Counting Vermeer


Editor’s note — Rick Johnson

October 21, 2017

This RKD Studies publication Counting Vermeer: Using Weave Maps to Study Vermeer's Canvases is the culmination of a decade of personal scholarship following my founding of the Thread Count Automation Project (TCAP) in 2007.1 Weave maps and matches were introduced and applied by participants in this project, who appear as co-authors in the ten references below.

My personal preparation for this excursion into computational art history began much earlier, in the 1972-73 academic year, with my first ever visit to a fine art museum while a fellowship student in Germany during my senior year as an undergraduate at Georgia Tech. I was attracted to the paintings by Rembrandt.

While a graduate student at Stanford from 1973-1977, I took my first art history course: a graduate-level seminar on Rembrandt. I was woefully unprepared. My second art history course was an undergraduate survey of seventeenth-century Dutch art taught by Madlyn Kahr. I was hooked. With Madlyn's encouragement I took enough art history courses to receive a PhD minor in Art History, the first Stanford granted, along with my PhD in Electrical Engineering in 1977. Along the way, Madlyn introduced me to Vermeer studies by providing me with a copy of Arthur Wheelock's PhD thesis for my consideration of Vermeer's use of the camera obscura.

After almost 30 years of focus on more typical topics – digital control and signal processing – in electrical engineering research and teaching, I began a period of tutelage with Ella Hendriks at the Van Gogh Museum in Amsterdam on the duties of a conservator. I was interested in tasks for which labor time could be reduced and the utility of the results amplified with the use of computer-based image processing tools. Ella introduced me to thread counting from X-radiographs in June 2007 as a useful forensic in the analysis of a painting's canvas. The periodic nature of the weave in the image suggested a spectral analysis, which I confirmed with a comparison of hand counting and a simple one-dimensional Fourier transform of a line of image data perpendicular to the threads being counted. TCAP was founded in summer 2007 and during the 2007-2008 academic year, participating teams were recruited for crafting and testing various more sophisticated approaches.

The first technical conference paper describing a spectral-based image processing procedure for canvas thread counting from X-radiographs appeared in Klein et al. 2008.2 Five years later, the first technical journal paper describing the two-dimensional Fourier analysis procedure, which became the primary computational engine for weave map construction and the correlation scheme for comparing and matching the striped patterns of the density maps, appeared in a special issue on image processing for art investigation, Johnson/Johnson Jr./Erdmann 2013.3

The first conservation conference paper introducing automated thread counting, weave thread density and angle maps, and weave-matching rollmates was Johnson Jr. et al. 2009.4 The first paper in a conservation journal on Fourier-spectral-analysis-based automated thread counting – and its dependence on a sufficient degree of regularity in the canvas weave – which included the first published automated thread counts for some of Vermeer's paintings was Johnson Jr. et al. 2011.5

The first papers in art history journals on the application of weave maps to rollmate identification with art historical implications studied paintings by Van Gogh (Van Tilborgh et al.),6 Velázquez (Pérez d'Ors/Johnson/Johnson Jr. 2012),7 and Vermeer (Liedtke/Johnson Jr./Johnson 2012).8 The first three weave-matching pairs of Vermeer paintings discovered were reported in Liedtke/Johnson Jr./Johnson 2012. The fourth weave-matching pair was reported in Johnson Jr./Sethares 2017.9

The thread angle map of the first Vermeer painting for which weave maps were drawn – The Art of Painting (L26) in the Kunsthistorisches Museum in Vienna – revealed a puzzling artifact that was eventually identified as due to a weaving flaw that only occurs in the weft threads (Johnson Jr. et al. 2013).10

A collection of advice on how to interpret matches of canvas weave density maps and the weave distortions visualized in weave angle maps based on the compilation of weave maps for hundreds of paintings by Van Gogh was presented in Hendriks/Johnson/Johnson Jr. 2013.11

The objective of collecting full-painting X-radiographs of all of Vermeer's paintings on canvas was conceived late in 2009. The presumption from the start was that the full collection of X-radiographs and their weave maps would be permanently archived by the RKD – Netherlands Institute for Art History in The Hague for public use. Within a year, with the invaluable, enthusiastic assistance of Walter Liedtke at The Metropolitan Museum of Art in New York, we had access to 21 of the 34 paintings by Vermeer. By the end of 2014, we had collected X-radiographs covering all 34. Rob Erdmann expertly stitched composites for all of them. Bill Sethares wrote software assisting in manual thread counting and providing automated creation of weave thread density and angle maps using Mathematica because of its downloadable reader allowing cost-free use. During the creation of weave maps for all 34 paintings using this software the fourth, fifth, and sixth weave-matching pairs of Vermeer paintings were discovered. The fifth and sixth are reported for the first time in this monograph.

