Neural Rendering I: Neural Radiance Fields (NeRF)

Define an implicit neural representation as a function that maps coordinates to physical properties (e.g., density, color).

Explain the concept of 'spectral bias' in MLPs and why it hinders the learning of high-frequency details.

Describe how positional encoding using Fourier features helps overcome spectral bias.

Derive the classical volumetric rendering equation for synthesizing an image from a ray's samples.

Describe the full NeRF architecture, including coarse/fine networks and hierarchical volume sampling.

Implement positional encoding for 3D coordinates and viewing directions in Python.

Implement the differentiable volume rendering function for a single ray from scratch in Python.

Decompose the original NeRF paper into its core problem, mathematical intuition, and architectural innovations.