update for version 0.5.0

2025-12-22 15:20:34 +08:00 · 2021-08-10 07:51:01 -07:00
parent 13e2fd2b5b
commit 3ccabda50d
65 changed files with 1660 additions and 1150 deletions
--- a/tutorials/render_densepose/index.html
+++ b/tutorials/render_densepose/index.html
@@ -1,4 +1,4 @@
-<!DOCTYPE html><html lang=""><head><meta charSet="utf-8"/><meta http-equiv="X-UA-Compatible" content="IE=edge"/><title>PyTorch3D · A library for deep learning with 3D data</title><meta name="viewport" content="width=device-width"/><meta name="generator" content="Docusaurus"/><meta name="description" content="A library for deep learning with 3D data"/><meta property="og:title" content="PyTorch3D · A library for deep learning with 3D data"/><meta property="og:type" content="website"/><meta property="og:url" content="https://pytorch3d.org/"/><meta property="og:description" content="A library for deep learning with 3D data"/><meta property="og:image" content="https://pytorch3d.org/img/pytorch3dlogoicon.svg"/><meta name="twitter:card" content="summary"/><meta name="twitter:image" content="https://pytorch3d.org/img/pytorch3dlogoicon.svg"/><link rel="shortcut icon" href="/img/pytorch3dfavicon.png"/><link rel="stylesheet" href="//cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/default.min.css"/><script>
+<!DOCTYPE html><html lang=""><head><meta charSet="utf-8"/><meta http-equiv="X-UA-Compatible" content="IE=edge"/><title>PyTorch3D · A library for deep learning with 3D data</title><meta name="viewport" content="width=device-width, initial-scale=1.0"/><meta name="generator" content="Docusaurus"/><meta name="description" content="A library for deep learning with 3D data"/><meta property="og:title" content="PyTorch3D · A library for deep learning with 3D data"/><meta property="og:type" content="website"/><meta property="og:url" content="https://pytorch3d.org/"/><meta property="og:description" content="A library for deep learning with 3D data"/><meta property="og:image" content="https://pytorch3d.org/img/pytorch3dlogoicon.svg"/><meta name="twitter:card" content="summary"/><meta name="twitter:image" content="https://pytorch3d.org/img/pytorch3dlogoicon.svg"/><link rel="shortcut icon" href="/img/pytorch3dfavicon.png"/><link rel="stylesheet" href="//cdnjs.cloudflare.com/ajax/libs/highlight.js/9.12.0/styles/default.min.css"/><script>
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@@ -82,7 +82,8 @@
 </div>
 </div>
 <div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
-</div><div class="inner_cell">
+</div>
+<div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
 <h1 id="Render-DensePose">Render DensePose<a class="anchor-link" href="#Render-DensePose">¶</a></h1><p>DensePose refers to dense human pose representation: <a href="https://github.com/facebookresearch/DensePose">https://github.com/facebookresearch/DensePose</a>. 
 In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p>
@@ -97,16 +98,18 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
 </div>
 </div>
 <div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
-</div><div class="inner_cell">
+</div>
+<div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
 <h2 id="Import-modules">Import modules<a class="anchor-link" href="#Import-modules">¶</a></h2>
 </div>
 </div>
 </div>
 <div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
-</div><div class="inner_cell">
+</div>
+<div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
-<p>If torch, torchvision and PyTorch3D are not installed, run the following cell:</p>
+<p>Ensure <code>torch</code> and <code>torchvision</code> are installed. If <code>pytorch3d</code> is not installed, install it using the following cell:</p>
 </div>
 </div>
 </div>
@@ -115,19 +118,25 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
 <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>pip install torch torchvision
-<span class="kn">import</span> <span class="nn">os</span>
+<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">sys</span>
 <span class="kn">import</span> <span class="nn">torch</span>
-<span class="k">if</span> <span class="n">torch</span><span class="o">.</span><span class="n">__version__</span><span class="o">==</span><span class="s1">'1.6.0+cu101'</span> <span class="ow">and</span> <span class="n">sys</span><span class="o">.</span><span class="n">platform</span><span class="o">.</span><span class="n">startswith</span><span class="p">(</span><span class="s1">'linux'</span><span class="p">):</span>
-    <span class="o">!</span>pip install pytorch3d
-<span class="k">else</span><span class="p">:</span>
-    <span class="n">need_pytorch3d</span><span class="o">=</span><span class="kc">False</span>
-    <span class="k">try</span><span class="p">:</span>
-        <span class="kn">import</span> <span class="nn">pytorch3d</span>
-    <span class="k">except</span> <span class="n">ModuleNotFoundError</span><span class="p">:</span>
-        <span class="n">need_pytorch3d</span><span class="o">=</span><span class="kc">True</span>
-    <span class="k">if</span> <span class="n">need_pytorch3d</span><span class="p">:</span>
+<span class="n">need_pytorch3d</span><span class="o">=</span><span class="kc">False</span>
+<span class="k">try</span><span class="p">:</span>
+    <span class="kn">import</span> <span class="nn">pytorch3d</span>
+<span class="k">except</span> <span class="ne">ModuleNotFoundError</span><span class="p">:</span>
+    <span class="n">need_pytorch3d</span><span class="o">=</span><span class="kc">True</span>