The list of my many collaborators, whom I wish to thank, begins with Ella Hendriks, Don Johnson, and Rob Erdmann, who were the stalwarts in the first half-dozen years of TCAP. I also wish to thank the authors of the essays in this monograph who have helped me to realize my goal of bringing my signal processing engineering skills to the study of seventeenth-century Dutch art: Petria Noble, Ige Verslype, Michiel Franken, Arthur Wheelock, and Bill Sethares. This goes double for Bill Sethares, who wrote two of the essays and all of the software. I thank all of my co-authors on the references cited in this Editor's Note for their contributions to this foundation for a new tool in painting analysis. This list also has to include the contacts with the institutions owning the Vermeers, who arranged access approval and data transfer of the X-radiographs during our years of study of Vermeer's paintings. The dataset assembled from their images is the reason this monograph exists. They are all cited below in the list of references. Finally, I would like to thank the team I have worked with for years at the RKD – Chris Stolwijk, Michiel Franken, Wietske Donkersloot, Sytske Weidema, and Sabine Craft-Giepmans – for their support at all stages of this long-brewing project, as well as the editorial team for this monograph: Patrick Larsen and Reinier van 't Zelfde.I am particularly grateful to Sytske Weidema for her professional management of the complexities of assembling the final product.

This monograph is the final ‘report’ I wish I could personally deliver to two mentors who fueled my devotion to this project. Instead, this monograph is dedicated to Madlyn Millner Kahr (1913-2004) and Walter Arthur Liedtke, Jr. (1946-2015).


1 A timeline of the first half-dozen years of TCAP activities can be viewed at

2 A.G. Klein, D.H. Johnson, W.A. Sethares, H. Lee, C.R. Johnson, Jr., and E. Hendriks, ‘Algorithms for Old Master Painting Canvas Thread Counting from X-rays’, Proceedings 42nd Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, October 26-29 2008 (DOI: 10.1109/ACSSC.2008.5074612).

3 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. (DOI: 10.1016/j.sigpro.2012.05.029).

4 C.R. Johnson Jr., E. Hendriks, P. Noble, and M. Franken, ‘Advances in Computer-Assisted Canvas Examination: Thread Counting Algorithms’, 37th Annual Meeting of American Institute for Conservation of Historic and Artistic Works, Los Angeles, May 19-22 2009.

5 C.R. Johnson, Jr., D.H. Johnson, N. Hamashima, H. Sung Yang, and E. Hendriks, ‘On the Utility of Spectral-Maximum-Based Automated Thread Counting from X-Radiographs of Paintings on Canvas’, Studies in Conservation 56 (2011), pp. 104-114. (DOI: 10.1179/sic.2011.56.2.104).

6 L. van Tilborgh, T. Meedendorp, E. Hendriks, D.H. Johnson, C.R. Johnson Jr, and R.G. Erdmann, ‘Weave matching and dating of Van Gogh's paintings: an interdisciplinary approach’, The Burlington Magazine 154 (2012), pp. 112-122.

7 P. Pérez d'Ors, R. Johnson, and D. Johnson, ‘Velázquez in Fraga: a new hypothesis about the portraits of El Primo and Philip IV’, The Burlington Magazine 154 (2012), pp. 620-625.

8 W. Liedtke, C.R. Johnson Jr., and D.H. Johnson, ‘Canvas Matches in Vermeer: A Case Study in the Computer Analysis of Fabric Supports’, Metropolitan Museum Journal 47 (2012), pp. 101-108.

9 C.R. Johnson Jr., and W.A. Sethares, ‘Canvas Weave Match Supports Designation of Vermeer's Geographer and Astronomer as a Pendant Pair’, in: Journal of Historians of Netherlandish Art 9 (2017), issue 1, (DOI: 10.5092/jhna.2017.9.1.17).

10 C.R. Johnson, Jr., D.H. Johnson, I. Verslype, R. Lugtigheid, and R.G. Erdmann, ‘Detecting Weft Snakes’ Art Matters 5 (2013), pp. 48-52.

11 E. Hendriks, D.H. Johnson, and C.R. Johnson Jr., ‘Interpreting Canvas Weave Matches’, Art Matters 5 (2013), pp. 53-61.

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