Enhancement of hidden patterns in paintings using statistical analysis

Multispectral acquisitions of paintings in the non-visible range, such as the ultraviolet or the near infrared, constitute nowadays a standard practice to complement the information contained in the visible part of the spectrum. Indeed, the various pigments employed generally show different spectral signatures, so that they may reflect only at specific wavelengths and tend to fade over different ones. In particular, infrared inspection can often reveal patterns that are hidden to the naked eye, such as author signatures or dates, or even preliminary drawings made by the artist to design the painting. Revealing the whole contents of a painting is thus an important aid for dating it or establishing its origin and author. However, the detected patterns are usually very faint and overlapped to the other painting contents, so that their interpretation is not easy. Although empirical strategies can sometimes be found to enhance the interesting pattern, these are usually laborious and specific for the case study at hand. In this paper, we approach the problem in a methodological, model-based manner, relying on the spectral diversity of the different patterns overlapped in the painting and on their spatial statistical independence. More in detail, we model the available painting observations as linear mixtures, with unknown coefficients, of a number of different patterns. The point of view is then that revealing hidden features, extracting pattern of interest, or removing unwanted interferences, can be seen as the problem of separating the mixed patterns. This is the typical formulation of a linear Blind Source Separation (BSS) problem, which can be solved through statistical analysis. Indeed, assuming that the source patterns are spectrally different and mutually independent, fast and fully unsupervised separation techniques, based on independent component analysis or channel decorrelation, can be effectively applied. This approach have been first proposed with some success for the restoration and the analysis of multispectral images of historical manuscripts, characterized by the presence of several layers of information, e.g. overlapped texts. In that case the aim was mainly to improve the manuscript legibility, by removing the interfering text. Our intent here is to extend the approach to the analysis of paintings as well, with the main aim at enhancing hidden patterns they might contain. From a theoretical point of view, an interference-free image of the pattern of interest could also be obtained. From our experimentation on a number of paintings where the inspection in some bands has revealed the presence of a hidden pattern, we derived a practical procedure for the optimal application of the method. Rather than feeding the statistical analysis technique with all the available channels, we found sufficient to apply it to two only maps, one containing the pattern, usually the infrared map, the other chosen among those channels where the pattern is not present. In this way, the already very low computational costs can also be further reduced.