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

Abstract

In a previous article, we modelled the spectral and temporal dimensions of the photodegradation behaviour of pigments in the painting “A Japanese Lantern” by Oda Krohg. In particular, we extracted the endmembers and spectral fading rate of pigments by applying tensor decomposition on a time-series of spectroscopic point measurements. Now, we capture the same painting with a hyperspectral imaging setup and propose an approach to render the fading effects as 2D images. More precisely, from the hyperspectral image, we compute the concentration maps of each previously identified endmember with a least-squares unmixing method. Subsequently, by using tensor algebra, we multiply the concentration maps with the endmembers and their corresponding fading rate and obtain a 4D tensor where each pixel in the image is described by a spectrum and a fading function. This way, we generate past and future spatio-temporal simulations of the painting’s appearance by reversing and elevating light exposure, respectively.