pytorch3d-image.tar.gz

pytorch3d

intro-to-3d-deep-learning

camera-parameters

transformations

differentiable-rendering

barycentric-coordinates

learn-texture

mesh-deformation

With the surge in XR, 3D printing, and the Metaverse, 3D is extremely popular. Likewise, investment in AI is growing exponentially in most industrial sectors. PyTorch3D is the leading machine learning framework that bridges the gap between AI and 3D. It is essential for tools that generate 3D models from single images and 3D rooms from text prompts. 

After an introduction to PyTorch3D, you’ll learn how 2D images are formed from a 3D world, covering camera parameters, projection models, etc. Next, you’ll explore the rendering pipeline and how 3D data is used to generate images. You’ll explore the differences between 3D formats, and look at machine learning methods such as heterogeneous batching, graph convolution, etc. Lastly, you’ll learn foundational models of 3D machine learning—PointNet, Mesh R-CNN, and Neural Radiance Fields.

By the time you’re done, you’ll have a solid understanding of 3D concepts, how to process various types of 3D data with PyTorch, and how to build 3D machine learning systems.

3D Machine Learning with PyTorch3D

Given an object distance of $200$ and focal length of $40$, what is the image distance?

Given an object distance of <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>200</mn></mrow><annotation encoding="application/x-tex">200</annotation></semantics></math>200 and focal length of <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>40</mn></mrow><annotation encoding="application/x-tex">40</annotation></semantics></math>40, what is the image distance?

**(True or False)** The following two sets of homogeneous coordinates are equivalent:

1. $(2, 0, -2, 2)$

2. $(4, 0, -4, 4)$

(True or False) The following two sets of homogeneous coordinates are equivalent:
<ol>
<li>
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>2</mn><mo separator="true">,</mo><mn>0</mn><mo separator="true">,</mo><mo>−</mo><mn>2</mn><mo separator="true">,</mo><mn>2</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(2, 0, -2, 2)</annotation></semantics></math>(2,0,−2,2)
</li>
<li>
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>4</mn><mo separator="true">,</mo><mn>0</mn><mo separator="true">,</mo><mo>−</mo><mn>4</mn><mo separator="true">,</mo><mn>4</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(4, 0, -4, 4)</annotation></semantics></math>(4,0,−4,4)
</li>
</ol>

A rotation of $\pi/4$ along the $x$ axis and a translation of $-1$ along the $x$, $y$, and $z$ axes.

A rotation of $\pi/4$ along the $z$ axis, a scaling of $2$ along the $x$ axis, and a translation of $-1$ along the $x$, $y$, and $z$ axes.

A translation of $2$ along the $x$ axis, a rotation of $\pi/4$ along the $x$ axis, and a scaling of $-1$ along the $x$, $y$, and $z$ axes.

A rotation of $\pi/4$ along the $z$ axis, a scaling of $2$ along the $z$ axis, and an inversion along the $x$, $y$, and $z$ axes.

Which statement describes the following transformation matrix $K$?

$\begin{bmatrix}2\cos(\pi/4) & -\sin(\pi/4) & 0 & 0\\\sin(\pi/4) & \cos(\pi/4) & 0 & 0\\0 & 0 & 1 & 0\\-1 & -1 & -1 & 1\end{bmatrix}$

Which statement describes the following transformation matrix <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>K</mi></mrow><annotation encoding="application/x-tex">K</annotation></semantics></math>K?
<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">[</mo><mtable rowspacing="0.16em" columnalign="center center center center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mn>2</mn><mi>cos</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>π</mi><mi mathvariant="normal">/</mi><mn>4</mn><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mi>sin</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>π</mi><mi mathvariant="normal">/</mi><mn>4</mn><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>sin</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>π</mi><mi mathvariant="normal">/</mi><mn>4</mn><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>cos</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>π</mi><mi mathvariant="normal">/</mi><mn>4</mn><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>0</mn></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mn>1</mn></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mn>1</mn></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>−</mo><mn>1</mn></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mn>1</mn></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><annotation encoding="application/x-tex">\begin{bmatrix}2\cos(\pi/4) &amp; -\sin(\pi/4) &amp; 0 &amp; 0\\\sin(\pi/4) &amp; \cos(\pi/4) &amp; 0 &amp; 0\\0 &amp; 0 &amp; 1 &amp; 0\\-1 &amp; -1 &amp; -1 &amp; 1\end{bmatrix}</annotation></semantics></math>⎣<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='1.216em' style='width:0.6667em' viewBox='0 0 666.67 1216' preserveAspectRatio='xMinYMin'><path d='M319 0 H403 V1216 H319z M319 0 H403 V1216 H319z'/></svg>⎡​2cos(π/4)sin(π/4)0−1​−sin(π/4)cos(π/4)0−1​001−1​0001​⎦<svg xmlns="http://www.w3.org/2000/svg" width='0.6667em' height='1.216em' style='width:0.6667em' viewBox='0 0 666.67 1216' preserveAspectRatio='xMinYMin'><path d='M263 0 H347 V1216 H263z M263 0 H347 V1216 H263z'/></svg>⎤​

**(True or False)** Rotations can be expressed in axis angle form, as quaternions, or as Lie group transforms.

(True or False) Rotations can be expressed in axis angle form, as quaternions, or as Lie group transforms.

The `transform_points_screen` function converts between which two coordinate spaces?

The <code>transform_points_screen</code> function converts between which two coordinate spaces?

Quiz

Quiz

Test your knowledge of cameras and projection.

Getting Started

Cameras and Projection

Rendering

Data Representations

Operations and Techniques

Key Models

Final Assessment

Conclusion

Appendix

Quiz Yourself on Cameras and Projections