  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.
