DJLougen / kakeya-orientation-encoder

Kakeya-Inspired Orientation Image Encoder

An efficient image encoder that applies geometric measure theory principles from the Kakeya conjecture to preserve directional/orientation information in compact latent representations.

Core Concept

The Kakeya conjecture (proven by Wang & Zahl, 2025) concerns the minimum size of sets containing unit line segments in every direction. The key insight applied here: directional information across all orientations can be captured efficiently with sparse, anisotropic sampling .

Architecture

1. Directional Decomposition — Fast Finite Shearlet Transform (FFST)

   • Anisotropic dilation: A_a = diag(a, √a)
   • Shearing: S_s = [[1, s], [0, 1]]
   • Coefficients indexed by (scale, shear/orientation, position)
   • Optimal for C² curves (parabolic scaling matches edge curvature)

2. Orientation Encoder — CNN on shearlet coefficient tensor

   • Processes (scale, orientation) as channels
   • Dedicated orientation branch aggregates directional energy
   • VAE-style latent space with orientation-preserving features

3. Decoder — Transposed convolutions reconstruct from latent

Installation

pip install torch torchvision numpy scipy
pip install git+https://github.com/grlee77/PyShearlets.git

Note: PyShearlets needs a small fix for NumPy 2.0+ compatibility:

import numpy as np
import FFST._scalesShearsAndSpectra as sss
import FFST.shearletScaleShear as sss2
sss.np.NaN = np.nan
sss2.np.NaN = np.nan

Usage

from kakeya_orientation_encoder import KakeyaAutoencoder, ShearletTransform
import torch

# Create model
model = KakeyaAutoencoder(
    input_channels=1,
    latent_dim=256,
    num_scales=3,
    output_size=128
)

# Encode image → latent representation (with orientation info)
x = torch.randn(1, 1, 128, 128)
z = model.encode(x)  # (1, 256)

# Decode back
x_recon = model.decode(z)

Training

python train_kakeya_encoder_fast.py \
    --dataset mnist \
    --image-size 64 \
    --latent-dim 256 \
    --num-scales 3 \
    --epochs 30 \
    --batch-size 32

References

• ShearletX (Kolek et al., 2023) — shearlet domain explanations
• SAD (Iinbor et al., 2025) — anisotropic spatial representation
• Kakeya Conjecture (Wang & Zahl, 2025) — geometric measure theory

License

MIT