# Beyond Global Shannon Entropy: A Channel-Specific Approach to Quantify Polychromia in Melanoma

## TL;DR

This study introduces a new method to objectively measure color diversity in melanoma using smartphone photos, improving on traditional methods that may miss true color complexity.

## Contribution

The paper proposes channel-specific entropy metrics to better capture chromatic heterogeneity in skin lesions compared to global entropy measures.

## Key findings

- Global Shannon entropy primarily reflects luminance contrast, not chromatic complexity.
- Channel-specific entropy metrics revealed significant chromatic heterogeneity in melanoma compared to benign nevi.
- The Polychromia Index effectively distinguished melanoma from nevi based on color variegation.

## Abstract

Polychromia remains one of the most reproducible dermoscopic indicators of melanoma, yet its clinical assessment is predominantly subjective. Shannon entropy has been proposed as an objective measure of color heterogeneity in pigmented skin lesions. However, global entropy derived from grayscale or composite RGB histograms may primarily capture luminance dispersion rather than true chromatic complexity. This proof-of-concept study evaluated whether global Shannon entropy quantifies polychromia and whether channel-specific entropy metrics more accurately reflect chromatic heterogeneity. Smartphone photographs (iPhone 13 Pro Max, Apple Inc.) of a histopathologically confirmed superficial melanoma, a benign junctional nevus, and their respective perilesional skin were analyzed using ImageJ (National Institutes of Health). Intensity histograms were generated in an 8-bit grayscale, composite RGB mode, and separately for the red, green, and blue channels. Shannon entropy (H, log₂), inter-channel entropy differences (ΔR-G, ΔR-B, and ΔG-B), red-channel asymmetry (Aᴿ), and a composite Polychromia Index (Iᴾ) were computed for each region of interest, with all metrics normalized to perilesional skin to control for illumination and baseline heterogeneity. Grayscale and RGB-composite histograms yielded nearly identical entropy values for both lesions, confirming that global entropy primarily reflects luminance contrast rather than chromatic structure. By contrast, channel-specific analysis revealed marked divergence in the melanoma, with normalized inter-channel entropy differences showing substantial residual chromatic heterogeneity (ΔG-B_residual = +12.31; ΔR-G_residual = +9.71), representing 600-4000% increases compared with the nevus. The normalized Polychromia Index (Iᴾ) demonstrated an 8.22-unit separation between the melanoma (+6.84) and the nevus (−1.38), closely aligning with the visual impression of color variegation. These findings indicate that global Shannon entropy does not meaningfully quantify polychromia under real-world smartphone imaging conditions. Channel-specific entropy and inter-channel metrics, however, reliably discriminate chromatically heterogeneous lesions from uniform ones. This low-cost, reproducible framework offers a physiologically interpretable approach to objective color heterogeneity assessment and holds potential for teledermatology and automated melanoma-detection systems.