Q1
while f(p)>epsilon:
\ t=t+f(p)
\ p=x0+td
, where x0 is the origins, f is the implicit function, t is the distance and d is the direction.
For each rays, update them with the distance to the closest sphere if they do not reach the sphere (distance bigger than threshold). For those rays that have reached the sphere, I won't update them.
I also set the max iterations. I only interate max iteration times.
Q2
For MLP I followed the last assignment, which is positional encoding (Harmonic Embedding), 6 linear layers with activations and one linear layer without activation.
For activation, I followed the neuS paper to use softplus with beta=100.
For eikonal loss I just calculate the norm of the gradient and calculate its MSE loss with 1.
Q3
The alpha is the constant density of a homogeneous object. The beta controls the smoothing amount of density decreasing near the object’s boundary.
1. High beta makes my result looks blurred. Low beta makes my result looks more accurate.
2. High. Because high beta provide us with a smooth density and it is easy to learn, which will also cause blurred.
3. Low. Because high beta provide us with a sharp density and it is more accurate.
I set alpha=10, beta=0.02. This is the lowest beta I can train the model. And the result is better than default setting because beta is lower.
Q4.2
For 20 images, I connot train VolSDF with beta 0.02. After several experiments, I choose alpha=10, beta=0.05. Here are results from volSDF and Nerf.
VolSDF:
Nerf:
Compared them, especially for the floor, we can see the result from volSDF is more smooth while the edge of nerf result is noisy. This demonstrates the result of volSDF is better regularized. The result from nerf is more sharp.