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

by   Gabriel Riutort-Mayol, et al.

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.


page 4

page 8

page 10

page 11


Gaussian process with derivative information for the analysis of the sunlight adverse effects on color of rock art paintings

Microfading Spectrometry (MFS) is a method for assessing light sensitivi...

Gaussian Process Conditional Copulas with Applications to Financial Time Series

The estimation of dependencies between multiple variables is a central p...

Spatiotemporal factor models for functional data with application to population map forecast

With the proliferation of mobile devices, an increasing amount of popula...

Bayesian Changepoint Estimation for Spatially Indexed Functional Time Series

We propose a Bayesian hierarchical model to simultaneously estimate mean...

varycoef: An R Package for Gaussian Process-based Spatially Varying Coefficient Models

Gaussian processes (GPs) are well-known tools for modeling dependent dat...

ALPS: A Unified Framework for Modeling Time Series of Land Ice Changes

Modeling time series is a research focus in cryospheric sciences because...

Multivariate Functional Data Modeling with Time-varying Clustering

We consider the situation where multivariate functional data has been co...

Please sign up or login with your details

Forgot password? Click here to reset