The End Of Knowledge - Vault 5/49 - CVPR - 2019 - DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation

graph LR classDef deepsdf fill:#f9d4d4, font-weight:bold, font-size:14px classDef representation fill:#d4f9d4, font-weight:bold, font-size:14px classDef performance fill:#d4d4f9, font-weight:bold, font-size:14px classDef applications fill:#f9f9d4, font-weight:bold, font-size:14px classDef related fill:#f9d4f9, font-weight:bold, font-size:14px A[DeepSDF: Learning Continuous
Signed Distance Functions
for Shape Representation] --> B[DeepSDF: regresses SDFs
with NNs. 1] A --> C[Deconvolutional nets: grow
for voxels. 2] A --> D[Point clouds: compact,
no surfaces. 3] A --> E[Triangle meshes: unknown
vertices, topologies. 4] A --> F[SDF: volumetric field,
distance to surface. 5] B --> G[FC NN: XYZ in,
SDF out. 6] B --> H[Latent code Z:
encodes shape. 7] B --> I[Autodecoder: learns space
sans encoder. 8] I --> J[Training: random code
per shape, SDFs. 9] I --> K[Latent space: obtained
post-training. 10] B --> L[Inference: optimal code
via gradient descent. 11] L --> M[Arbitrary SDF samples:
e.g. depth map. 12] L --> N[Visualization: code matches
depth observation. 13] B --> O[Rendering: ray casting,
gradient normals. 14] B --> P[Marching cubes: mesh
from SDF. 15] B --> Q[Performance: outperforms voxels,
meshes. 16] Q --> R[Network size: 100x
smaller than octrees. 17] Q --> S[Expressive power: exceeds
mesh SOTAs. 18] B --> T[Shape completion: optimal
from depth map. 19] A --> U[Related CVPR works:
for reference. 20] class A,B deepsdf class C,D,E,F representation class G,H,I,J,K,L,M,N,O,P,Q,R,S performance class T applications class U related

Resume:

1.- DeepSDF: Directly regresses continuous signed distance functions using neural networks for efficient and expressive shape representation.

2.- Deconvolutional networks: Commonly used for image-based approaches but grow quickly in space and time when applied to voxels.

3.- Point clouds: More compact representations than voxels but do not describe surfaces.

4.- Triangle meshes: Have unknown number of vertices and topologies.

5.- Signed distance function (SDF): Volumetric field where magnitude is distance to closest surface and sign indicates inside/outside. Shape is zero level set.

6.- Fully connected neural network: Takes XYZ coordinate as input and outputs predicted SDF value.

7.- Latent code (Z): Encodes shape information interpreted by decoder network. Conditioned on Z to model dataset of shapes.

8.- Autodecoder: Learning scheme to obtain meaningful latent space without encoder. Codes and decoder weights jointly optimized.

9.- Training: Random code initialized per shape, attached to XYZ input. Optimized with decoder weights given ground truth SDFs.

10.- Latent space of shapes: Obtained after training autodecoder.

11.- Inference: Optimal code found via gradient descent to best explain input shape. Decoder weights frozen.

12.- Arbitrary SDF samples: Autodecoder allows inference on any number of samples, e.g. from single depth map.

13.- Visualization of inference: Optimization finds best code matching depth map observation.

14.- Rendering: Ray casting to zero crossing for depth map. Surface normals via backpropagation gradients.

15.- Marching cubes: Algorithm to extract mesh from SDF.

16.- Shape representation performance: DeepSDF significantly outperforms previous voxel and mesh-based methods on unseen shapes.

17.- Network size efficiency: 100x smaller than octree voxel methods while providing higher accuracy and surface normals.

18.- Expressive power: Much higher than state-of-the-art mesh-based methods.

19.- Shape completion: Finds optimal high-quality shape given input depth map. Outperforms state-of-the-art.

20.- Related CVPR works: Mentioned for further reference.

Knowledge Vault built byDavid Vivancos 2024