Why XCR and SD-Retinex work

A review site that checks, from ten perspectives and with derivations and reproducible experiments, why my low-light enhancement methods XCR and SD-Retinex work although they look as if they should not.

Looked at closely, XCR and SD-Retinex brighten images in a way that “should not normally work”: XCR estimates illumination with a kernel that gives the centre the least weight and has poles, and SD-Retinex divides by 60 % of a 3.6-pixel “illumination” computed on gamma-encoded values. This review checks why they work anyway, from ten perspectives: kernel mathematics, Retinex theory, tone mapping, noise, colour, numerical precision, cost, prior art, failure modes and novelty.

Findings

On dark images XCR effectively does not use its kernel. Its gain is capped at 1.5, so the output nearly equals a single tone curve, min(1.5c, 1)^0.8.
Nearly all of SD-Retinex’s brightening comes from a Naka–Rushton-type tone curve. Removing its kernel and noise gate barely changes the scores.
XCR’s main lobe jumps following rational approximations of π (3, 19/6, 22/7, 333/106, 355/113): a mathematically delightful property, but not the reason for the image quality.

What is published

Site (Japanese and English): toma-okugawa.github.io/retinex-why-it-works, with interactive kernel and tone-curve figures and an in-browser lab
Code: GitHub. One command regenerates every figure and number (CPU only, synthetic images only)
License: code under MIT; text and figures under CC BY 4.0