1 WEAVE MAP REPORT The Procuress Johannes Vermeer 1656 L03 / Gal.-Nr. 1335 Staatliche Kunstsammlungen Dresden C. Richard Johnson, Jr. Cornell University johnson@ece.cornell.edu William A. Sethares University of Wisconsin - Madison sethares@gmail.com August 2017 In this report, paintings by Vermeer are referred to by L-numbers, based on their numbering in W. Liedtke, Vermeer: The Complete Paintings, Ludion, 2008. The dates cited on this cover page span the range of dates estimated in the oeuvre catalogs by Wheelock (1997), Liedtke (2008), and Franits (2015) as compiled in the table at www.essentialvermeer.com/ references/dates.html.
Johnson and Sethares, Weave Map Report, August 2017 2 Summary This document applies spectral-based, automated thread counting to The Procuress (L03) by Johannes Vermeer and includes the following: 1. stitched x-radiograph of full painting 2. vertical thread density map 3. horizontal thread density map 4. histograms of vertical and horizontal thread counts 5. vertical thread angle map 6. horizontal thread angle map 7. a listing of all close count matches (wthin ±1 th/cm in both directions) among Vermeer s 34 paintings on canvas 8. a composite image containing thread density maps of the painting being studied and its close count matches to the same scale and colorbar for weave match hunting 9. comments on observed cusping and weft snakes Observations: The average thread density of The Procuress is (H x V) is 14.19 x 11.46 th/cm. The Procuress has cusping on all four sides. [The depth of cusping must be carefully assessesd as the x-radiograph, which is one-to-one in size with the painting, is missing part of the painting on its edges.] The Procuress has two close count matches but no apparent weave matches among Vermeer s other paintings on canvas. The Procuress has a horizontal seam and a vertical weft snake indiccator in its upper segment.
Johnson and Sethares, Weave Map Report, August 2017 3 Background Thread counting has been used for several decades. One canvas descriptor that has been routinely collected is the average thread count of the threads in each direction (vertical and horizontal) in a painting s canvas. This information has been used to discount the possibility of two canvases coming from the same original roll if their average thread counts (smaller compared to smaller and larger coompared to larger) are too diffferent, e.g. by more than 1 th/cm. In 2009, the first weave maps derived from automated thread counts based on a spectral analysis of the painting s x-radiograph were shown at the annual AIC meeting in Los Angeles. The stripes that arise in color-coded images of thread count in small evaluation squares covering the entire painting were immediately recognized as a fingerprint of a specific roll. The first weave match was also shown in this talk [1]. The utility of automated thread counting for canvases with a sufficiently regular weave was confirmed in [2]. Weave matches with art historical implications have been reported for paintings by van Gogh [3], Velázquez [4], and Vermeer [5] [6]. Spectral-based automated thread counting also provides angle maps that make cusping assessement [7] and weft snake hunting [8] easier. Descriptions of the revelations possible from these new visualizations of canvas weave density and thread angle are provided in [9]. Technical description appears in [10] of the algorithms used in composing and comparing weave maps. References [1] 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, CA, May 2009. [2] C. R. Johnson, Jr., D. H. Johnson, N. Hamashima, H. S. Yang, and E. Hendriks, On the Utility of Spectral-Maximum-Based Automated Thread Counting from X-Rays of Paintings on Canvas, Studies in Conservation, vol. 56, pp. 104-114, 2011. [3] L. van Tilborgh, T. Meedendorp, E. Hendriks, D. H. Johnson, C. R. Johnson, Jr., and R. G. Erdmann, Weave Matching and Dat-
