16-889 Assignment 4

1. Sphere Tracing (30pts)

First, the points at the nearest distance (self.near) are sampled. Second, if the distances are smaller than threshold, the corresponding points are considered to intersect with the object surface and stored in the points variable. Third, the next points on the rays are sampled based on the distances (e.g., rays = rays + distances * directions). Fourth, iterate the second and third process up to N (self.max_iters) times.

2. Optimizing a Neural SDF (30pts)

3. VolSDF (30 pts)

3.1. Intuitive Explanation of what the parameters alpha and beta are doing

Alpha represents a uniform density on the object surface. Beta is a parameter to specify how blurry (smooth) the dencity nearby the object surface is.

3.2. How does high beta bias your learned SDF? What about low beta?

The high beta will make the learned SDF much more blurry. However, a more smooth gradient is given, and training would be more stable. On the contrary, we expect a highly accurate occupancy map with low beta. However, the training can be unstable due to the more sensitive gradient.

3.3. Would an SDF be easier to train with volume rendering and low beta or high beta? Why?

High beta would make training easier since it gives a smoother gradient.

3.4. Would you be more likely to learn an accurate surface with high beta or low beta? Why?

Low beta (low variance) would give a step function-like CDF that can accurately reconstruct the original surface.

This is the best results where I set the beta to 0.04. The training is really sensitive to beta. For example, when I tried to decrease beta to 0.03, the training did not converge.

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

4.1. Render a Large Scene with Sphere Tracing (10 pts)

4.2 Fewer Training Views (10 pts)

Training with 100 views (Left: VolSDF, Right: NeRF)

Training with 20 views (Left: VolSDF, Right: NeRF)