Title: On the Power Spectral Density Applied to the Analysis of Old Canvases,
Abstract: A routine task for art historians is painting diagnostics, such as dating or
attribution. Signal processing of the X-ray image of a canvas provides useful
information about its fabric. However, previous methods may fail when very old
and deteriorated artworks or simply 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 fingerprint that characterizes the whole canvas. We search and
discuss some distinctive features we may find in that fingerprint. 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.