Assignment 3 : Neural Volume Rendering and Surface Rendering

A. Neural Volume Rendering (80 points)

0. Transmittance Calculation (10 points)

1.3. Ray sampling (5 points)

Ray Bundle

XY Grid

1.4. Point sampling (5 points)

1.5. Volume rendering (20 points)

2. Optimizing a basic implicit volume

2.1. Random ray sampling (5 points)

2.2. Loss and training (5 points)

Estimated box Parametrs:

Center : (0.25,0.25,0)

Side Length : (2,1.5,1.5)

2.3. Visualization

Before Training

After Training

3. Optimizing a Neural Radiance Field (NeRF) (20 points)

B. Neural Surface Rendering (50 points)

5. Sphere Tracing (10 points)

6. Optimizing a Neural SDF (15 points)

7. VolSDF (15 points)

Settings used alpha=10 and beta=0.05

The parameter alpha controls the density scale (opacity), while beta determines the softness of the surface transition. Essentially, beta dictates how sharply the object's boundary is defined in the rendered volume.

1. How does high beta bias your learned SDF? What about low beta? A high beta biases the learned SDF towards making boundaries more diffused whereas a smaller beta makes the boundaries look more sharp.

2. Would an SDF be easier to train with volume rendering and low beta or high beta? Why? Its easier to train on a higher beta as a very small beta makes the mapping almost binary.

3. Would you be more likely to learn an accurate surface with high beta or low beta? Why? A smaller beta yields a more narrow and tight boundary yielding a sharper surface reconstruction.

8. Neural Surface Extras (CHOOSE ONE! More than one is extra credit)

8.2 Fewer Training Views (10 points)

VolSDF

Since VolSDF explicitly learns the underlying 3D structure and NeRF relies on view-dependent appearance, VolSDF maintains clean rendering under few-view conditions while NeRF overfits to limited views, resulting in noticeable artifacts.