Machine learning regression algorithms for generating chemical element maps from X-ray fluorescence data of paintings

Aug 3, 2026

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Generating chemical element maps of paintings from X-ray fluorescence (XRF) data supports conservators and art historians by revealing pigment distributions used for dating, restoration detection, and conservation decisions. Hand-held XRF scanners are portable but yield sparse measurements, requiring improved reconstruction methods. A SmART_Scan approach based on minimum hypercube distance (MHD) exists, yet this study proposes regression-based machine learning alternatives. Eight regression models are evaluated against MHD on two paintings with different features, using hold-out validation and cross-validation.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages14

Reading Time35 min

AccessFree to download

Introduction

XRF scanners and pigment characterization

MacroXRF vs hand-held XRF

Prior work: SmART_Scan and MHD approach

Chemometrics and Intelligent Laboratory Systems 248 (2024) 105116 Contents lists available at ScienceDirect Chemometrics and Intelligent Laboratory Systems journal [homepage: www.elsevier.com/locate/chemometrics](homepage: www.elsevier.com/locate/chemometrics) | Machine learning regression algorithms for generating chemical element maps from X-ray fluorescence data of paintings
Juan Ruiz de Miras a, *, María Jos´e Gacto a, María Rosario Blanc b, Germ´an Arroyo a, Luis L´opez a, Juan Carlos Torres a, Domingo Martín a
a Software Engineering Department, University of Granada, Granada, Spain b Department of Analytical Chemistry, University of Granada, Spain | | | | --- | --- | --- | | A R T I C L E I N F O | | A B S T R A C T | | Keywords:
Machine learning Random forest Regression problem X-ray fluorescence Chemical element maps | | Generating chemical element maps of paintings from X-ray fluorescence (XRF) data is a very valuable tool for the scientific community of conservators and art historians. Hand-held XRF scanners are cheap and easily portable but their use provides scans with a few data, so additional analytical tools are needed to obtain reliable chemical element maps from them. Recently, the software tool SmART_Scan was released, which uses an algorithm based on the minimum hypercube distance (MHD) to compute this kind of maps. In this paper, we propose a new methodology to address this problem by using machine learning algorithms for regression as alternative and more accurate techniques than MHD. We tested MHD versus eight machine learning regression algorithms on two paintings with different features. Our results showed that machine learning algorithms Random Forest and kNN significantly outperformed MHD in Mean Squared Error (MSE) and coefficient of determination (R2) for all the experiments. When using experts’ data and a hold-out validation, kNN was the best-ranked algorithm. Random Forest was the best-ranked algorithm when cross-validation was used. We did not find significant differences in average MSE nor in R2 between kNN and Random Forest, so we can conclude that Random Forest is the best-suited algorithm for computing chemical element maps of paintings from XRF data. | 1. Introduction X-ray fluorescence (XRF) scanners are very valuable tools for analyzing the distribution of pigments on paintings, among many other applications [1]. These scanners are very useful for the scientific community of conservators and art historians because analyzing the pigments used in a painting allow them to date the work, identify previous restorations and perform conservation techniques [2]. An XRF scan on a certain point of a painting returns an energy spectrum whose peaks correspond to the XRF emissions of chemical elements. As the characteristic energy of each chemical element is known, it is possible to identify the elements present in that point from the XRF spectrum [2]. XRF scanners can be grouped into two main families: MacroXRF and hand-held scanners. MacroXRF scanners produce very precise results allowing the users to scan thousands of samples on the painting, but they are much more expensive and difficult to transport than hand-held portable scanners. These are the reasons why the development of efficient and accurate data analysis tools for those less expensive and less complex hand-held scanners is an important focus of study nowadays [1]. In this line of work, Martin-Ramos et al. presented SmART_Scan [3], a computer program for generating chemical element maps showing the distribution of chemical elements in the painting. These maps are generated using as inputs an RGB image of the painting and a limited number of XRF scanned points selected by an expert. SmART_Scan obtains the maps by combining the data through a method called Minimum Hypercube Distance (MHD). The short processing time and the quality of the maps generated position SmART_Scan as a valuable alternative approach to an

FAQs

Why are chemical element maps important for paintings?

They support conservators and art historians by revealing pigment distributions that help with dating artworks, identifying prior restorations, and informing conservation techniques.

What limitation of hand-held XRF motivates new analysis methods?

Hand-held scanners are portable but provide scans with only a few data points, so additional tools are needed to generate reliable element maps.

Which regression models outperform the MHD baseline in the experiments?

Random Forest and kNN significantly outperform MHD in mean squared error (MSE) and R2 across experiments; kNN ranks best with hold-out validation, while Random Forest ranks best with cross-validation.

Aug 3, 2026

Upload by Oliver