+<span class="k">if</span> <span class="n">need_pytorch3d</span><span class="p">:</span>
+    <span class="k">if</span> <span class="n">torch</span><span class="o">.</span><span class="n">__version__</span><span class="o">.</span><span class="n">startswith</span><span class="p">(</span><span class="s2">"1.9"</span><span class="p">)</span> <span class="ow">and</span> <span class="n">sys</span><span class="o">.</span><span class="n">platform</span><span class="o">.</span><span class="n">startswith</span><span class="p">(</span><span class="s2">"linux"</span><span class="p">):</span>
+        <span class="c1"># We try to install PyTorch3D via a released wheel.</span>
+        <span class="n">version_str</span><span class="o">=</span><span class="s2">""</span><span class="o">.</span><span class="n">join</span><span class="p">([</span>
+            <span class="sa">f</span><span class="s2">"py3</span><span class="si">{</span><span class="n">sys</span><span class="o">.</span><span class="n">version_info</span><span class="o">.</span><span class="n">minor</span><span class="si">}</span><span class="s2">_cu"</span><span class="p">,</span>
+            <span class="n">torch</span><span class="o">.</span><span class="n">version</span><span class="o">.</span><span class="n">cuda</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s2">"."</span><span class="p">,</span><span class="s2">""</span><span class="p">),</span>
+            <span class="sa">f</span><span class="s2">"_pyt</span><span class="si">{</span><span class="n">torch</span><span class="o">.</span><span class="n">__version__</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">5</span><span class="p">:</span><span class="mi">2</span><span class="p">]</span><span class="si">}</span><span class="s2">"</span>
+        <span class="p">])</span>
+        <span class="o">!</span>pip install pytorch3d -f https://dl.fbaipublicfiles.com/pytorch3d/packaging/wheels/<span class="o">{</span>version_str<span class="o">}</span>/download.html
+    <span class="k">else</span><span class="p">:</span>
+        <span class="c1"># We try to install PyTorch3D from source.</span>
        <span class="o">!</span>curl -LO https://github.com/NVIDIA/cub/archive/1.10.0.tar.gz
        <span class="o">!</span>tar xzf <span class="m">1</span>.10.0.tar.gz
        <span class="n">os</span><span class="o">.</span><span class="n">environ</span><span class="p">[</span><span class="s2">"CUB_HOME"</span><span class="p">]</span> <span class="o">=</span> <span class="n">os</span><span class="o">.</span><span class="n">getcwd</span><span class="p">()</span> <span class="o">+</span> <span class="s2">"/cub-1.10.0"</span>
@@ -157,17 +166,16 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
 <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">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
-<span class="kn">from</span> <span class="nn">skimage.io</span> <span class="k">import</span> <span class="n">imread</span>
 <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>

 <span class="c1"># libraries for reading data from files</span>
-<span class="kn">from</span> <span class="nn">scipy.io</span> <span class="k">import</span> <span class="n">loadmat</span>
-<span class="kn">from</span> <span class="nn">pytorch3d.io.utils</span> <span class="k">import</span> <span class="n">_read_image</span>
+<span class="kn">from</span> <span class="nn">scipy.io</span> <span class="kn">import</span> <span class="n">loadmat</span>
+<span class="kn">from</span> <span class="nn">PIL</span> <span class="kn">import</span> <span class="n">Image</span>
 <span class="kn">import</span> <span class="nn">pickle</span>

 <span class="c1"># Data structures and functions for rendering</span>
-<span class="kn">from</span> <span class="nn">pytorch3d.structures</span> <span class="k">import</span> <span class="n">Meshes</span>
-<span class="kn">from</span> <span class="nn">pytorch3d.renderer</span> <span class="k">import</span> <span class="p">(</span>
+<span class="kn">from</span> <span class="nn">pytorch3d.structures</span> <span class="kn">import</span> <span class="n">Meshes</span>
+<span class="kn">from</span> <span class="nn">pytorch3d.renderer</span> <span class="kn">import</span> <span class="p">(</span>
    <span class="n">look_at_view_transform</span><span class="p">,</span>
    <span class="n">FoVPerspectiveCameras</span><span class="p">,</span> 
    <span class="n">PointLights</span><span class="p">,</span> 
@@ -190,7 +198,8 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
 </div>
 </div>
 <div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
-</div><div class="inner_cell">
+</div>
+<div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
 <h2 id="Load-the-SMPL-model">Load the SMPL model<a class="anchor-link" href="#Load-the-SMPL-model">¶</a></h2><h4 id="Download-the-SMPL-model">Download the SMPL model<a class="anchor-link" href="#Download-the-SMPL-model">¶</a></h4><ul>
 <li>Go to <a href="http://smpl.is.tue.mpg.de/downloads">http://smpl.is.tue.mpg.de/downloads</a> and sign up.</li>
@@ -222,7 +231,8 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
 </div>
 </div>
 <div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
-</div><div class="inner_cell">
+</div>
+<div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
 <p>Load our texture UV data and our SMPL data, with some processing to correct data values and format.</p>
 </div>
@@ -253,13 +263,15 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
