Assignment 4

Jianchun Chen jianchuc@andrw.cmu.edu

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1. Sphere Tracing (30pts)

This equation implement the sphere tracing iteration from the slides.

for f(p)>eps:
    t = t+f(p)
    p = x_0+t*d

2. Optimizing a Neural SDF (30pts)

The network structure follows the yaml file, where I use a 6 layer MLP with 128 hidden neuron to encode the SDF. Re-running default parameter gives reasonable result, whereas increasing positional encoding frequencies generates discontinuous shape with holes.

3. VolSDF (30 pts)

$\beta$ controls the bandwith of the density i.e. within which distance to the surface a point has a larger density. $\alpha$ controls the scale of the density i.e. how large is the density of the point in the surface.

• How does high beta bias your learned SDF? What about low beta?
  High $\beta$ results in too smooth density function and blurry image and inaccurate geometry. Low $\beta$ generate sharper boundary of density function and image therefore more accurate SDF.

• Would an SDF be easier to train with volume rendering and low beta or high beta? Why?
  High $\beta$ is easier to train and converge but poorly optimized since it is too blurry. Low $\beta$ is harder to train because only points around the boundary has postive density to be optimized.

• Would you be more likely to learn an accurate surface with high beta or low beta? Why?
  Low $\beta$ is more likely to learn accurate shape because only points near the surface has positive densities, which renders images with a sharpe boundary. Then the surface is better optimized.

The first row is the result from default $\alpha=10$ and $\beta=0.05$ and the second row has $\beta=0.5$. We see that larger $\beta$ results in blurry image and inaccurate geometry.

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

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

Here I render 3*7=21 objects including torus, sphere and box.

4.2 Fewer Training Views (10 pts)

The first two gifs are from NeRF and the second gifs are from VolSDF. The left gifs are trained with uniformly sampled 20 images and the right gifs are trained with 100 images.

From the result we can see that sparse view yeild a more difficult training problem. However, with same 20 view, NeRF generates more details than VolSDF.