On the power spectral density applied to the analysis of old canvases

A routine task for art historians is painting diagnostics, such as dating or attribution. Signal processing of the X-ray image of a canvas painting provides useful information about its fabric. However, previous methods may fail when very old and deteriorated artworks or canvases of small size are studied. We present a new framework to analyze and further characterize the paintings from their radiographs. First, we start from a general analysis of lattices and provide new unifying results about the theoretical spectra of weaves. Then, we use these results to infer the main structure of the fabric, like the type of weave and the thread densities. We propose a practical estimation of these theoretical results from paintings with the averaged power spectral density (PSD), which provides a more robust tool. Furthermore, we found that the PSD provides a characterization of the whole cloth. We search and discuss some distinctive features we may find in this characterization. We apply these results to several masterpieces of the 17th and 18th centuries from the Museo Nacional del Prado to show that this approach yields accurate results in thread counting and is very useful for paintings comparison, even in situations where previous methods fail.