    <span class="n">data</span> <span class="o">=</span> <span class="n">pickle</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">encoding</span><span class="o">=</span><span class="s1">'latin1'</span><span class="p">)</span> 
    <span class="n">v_template</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="s1">'v_template'</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"># (6890, 3)</span>
 <span class="n">ALP_UV</span> <span class="o">=</span> <span class="n">loadmat</span><span class="p">(</span><span class="n">data_filename</span><span class="p">)</span>
-<span class="n">tex</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">_read_image</span><span class="p">(</span><span class="n">file_name</span><span class="o">=</span><span class="n">tex_filename</span><span class="p">,</span> <span class="nb">format</span><span class="o">=</span><span class="s1">'RGB'</span><span class="p">)</span> <span class="o">/</span> <span class="mf">255.</span> <span class="p">)</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="mi">0</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="k">with</span> <span class="n">Image</span><span class="o">.</span><span class="n">open</span><span class="p">(</span><span class="n">tex_filename</span><span class="p">)</span> <span class="k">as</span> <span class="n">image</span><span class="p">:</span>
+    <span class="n">np_image</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">image</span><span class="o">.</span><span class="n">convert</span><span class="p">(</span><span class="s2">"RGB"</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="n">tex</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">np_image</span> <span class="o">/</span> <span class="mf">255.</span><span class="p">)[</span><span class="kc">None</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="n">verts</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">ALP_UV</span><span class="p">[</span><span class="s2">"All_vertices"</span><span class="p">])</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">int</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">to</span><span class="p">(</span><span class="n">device</span><span class="p">)</span> <span class="c1"># (7829, 1)</span>
+<span class="n">verts</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">ALP_UV</span><span class="p">[</span><span class="s2">"All_vertices"</span><span class="p">])</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">int</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">to</span><span class="p">(</span><span class="n">device</span><span class="p">)</span> <span class="c1"># (7829,)</span>
 <span class="n">U</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">(</span><span class="n">ALP_UV</span><span class="p">[</span><span class="s1">'All_U_norm'</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"># (7829, 1)</span>
 <span class="n">V</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">(</span><span class="n">ALP_UV</span><span class="p">[</span><span class="s1">'All_V_norm'</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"># (7829, 1)</span>
 <span class="n">faces</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">ALP_UV</span><span class="p">[</span><span class="s1">'All_Faces'</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="nb">int</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"># (13774, 3)</span>
-<span class="n">face_indices</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">(</span><span class="n">ALP_UV</span><span class="p">[</span><span class="s1">'All_FaceIndices'</span><span class="p">])</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span>
+<span class="n">face_indices</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">Tensor</span><span class="p">(</span><span class="n">ALP_UV</span><span class="p">[</span><span class="s1">'All_FaceIndices'</span><span class="p">])</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span>  <span class="c1"># (13774,)</span>
 </pre></div>
 </div>
 </div>
@@ -273,7 +285,6 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
 <div class="highlight hl-ipython3"><pre><span></span><span class="c1"># Display the texture image</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">imshow</span><span class="p">(</span><span class="n">tex</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">cpu</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>
 </pre></div>
 </div>
@@ -281,7 +292,8 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
 </div>
 </div>
 <div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
-</div><div class="inner_cell">
+</div>
+<div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
 <p>In DensePose, the body mesh is split into 24 parts. In the texture image, we can see the 24 parts are separated out into individual (200, 200) images per body part.  The convention in DensePose is that each face in the mesh is associated with a body part (given by the face_indices tensor above). The vertex UV values (in the range [0, 1]) for each face are specific to the (200, 200) size texture map for the part of the body that the mesh face corresponds to. We cannot use them directly with the entire texture map. We have to offset the vertex UV values depending on what body part the associated face corresponds to.</p>
 </div>
@@ -301,6 +313,9 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
        <span class="n">part</span> <span class="o">=</span> <span class="n">rows</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="n">j</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># parts are 1-indexed in face_indices</span>
