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Jeremy Francis Reizenstein
2021-10-06 12:40:17 -07:00
parent a4725d2421
commit 416cd21881
55 changed files with 347 additions and 97 deletions
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tutorials/bundle_adjustment/index.html
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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>
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@@ -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>
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<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>
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