Integrated chemometric pipeline combining point-based X-ray fluorescence and chromatic-textural fractal metrics for cultural heritage analysis

Portable X-ray fluorescence (pXRF) spectroscopy enables precise, non-destructive elemental characterization of cultural heritage materials, yet traditional point-based measurements inherently overlook the spatial and chromatic variability of the pictorial application. To address this limitation, a data-driven chemometric pipeline was developed to integrate high-dimensional compositional data (pXRF) with chromatic and textural descriptors derived from multidimensional fractal analysis (FD-RGB and FD-Gray). Using a historical copy of Raphael's “The Transfiguration” as a comprehensive case study, 165 localized XRF elemental profiles were statistically associated with fractal descriptors extracted from high-resolution digital patches. This single-painting case study is framed as a proof of concept, and the resulting pigment-texture relationships are interpreted as preliminary and case-dependent rather than as universal thresholds. Rank-based correlation analysis, Kruskal-Wallis tests, Dunn post-hoc comparisons with Benjamini–Hochberg control across contrasts, and Principal Component Analysis (PCA) were applied to evaluate the multivariate behavior of specific major chemical families. The integrated analysis demonstrates a directional mathematical decoupling of luminance-based texture from chromatic complexity. Results indicate that luminance variations (quantified via FD-Gray) show minimal dependence on the localized chemical palette, while multiscale chromatic variance (FD-RGB) effectively discriminates between opaque and multilayered applications (|ρ| ≈ 0.17-0.22; several remained significant under within-descriptor false-discovery-rate control). Specifically, pigments defining high-hiding matrices (based on Pb, Sn) reduce the chromatic complexity (FD-RGB), whereas pigments historically associated with chiaroscuro and translucent glazes (based on Hg, Mn, Ca) markedly increase this fractal complexity. In a dominance-based variance analysis, FD-RGB differed across groups ( p = 0.018; η 2 = 0.222), while Dunn pairwise differences were nominal at the unadjusted level. PCA of the standardized matrix (18 elemental variables + FD-RGB/FD-Gray) showed that PC1 (33.03%) aligns with an opacity-translucency continuum driven by Pb, Ba, As, Cd, and Sb, opposed to FD-RGB, whereas PC2 (11.77%) separates cool (based on Co, Ni, and Cu) from warm/shadow domains (based on Ca, Mn, Fe, and Hg) with FD-RGB loading negatively. This data-driven framework transforms raw chemical data into objective art-technical knowledge, demonstrating its capacity to characterize painterly execution beyond pigment concentration, and offering a robust new computational tool for Heritage Science.