16-889 Assignment 3

Byeongjoo Ahn (bahn@andrew.cmu.edu)

1. Differentiable Volume Rendering

1.3. Ray sampling (10 points)

The visualizations of grid and ray are shown below.

1.4. Point sampling (10 points)

The visualization of point samples is shown below.

1.5. Volume rendering (30 points)

The visualizations of the rendered gif and depth are shown below.

2. Optimizing a basic implicit volume

2.2. Loss and training (5 points)

• Center: (0.25, 0.25, 0.00)

• Side length: (2.01, 1.50, 1.50)

2.3. Visualization

The gif of the optimized volume are shown below.

3. Optimizing a Neural Radiance Field (NeRF) (30 points)

The results of part3 are shown below.

# nerf_lego.yaml
n_harmonic_functions_xyz: 6
n_hidden_neurons_xyz: 128
n_hidden_neurons_dir: 64
density_noise_std: 0.0
n_layers_xyz: 6
append_xyz: [3]

4. NeRF Extras

I chose 4.1 (view dependence) and 4.3 (high resolution imagery).

4.1 View Dependence (10 pts)

The results of adding view dependence and the used parameters are shown below. Compared to the result of part 3, the difference is not huge partly because of the low resolution.

The generalization quality generally becomes worse as the view dependence increases because the network can overfit to the ray direction and thereby the rendering does not satisfy the multi-view consistency and reduces the quality of novel-view rendering. These artifacts are avoided by adding the viewing direction as a feature only for color, not density, as the multi-view consistency is enforced by the density.

# nerf_lego_view.yaml
n_harmonic_functions_xyz: 6
n_harmonic_functions_dir: 2
n_hidden_neurons_xyz: 128
n_hidden_neurons_dir: 64
density_noise_std: 0.0
n_layers_xyz: 6
append_xyz: [3]

4.3 High Resolution Imagery (10 pts)

The results of high resolution imagery and the used parameters are shown below. We can observe more detailed geometry in the high resolution results.

# nerf_lego_highres.yaml
n_harmonic_functions_xyz: 6
n_harmonic_functions_dir: 2
n_hidden_neurons_xyz: 128
n_hidden_neurons_dir: 64
density_noise_std: 0.0
n_layers_xyz: 6
append_xyz: [3]