Parabolic Orientation Sihti
A lossless sieve that splits every octave by direction, under six direction laws. Keep only the strongest coefficients and see what survives: object outlines or texture. The parabolic law narrows the directional window as 2−j/2 at finer scales; ray is the window from OpenAI's local-smoothing proof, exp(−ρ|ξ||ω−ξ̂|²/2), obtained by sliding the wave along an imaginary light ray. Same maths as the Python benchmark in this repo, on luminance.
input (128 px, luminance)
rebuilt from kept coefficients
PSNR – dB ·
kept detail (rebuild − core)
what the budget bought, above the >64 px core
dropped (image − rebuild)
where the leftover went
cross-scale coherence ρ
|b|-weighted local phase agreement between adjacent octaves (octaves 1–5). Bright = edge-like, dark = texture-like.
frequency plane: the direction law
each cell coloured by its dominant band: hue = direction, lightness = octave. Centre = DC.
Benchmark (BSDS500 test, 120-px protocol of Sihti G4)
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