Counting Vermeer


4.1 Why semi-automatic?

Given the repetitive nature of the thread counting task, it is tempting to delegate all the tedious tasks to the computer. The next chapter describes one such automated computer-based solution in detail. However, there are two good reasons to first consider an intermediate semi-automated procedure that closely mimics the manual procedure, but uses the computer to help organize and record the data.

The first reason is that computer-based calculations of ‘thread count’ do not actually count individual threads the way a person might. Rather, they carry out a numerical procedure whose result closely resembles the thread count. For example, the specific method detailed in Johnson et al. 2009, and which is used in chapter 5, is based on the Fourier Transform.1 This calculates an average frequency over each image patch and is discussed in greater detail in chapter 5. The method of Erdmann et al. 2013 is called ‘autocorrelation’, a technique that looks for and quantifies repetitive patterns in numerical sequences.2 Even the most recent methods of Tobin and Erdmann3 trace the paths of all possible threads and estimate their likelihood in a given region rather than literally counting visible traces of the thread pattern. In normal situations, where the canvas is clearly visible in the X-ray images, all of the above methods give answers that closely match the underlying thread count. But with poorly lit images, with noisy images, with images where the canvas is not clearly visible, or with images where the canvas has a wildly varying thread count, the different methods may return different results. Thus there is a need to gather direct manual measurements of the thread count on a set of patches (that is, a set of ‘ground truth’ data) to which the output of the various computational methods can be compared. This is a necessary step in order to verify and validate the functioning of the automated methods. The manually assisted method of this chapter provides a way to establish this ground truth in order to provide a reality check on the automated methods.

The second reason to consider the manually-assisted thread counts is that all of the above methods need to be initialized or trained in a sensible fashion. For example, as described in the next chapter, the Fourier method needs to be told ‘approximately’ what the thread count is, and it can then quite reliably fine tune this answer. But if the initial guess is far from the correct value (say by a factor of two) then the resulting answer may well also be off by a factor of two. Similarly, the other numerical techniques have their own requirements, and a manual thread count is helpful to ensure that the computer-generated counts make sense.


1 D.H. Johnson, C.R. Johnson Jr., A.G. Klein, W.A. Sethares, H. Lee, and E. Hendriks, ‘A thread counting algorithm for art forensics’, in: Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop (DSP/SPE) IEEE 13th, Marco Island, 2009, pp. 679–684. A more comprehensive discussion may be found in D.H. Johnson, C.R. Johnson Jr. and R.G. Erdmann, ‘Weave analysis of paintings on canvas from radiographs’, Signal Processing 93 (2013), pp. 527–540.

2 R.G. Erdmann, C.R. Johnson Jr., M. Schafer, J. Twilley, and T. Sawyer, ‘Reuniting Poussin’s Bacchanals painted for Cardinal Richelieu through quantitative canvas weave analysis’, in: (date consulted: August 29, 2017); 41st Annual Meeting of American Institute for Conservation of Historic and Artistic Works (Indianapolis, IN, May 29 - June 1, 2013), pp. 64-65. See also: L. van der Maaten, and R. Erdmann, ‘Automatic Thread-Level Canvas Analysis’, IEEE Signal Processing Magazine 32 (July 2015), issue 4, pp. 38-45.

3 B. Tobin and R. Erdmann, ‘Vermeer Thread Spacing Comparison’, (date consulted: August 29, 2017)

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