n">i</span> <span class="o">%</span> <span class="mi">10</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">R</span> <span class="o">=</span> <span class="n">look_at_rotation</span><span class="p">(</span><span class="n">model</span><span class="o">.</span><span class="n">camera_position</span><span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="p">:],</span> <span class="n">device</span><span class="o">=</span><span class="n">model</span><span class="o">.</span><span class="n">device</span><span class="p">)</span>
<span class="n">T</span> <span class="o">=</span> <span class="o">-</span><span class="n">torch</span><span class="o">.</span><span class="n">bmm</span><span class="p">(</span><span class="n">R</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">model</span><span class="o">.</span><span class="n">camera_position</span><span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="p">:,</span> <span class="kc">None</span><span class="p">])[:,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">]</span> <span class="c1"># (1, 3)</span>
<span class="n">image</span> <span class="o">=</span> <span class="n">phong_renderer</span><span class="p">(</span><span class="n">meshes_world</span><span class="o">=</span><span class="n">model</span><span class="o">.</span><span class="n">meshes</span><span class="o">.</span><span class="n">clone</span><span class="p">(),</span> <span class="n">R</span><span class="o">=</span><span class="n">R</span><span class="p">,</span> <span class="n">T</span><span class="o">=</span><span class="n">T</span><span class="p">)</span>
<span class="n">image</span> <span class="o">=</span> <span class="n">image</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="o">...</span><span class="p">,</span> <span class="p">:</span><span class="mi">3</span><span class="p">]</span><span class="o">.</span><span class="n">detach</span><span class="p">()</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span><span class="o">.</span><span class="n">cpu</span><span class="p">()</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span>
<span class="n">image</span> <span class="o">=</span> <span class="n">img_as_ubyte</span><span class="p">(</span><span class="n">image</span><span class="p">)</span>
<span class="n">writer</span><span class="o">.</span><span class="n">append_data</span><span class="p">(</span><span class="n">image</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">image</span><span class="p">[</span><span class="o">...</span><span class="p">,</span> <span class="p">:</span><span class="mi">3</span><span class="p">])</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"iter: </span><span class="si">%d</span><span class="s2">, loss: </span><span class="si">%0.2f</span><span class="s2">"</span> <span class="o">%</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">loss</span><span class="o">.</span><span class="n">data</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"off"</span><span class="p">)</span>
<span class="n">writer</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
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<h2 id="5.-Conclusion">5. Conclusion<a class="anchor-link" href="#5.-Conclusion"></a></h2><p>In this tutorial we learnt how to <strong>load</strong> a mesh from an obj file, initialize a PyTorch3D datastructure called <strong>Meshes</strong>, set up an <strong>Renderer</strong> consisting of a <strong>Rasterizer</strong> and a <strong>Shader</strong>, set up an optimization loop including a <strong>Model</strong> and a <strong>loss function</strong>, and run the optimization.</p>
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