NeRF: 3D Scene Reconstruction

The NeRF implementation consists of several key components:

Ray Generation computes camera rays for each pixel in an image by transforming pixel coordinates from image space to world coordinates using camera intrinsics and extrinsics. Each ray represents a line of sight from the camera center through a pixel, defining the path along which 3D points will be sampled.

Stratified Sampling implements hierarchical sampling along each ray to efficiently query 3D points. Points are sampled uniformly between near and far planes, creating a set of 3D coordinates that will be evaluated by the neural network. This sampling strategy is crucial for capturing both fine details and overall scene structure.

NeRF Network Architecture implements the core NeRF neural network, a multi-layer perceptron (MLP) that takes positionally encoded 3D coordinates and viewing directions as input. The network outputs volume density (σ), a scalar value representing the opacity at each 3D point, and RGB color, the color emitted from each point in a specific viewing direction. The architecture uses positional encoding to help the network learn high-frequency details, and includes skip connections to preserve fine geometric features.

Positional Encoding applies sinusoidal encoding to both 3D coordinates and viewing directions, enabling the network to represent high-frequency variations in geometry and appearance. This encoding is essential for NeRF's ability to capture fine details.

Volumetric Rendering implements the differentiable volume rendering equation that composites sampled points along each ray into a final pixel color. This process computes transmittance and alpha values for each sample, applies alpha compositing to blend colors along the ray, and produces photorealistic images that respect the learned 3D geometry.

End-to-End Training Pipeline combines all components into a complete forward pass that generates rays for a given camera pose, samples 3D points along rays, processes points through the NeRF network in batches, and renders the final image using volumetric rendering. The model is trained by minimizing the mean-squared error between rendered images and ground truth images from multiple viewpoints, enabling the network to learn a coherent 3D representation of the scene.

• Ray Generation: Transforms pixel coordinates to world coordinates using camera intrinsics and extrinsics
• Stratified Sampling: Implements hierarchical sampling along rays for efficient 3D point querying
• NeRF Network Architecture: Multi-layer perceptron with positional encoding for volume density and RGB color prediction
• Positional Encoding: Sinusoidal encoding for high-frequency detail representation in geometry and appearance
• Volumetric Rendering: Differentiable volume rendering equation for photorealistic image synthesis
• End-to-End Training: Complete pipeline trained to minimize MSE between rendered and ground truth images from multiple viewpoints