Neural Radiance Fields

Module: Computer Vision | Difficulty: Advanced

NeRF Formulation

Volume Rendering

where .

Positional Encoding

NeRF Loss

import torch
import torch.nn as nn

class NeRF(nn.Module):
    def __init__(self, pos_enc_dim=10, dir_enc_dim=4, hidden=256):
        super().__init__()
        pos_in = pos_enc_dim * 2 * 3 + 3
        dir_in = dir_enc_dim * 2 * 3 + 3
        
        self.pos_mlp = nn.Sequential(
            nn.Linear(pos_in, hidden), nn.ReLU(True),
            nn.Linear(hidden, hidden), nn.ReLU(True),
            nn.Linear(hidden, hidden), nn.ReLU(True),
            nn.Linear(hidden, hidden), nn.ReLU(True),
        )
        self.sigma = nn.Linear(hidden, 1)
        self.color = nn.Sequential(
            nn.Linear(hidden + dir_in, hidden // 2), nn.ReLU(True),
            nn.Linear(hidden // 2, 3), nn.Sigmoid()
        )
    
    def forward(self, pos, dir):
        h = self.pos_mlp(pos)
        sigma = self.sigma(h)
        color = self.color(torch.cat([h, dir], dim=-1))
        return color, sigma

def positional_encoding(x, L=10):
    freqs = 2 ** torch.arange(L).float()
    return torch.cat([torch.sin(freqs * x), torch.cos(freqs * x)], dim=-1)

Key Takeaways

• NeRF represents scenes as continuous volumetric radiance fields
• Positional encoding enables learning high-frequency details
• Volume rendering produces photorealistic novel views