Correlated Functional Models with Derivative Information for Modeling Microfading Spectrometry Data on Rock Art Paintings

Abstract

Rock art paintings present high sensitivity to light, and an exhaustive evaluation of the potential color degradation effects is essential for further conservation and preservation actions on these rock art systems. Microfading spectrometry (MFS) is a technique that provides time series of stochastic observations that represent color fading over time at the measured points on the surface under study. In this work, a reliable and robust modeling framework for a short and greatly fluctuating observation dataset collected over the surfaces of rock art paintings located on the walls of Cova Remigia in Ares del Maestrat, Castellón, Spain, is presented. The model is based on a spatially correlated spline-based time series model that takes into account prior information in the form of model derivatives to guarantee monotonicity and long-term saturation for predictions of new color fading estimates at unobserved locations on the surface. The correlation among the (spatially located) time series is modeled by defining Gaussian process (GP) priors over the spline coefficients across time series. The goal is to obtain a complete spatio-temporal mapping of color fading estimates for the study area, which results in very important and useful information that will potentially serve to create better policies and guidelines for heritage preservation and sustainable rock art cultural tourism.

Tensor decomposition for painting analysis. Part 2: spatio-temporal simulation

“…Riutort-Mayol et al [8] proposed an interpolation method based on a multivariate Gaussian process, that correlates the set of microfaded points with a trichromatic image of the same scene. The Gaussian process considers the covariance between the faded spots and the pixels in color image based on their similarity in the HSV (hue, saturation, value) color space and spatial proximity.…”

“…This method was applied to predict color changes for Spanish Levantine rock art paintings [19]. While potentially, given a hyperspectral image, the Gaussian process interpolation could be extended to the spectral domain as well, no such feasibility prospects were discussed in the papers [8] and [19].…”

“…1. The result is a 2D matrix with dimensions 581,440 * 648, where the second dimension corresponds to the number of time steps (8) multiplied by the number of wavelengths (81). This is then reshaped to a 4D array with size 736 * 790 * 8 * 81, that contains the spectral simulations along the 81 wavelengths for the 8 time steps, spatially distributed for the entire surface of the central lantern.…”

“…Other approaches are hybrid, combining physical models with data-driven methods [4]. There are also purely data-driven approaches, where analytical data and measurements of accelerated aging are combined with linear regression methods to virtually restore and/or age an artwork [7,8].…”

Color degradation mapping of rock art paintings using microfading spectrometry

“…Estimation of the spectral response change based on color differences ∆𝑬 𝒂𝒃 * for times t=3, 4, 5, 6, 8, and 11. (Taken from[40]).…”