16-889 Homework Three

Question 1

Q1.3

Here is the result from my grid calculation.

And here is the result from the ray calculation.

Q1.4

Here is a picture of the sampled points spreading out from the camera. They form this "fan" shape.

Q1.5

Shown here is the depth map for the cube.

And here is the rotating cube.

Question 2

Q2.1

The way I am sampling is by creating a randomized integer tensor using torch.randint(0, n_rays, (n_points, )) and then using it to index into the xy_grid tensor.

Q2.2

I just used the torch.nn.MSELoss() function. The box center after my optimization was: (0.25, 0.25, -0.00). The side length was: (2.00, 1.50, 1.50)

Q2.3

Question 3

The result of my Neural Radiance Field is shown below:

To acheive this result I am using a mean squared error loss function: $$ \mathcal{L} = \sum_{r \in \mathcal{R}} || \hat{L}_r(\mathbf{x}) - L_r(\mathbf{ x }) ||_2^2 $$ where, $\hat{L}$ is the color produced by the network.

Question 4

For this question I decided to train the high-res NeRF model using the nerf_lego_highres.yaml configuration.

We can see that my image is still a bit blurry, which I believe could be due to the fact I'm only using one linear layer before I apply sigmoid and ReLU to the raw data. If I tried to increase the size of my ray samples beyond around 52 for this, I get an out of memory error. Interestingly though, if I use more linear layers with the appropriate number of ray samples, then the quality improves.