        <span class="n">offset_per_part</span><span class="p">[</span><span class="n">part</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span>

+<span class="n">U_norm</span> <span class="o">=</span> <span class="n">U</span><span class="o">.</span><span class="n">clone</span><span class="p">()</span>
+<span class="n">V_norm</span> <span class="o">=</span> <span class="n">V</span><span class="o">.</span><span class="n">clone</span><span class="p">()</span>
+
 <span class="c1"># iterate over faces and offset the corresponding vertex u and v values</span>
 <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">faces</span><span class="p">)):</span>
    <span class="n">face_vert_idxs</span> <span class="o">=</span> <span class="n">faces</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
@@ -311,15 +326,15 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
        <span class="c1"># vertices are reused, but we don't want to offset multiple times</span>
        <span class="k">if</span> <span class="n">vert_idx</span><span class="o">.</span><span class="n">item</span><span class="p">()</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">already_offset</span><span class="p">:</span>
            <span class="c1"># offset u value</span>
-            <span class="n">U</span><span class="p">[</span><span class="n">vert_idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">U</span><span class="p">[</span><span class="n">vert_idx</span><span class="p">]</span> <span class="o">/</span> <span class="n">cols</span> <span class="o">+</span> <span class="n">offset_u</span>
+            <span class="n">U_norm</span><span class="p">[</span><span class="n">vert_idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">U</span><span class="p">[</span><span class="n">vert_idx</span><span class="p">]</span> <span class="o">/</span> <span class="n">cols</span> <span class="o">+</span> <span class="n">offset_u</span>
            <span class="c1"># offset v value</span>
            <span class="c1"># this also flips each part locally, as each part is upside down</span>
-            <span class="n">V</span><span class="p">[</span><span class="n">vert_idx</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">V</span><span class="p">[</span><span class="n">vert_idx</span><span class="p">])</span> <span class="o">/</span> <span class="n">rows</span> <span class="o">+</span> <span class="n">offset_v</span>
+            <span class="n">V_norm</span><span class="p">[</span><span class="n">vert_idx</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">V</span><span class="p">[</span><span class="n">vert_idx</span><span class="p">])</span> <span class="o">/</span> <span class="n">rows</span> <span class="o">+</span> <span class="n">offset_v</span>
            <span class="c1"># add vertex to our set tracking offsetted vertices</span>
            <span class="n">already_offset</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">vert_idx</span><span class="o">.</span><span class="n">item</span><span class="p">())</span>

 <span class="c1"># invert V values</span>
-<span class="n">U_norm</span><span class="p">,</span> <span class="n">V_norm</span> <span class="o">=</span> <span class="n">U</span><span class="p">,</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">V</span>
+<span class="n">V_norm</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">V_norm</span>
 </pre></div>
 </div>
 </div>
@@ -338,20 +353,18 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
 <span class="c1"># Therefore when initializing the Meshes class,</span>
 <span class="c1"># we need to map each of the vertices referenced by the DensePose faces (in verts, which is the "All_vertices" field)</span>
 <span class="c1"># to the correct xyz coordinate in the SMPL template mesh.</span>
-<span class="n">v_template_extended</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">stack</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">vert</span><span class="p">:</span> <span class="n">v_template</span><span class="p">[</span><span class="n">vert</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">verts</span><span class="p">)))</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="mi">0</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"># (1, 7829, 3)</span>
-
-<span class="c1"># add a batch dimension to faces</span>
-<span class="n">faces</span> <span class="o">=</span> <span class="n">faces</span><span class="o">.</span><span class="n">unsqueeze</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<span class="n">v_template_extended</span> <span class="o">=</span> <span class="n">v_template</span><span class="p">[</span><span class="n">verts</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="kc">None</span><span class="p">]</span> <span class="c1"># (1, 7829, 3)</span>
 </pre></div>
 </div>
 </div>
 </div>
 </div>
 <div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
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+</div>
+<div class="inner_cell">
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 <h3 id="Create-our-textured-mesh">Create our textured mesh<a class="anchor-link" href="#Create-our-textured-mesh">¶</a></h3><p><strong>Meshes</strong> is a unique datastructure provided in PyTorch3D for working with batches of meshes of different sizes.</p>
-<p><strong>TexturesUV</strong> is an auxillary datastructure for storing vertex uv and texture maps for meshes.</p>
