A thread counting algorithm for art forensics

Abstract

Thread counting algorithms seek to determine the vertical and horizontal weave densities of the canvas underlying a painting. X-ray images of a painting serve as the raw data. Canvas texture can be modeled as a sum of two sinusoids having nearly orthogonal spatial frequencies. The actual painting serves as an additive signal that only distracts from the thread-counting process. The algorithm employs a variant of short-time Fourier analysis to the image domain. In simple cases, two-dimensional Fourier transforms of small areas reveal isolated peaks at the proper vertical and horizontal frequencies. In more challenging cases, even within the same painting, additional peaks appear in the expected frequency range, requiring heuristics to extract from the spectral measurements representative thread-count estimates for a painting. The resulting algorithm, while still under development, can analyze weave density for entire paintings with an accuracy comparable to human measurements.

Matching canvas weave patterns from processing x-ray images of master paintings

“…In an internal competition among Project members, a completely automatic spectral algorithm [7], illustrated in Figures 2 and 3, achieved the best performance [8]. Briefly, the spectral algorithm is rooted in the observation that the various layers of paint, including the ground that fills the canvas weave, additively contribute to opacity as expressed by (1).…”

On the Utility of Spectral-Maximum-Based Automated Thread Counting from X-Radiographs of Paintings on Canvas

“…in the original development of a two-dimensional Fourier-transform-maximum-based scheme relying on the dominant peak in the frequency range of interest corresponding to the thread density, a set of test line segments and the number of crossing threads were recorded for over 900 spots in 21 van the spectral-maximum-based algorithm [1] begins by performing a two-dimensional Fourier transform on each evaluation square after high-pass pre-processing. With the X-radiograph displaying waves of vertically and horizontally oriented threads, the tall peaks quantifying thread density are to be found near the horizontal and vertical axes in the two-dimensional Fourier transform.…”

“…a recently introduced algorithm [1] for automated thread counting relies upon the topography of the twodimensional Fourier transform of the X-radiograph. (For a description of the two-dimensional Fourier transform see the appendix.)…”

Simultaneous capture of the color and topography of paintings using fringe encoded stereo vision

“…Such sub-surface features often reveal never before seen features or entire depictions. The canvas of a painting can also be subjected to study, and by counting its threads, separate paintings originating from the same roll of canvas can be matched [3]. All the data resulting from such applied methods will help build up a solid basis of information about the work of art.…”