Algorithms for Old Master painting canvas thread counting from x-rays

The task of determining the weave density in the canvas support of Old Master paintings is introduced as a period extraction problem. Because of the way paintings were commonly prepared and preserved, the threads in the horizontal and vertical directions in the canvas support can be counted from x-ray images of the painting. Current procedures are tedious, time-consuming, and (usually) insufficiently documented. This paper describes the design of an algorithm for counting threads from x-rays that uses the Fourier Transform of the Radon Transform of a portion of the image with some crude, but appropriate, decision-making. The algorithm is presented as a sequence of refinements based on a simple mathematical model of the available image data: high resolution x-rays of paintings by Vincent van Gogh from the collection of the Van Gogh Museum. Over 900 spot counts were performed manually by a student team at Cornell using a graphical user interface created for this project. These manual counts provide a dataset for evaluating performance of the algorithm. A major goal is to convince art historians of the viability of automated (and semi-automated) counting procedures.