+<p><strong>TexturesUV</strong> is an auxiliary datastructure for storing vertex uv and texture maps for meshes.</p>
 </div>
 </div>
 </div>
@@ -360,15 +373,16 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
 <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="n">texture</span> <span class="o">=</span> <span class="n">TexturesUV</span><span class="p">(</span><span class="n">maps</span><span class="o">=</span><span class="n">tex</span><span class="p">,</span> <span class="n">faces_uvs</span><span class="o">=</span><span class="n">faces</span><span class="p">,</span> <span class="n">verts_uvs</span><span class="o">=</span><span class="n">verts_uv</span><span class="p">)</span>
-<span class="n">mesh</span> <span class="o">=</span> <span class="n">Meshes</span><span class="p">(</span><span class="n">v_template_extended</span><span class="p">,</span> <span class="n">faces</span><span class="p">,</span> <span class="n">texture</span><span class="p">)</span>
+<div class="highlight hl-ipython3"><pre><span></span><span class="n">texture</span> <span class="o">=</span> <span class="n">TexturesUV</span><span class="p">(</span><span class="n">maps</span><span class="o">=</span><span class="n">tex</span><span class="p">,</span> <span class="n">faces_uvs</span><span class="o">=</span><span class="n">faces</span><span class="p">[</span><span class="kc">None</span><span class="p">],</span> <span class="n">verts_uvs</span><span class="o">=</span><span class="n">verts_uv</span><span class="p">)</span>
+<span class="n">mesh</span> <span class="o">=</span> <span class="n">Meshes</span><span class="p">(</span><span class="n">v_template_extended</span><span class="p">,</span> <span class="n">faces</span><span class="p">[</span><span class="kc">None</span><span class="p">],</span> <span class="n">texture</span><span class="p">)</span>
 </pre></div>
 </div>
 </div>
 </div>
 </div>
 <div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
-</div><div class="inner_cell">
+</div>
+<div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
 <h2 id="Create-a-renderer">Create a renderer<a class="anchor-link" href="#Create-a-renderer">¶</a></h2>
 </div>
@@ -396,7 +410,7 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
 <span class="c1"># Place a point light in front of the person. </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">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">]])</span>

-<span class="c1"># Create a phong renderer by composing a rasterizer and a shader. The textured phong shader will </span>
+<span class="c1"># Create a Phong renderer by composing a rasterizer and a shader. The textured Phong shader will </span>
 <span class="c1"># interpolate the texture uv coordinates for each vertex, sample from a texture image and </span>
 <span class="c1"># apply the Phong lighting model</span>
 <span class="n">renderer</span> <span class="o">=</span> <span class="n">MeshRenderer</span><span class="p">(</span>
@@ -416,7 +430,8 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
 </div>
 </div>
 <div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
-</div><div class="inner_cell">
+</div>
+<div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
 <p>Render the textured mesh we created from the SMPL model and texture map.</p>
 </div>
@@ -430,7 +445,6 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
 <div class="highlight hl-ipython3"><pre><span></span><span class="n">images</span> <span class="o">=</span> <span class="n">renderer</span><span class="p">(</span><span class="n">mesh</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">imshow</span><span class="p">(</span><span class="n">images</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">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">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>
 </pre></div>
 </div>
@@ -438,7 +452,8 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
 </div>
 </div>
 <div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
-</div><div class="inner_cell">
+</div>
+<div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
 <h3 id="Different-view-and-lighting-of-the-body">Different view and lighting of the body<a class="anchor-link" href="#Different-view-and-lighting-of-the-body">¶</a></h3><p>We can also change many other settings in the rendering pipeline. Here we:</p>
 <ul>
@@ -474,7 +489,6 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
 <div class="input_area">
 <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">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">images</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">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">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>
 </pre></div>
 </div>
@@ -482,10 +496,11 @@ In this tutorial, we provide an example of using DensePose data in PyTorch3D.</p
 </div>
 </div>
 <div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
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+<div class="inner_cell">
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 <h2 id="Conclusion">Conclusion<a class="anchor-link" href="#Conclusion">¶</a></h2><p>In this tutorial, we've learned how to construct a <strong>textured mesh</strong> from <strong>DensePose model and uv data</strong>, as well as initialize a <strong>Renderer</strong> and change the viewing angle and lighting of our rendered mesh.</p>
 </div>
 </div>
 </div>
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