[FLF] Fourier Light Fields Implementation

[CalebisGross]

Fourier Light Fields (FLF)

Priority: ⭐ Medium (Tier 2)
Documentation: 02_fourier_light_fields.md

Overview

Represent 4D light fields in their natural Fourier basis. Rendering becomes a 2D inverse FFT - extremely fast and physically grounded.

Key Innovation

Light field: L(x, y, θ, φ) = Σ_k Σ_{l,m} c_{k,l,m} · exp(2πik·[x,y]) · Y_l^m(θ,φ)
Rendering:   I(x,y) = IFFT2(Σ_{l,m} c_{*,l,m} · Y_l^m(θ₀,φ₀))

Predict Fourier coefficients + spherical harmonics; view synthesis is just inverse FFT.

Implementation Phases

Phase 1: Basic FLF (2-3 days)

• Spherical harmonic computation (up to L=16)
• Coefficient predictor network
• 2D IFFT rendering
• Train on synthetic data with known views

Phase 2: Optimization (2-3 days)

• Sparse coefficient prediction
• Factorized representation
• GPU-optimized SH computation
• cuFFT integration

Phase 3: Quality (ongoing)

• Layered light fields for depth
• Adaptive frequency allocation
• Specular handling with high-L
• Real-world dataset training

Technical Details

Coefficients: K² × (L+1)² × 3 × 2 = 64² × 17² × 6 ≈ 7M params
Rendering: ~50 MFLOPS per view (<1ms after encoding)
Speedup: 200× faster than NeRF

Key Equations

Light field: L(x,y,θ,φ) = Σ_k Σ_{l,m} c_{k,l,m} · φ_k(x,y) · Y_l^m(θ,φ)
View synthesis: I(x,y;θ₀,φ₀) = IFFT2(Σ_{l,m} c_{*,l,m} · Y_l^m(θ₀,φ₀))
Natural prior: E[|c_k|²] ∝ |k|^{-α} where α ≈ 2-3

References

• Levoy & Hanrahan (1996): Light Field Rendering
• Ramamoorthi & Hanrahan (2001): Irradiance Environment Maps
• Sitzmann et al. (2021): Light Field Networks

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Parent: #6