Correlated functional models with derivative information for modeling MFS data on rock art paintings

TL;DR

This paper introduces a novel Gaussian process-based spline model incorporating derivatives for predicting color fading in rock art, improving accuracy and interpretability in cultural heritage preservation.

Contribution

It develops a correlated spline model with derivatives and Gaussian process priors to effectively model and predict MFS data on rock art surfaces.

Findings

Derivatives improve predictive accuracy.

Colorimetric variables enhance prediction.

Model captures non-decreasing fading behavior.

Abstract

Microfading Spectrometry (MFS) is a method for assessing light sensitivity color (spectral) variations of cultural heritage objects. Each measured point on the surface gives rise to a time-series of stochastic observations that represents color fading over time. Color degradation is expected to be non-decreasing as a function of time and stabilize eventually. These properties can be expressed in terms of the derivatives of the functions. In this work, we propose spatially correlated splines-based time-varying functions and their derivatives for modeling and predicting MFS data collected on the surface of rock art paintings. The correlation among the splines models is modeled using Gaussian process priors over the spline coefficients across time-series. A multivariate covariance function in a Gaussian process allows the use of trichromatic image color variables jointly with spatial locations as inputs to evaluate the correlation among time-series, and demonstrated the colorimetric variables as useful for predicting new color fading time-series. Furthermore, modeling the derivative of the model and its sign demonstrated to be beneficial in terms of both predictive performance and application-specific interpretability.