Johnson and Sethares, Weave Map Report, August 2017 4 ing of Van Gogh s Paintings: An Interdisciplinary Approach, The Burlington Magazine, vol. CLIV, pp. 112-122, February 2012. [4] Pablo Pérez D Ors, C. R. Johnson, Jr., and D. H. Johnson, Velázquez in Fraga: a New Hypothesis about the Portraits of El Primo and Philip IV, The Burlington Magazine, vol. CLIV, pp. 620-625, September 2012. [5] 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, vol. 47, pp. 99-106, 2012. [6] C. R. Johnson, Jr. and W. A. Sethares, Canvas Weave Match Supports Designation of Vermeer s Geographer and Astronomer as a Pendant Pair, Journal of Historians of Netherlandish Art, vol. 9, issue 1, Winter 2017. DOI: 10.5092/jhna.2017.9.1.17 [7] P. Noble, A. van Loon, C. R. Johnson, Jr., and D. H. Johnson, Technical Investigation of Rembrandt and/or Studio of Saul and David c. 1660 from the Collection of the Mauritshuis, ICOM-CC 2011 Lisbon Triennial Conference, Lisbon, Portugal, September 2011. [8] C. R. Johnson, Jr., D. H. Johnson, I. Verslype, R. Lugtigheid, and R. G. Erdmann, Detecting Weft Snakes, Art Matters, vol. 5, pp. 48-52, 2013. [9] D. H. Johnson, E. Hendriks, and C. R. Johnson, Jr., Interpreting Canvas Weave Matches, Art Matters, vol. 5, pp. 53-61, 2013. [10] D. H. Johnson, C. R. Johnson, Jr., and R. G. Erdmann, Weave Analysis of Paintings on Canvas from Radiographs, Signal Processing (Special Issue on Image Processing for Art Investigation), vol. 93, pp. 527-540, March 2013. Note: All of these references are available for download from http://people.ece.cornell.edu/johnson/selpubs.html
Johnson and Sethares, Weave Map Report, August 2017 5 Observations X-Radiograph: From Figure 2, it appears that the separate x-ray films have been sliced to build a composite. Without overlap between the consituent x-radiographs a precise stitched composite is impossible to assemble. The resulting composite in Figure 2 fails to cover the entire image. This is most easily seen when comparing the features in the visible light image in Figure 1 at the right and left edges to corresponding features in the x-radiograph in Figure 2. Average Thread Count: The average thread count (H x V) is 14.19 x 11.46 th/cm. These values are noted at the top of the images in the top row of Figure 3 along with the standard deviations of ± 1.67 th/cm (H) and ± 1.27 th/cm (V). L03 is composed from two pieces, as clearly illustrated by the change in thread count patterns in Figure 6 along the horizontal line about 30% of the image height from the bottom edge. The average thread counts in the upper and lower pieces are so similar (as indicated by the similar colors in the two pieces in Figures 5 and 6 that we lump them together in the single average thread count for each thread direction. The thread counts were computed in evaluation squares 0.5 cm on a side centered on a grid of points with 0.25 cm horizontal and vertical spacings. The histograms of the thread counts in each thread direction in the evaluation squares, as well as the histograms of the thread angles computed in the same evaluation squares, are plotted in Figure 4. Tight Count Matches: All of the weave matches discovered so far among the canvases of paintings by Vermeer have had both thread counts within 1 th/cm of each other. Using this metric for the designation of a tight count match, L03 has two: L20 (A Lady Writing, National Gallery of Art - DC) and L32 (Allegory of he Catholic Faith, Metropolitan Museum of Art). Weave Matches: Figure 9 is designed to assist in assessing if either L20 or L32 is a weave match to L03. In Figure 9 all images are to the same scale, which is necessary for visual evaluation of potentially matching stripe patterns. The first two images in the second row (when the figure is viewed so the writing on the left is properly oriented) are the horizontal thread density map of L20 and the vertical thread density map of L20 - rotated 90 degrees so the stripes are horizontal - with the same colorbar
Johnson and Sethares, Weave Map Report, August 2017 6 as used for the horizontal thread count for L03 on the left in the top row of Figure 9. These are to be placed on either the right or the left of the left image in the top row and moved around looking for a match of the stripe patterns. Because the average vertical thread count in L20 is much lower than the average horizontal thread count in L03, the second image in the second row is quite dark. So, only the horizontal thread density map of L20 need be compared to the horizontal thread density map of L03. A similar visual check is made with the third and fourth images in the second row of Figure 9 against the right image in the top row. The last two images in the second row (when the figure is viewed so the writing on the left is properly oriented) are the vertical thread density map of L20 and the horizontal thread density map of L20 - rotated 90 degrees so the stripes are vertical - with the same colorbar as used for the vertical thread count for L03 on the right in the top row of Figure 9. These are to be placed either above or below of the right image in the top row and moved around looking for a match of the vertical stripe patterns. Because the average horizontal thread count in L20 is much higher than the average vertical thread count in L03, the second image in the second row is quite light. So, only the vertical thread density map of L20 need be compared to the horizontal thread density map of L03. Of these four images in the second row, only one (or none) can have a match. In this case none appear to have a match. The same conclusion is drawn about L32 after repeating the similar comparisons with the third row and the first row in Figure 9. Weft Snake Indicators: A vertical weft snake indicator about 15 cm in from the right edge of the canvas traverses the upper portion of the painting from its top to the horizontal seam. It does not continue below the seam. This is because the two pieces of canvas are joined along a seam in the warp direction, so that the weft snake indicator in the upper portion, the height of which corresponds to the loom width, captures the full extent of the potential weft snake. The piece at the bottom is taken from further along the canvas in the warp direction and does not include the weft snake of the upper portion. In any event, the weft snake indicator is in the weft direction as it is perpendicular to the seam in the warp direction. The weft snake appears to go through the blue and white pitcher on the right end of the table. A close-up look reveals a wiggly bunch of threads with such a slight wiggle that they might be overlooked without
Johnson and Sethares, Weave Map Report, August 2017 7 the presence of the weft snake indicator in the vertical thread angle map of Figure 8. Cusping: The cusping is greater than 5cm in depth on all four sides. The bottom and the right edges have deeper cusping than their corresponding opposite sides at the top edge of Figure 7 and the left edge of Figure 8. Before drawing any conclusions from this imbalance, consider the possibility of trimming in the x-radiograph in Figure 2 relative to the painting in Figure 1. Indeed the horizontal dimension of the x-radiograph is a bit over 10 cm less than the horizontal image of the painting.
Johnson and Sethares, Weave Map Report, August 2017 8 Acknowledgments The authors of this weave map report on one of Vermeer s paintings on canvas are grateful to the owners of Vermeer s paintings, all of whom gave us access to high resolution digitized x-radiographs of their Vermeers Walter Liedtke (Metropolitan Museum of Art) and Gregor Weber (Rijksmuseum) for their help in persuading the owners of paintings by Vermeer to grant us access to their x-radiographs Rob Erdmann (Rijksmuseum) for expertly assembling full-painting composite x-radiographs all of our research collaborators and thread-counting students over the past decade since the founding of TCAP: the Thread Count Automation Project (http://people.ece.cornell.edu/johnson/ tcap.html).
Johnson and Sethares, Weave Map Report, August 2017 9 Images Figure 1: The Procuress (L03) Note: All of the following images (Figures 2-9) are available on request as high resolution tiff or pdf files.
Johnson and Sethares, Weave Map Report, August 2017 10 Figure 2: X-Radiograph of L03
Johnson and Sethares, Weave Map Report, August 2017 horizontal thread density (14.19 +/- 1.67 threads/cm) vertical thread density (11.46 +/- 1.27 threads/cm) horizontal thread angles (+/-3.16922 degrees) vertical thread angles (+/-3.13772 degrees) Figure 3: Weave Maps of L03 11
Johnson and Sethares, Weave Map Report, August 2017 12 Figure 4: Histograms of Thread Count and Angle Computations for L03
Johnson and Sethares, Weave Map Report, August 2017 13 18 16 14 12 Figure 5: Horizontal Thread Density Map of L03
Johnson and Sethares, Weave Map Report, August 2017 14 14 12 10 8 Figure 6: Vertical Thread Density Map of L03
Johnson and Sethares, Weave Map Report, August 2017 15 15 10 5 0-5 -10-15 Figure 7: Horizontal Thread Angle Map of L03
Johnson and Sethares, Weave Map Report, August 2017 16 110 100 90 80 70 Figure 8: Vertical Thread Angle Map of L03
Johnson and Sethares, Weave Map Report, August 2017 17 Figure 9: Tight Count Matches of L03