RKD STUDIES

A weave angle map provides a color-coded indication of the local orientation of the (essentially) horizontal and (essentially) vertical threads. Consider the weave angle map for the vertical threads of Woman with a Lute (L14) at the lower right position of the four weave maps in figure 2 in § 6.1. The bulk ofthe image – except along the edges – is a single color, which indicates straight threads. The scalloped variations in color at the left and right edges are indicative of cusping.

Also, note the vertical line of smaller deformations about 18 cm from the right edge in the vertical thread angle map in figure 2 in § 6.1. This suggests a wavy rather than straight bundle of threads. When this artifact appears in a weave angle map, it is called a ‘weft snake indicator’.¹ The X-radiograph needs to be consulted to determine if this indicator is actually marking a wavy bundle of threads, rather than some other flaw such as a tear or a seam. The wavy threads are perceptible in figure [1], which is generated via ZoomIn, but the wiggles are so slight that they would be difficult to locate without the weft snake indicator.

The weft snake indicator, in the vertical thread angle map of Woman with a Lute (L14) in figure 2 in § 6.1 continues in the vertical thread angle map of Woman with a Pearl Necklace (L18) in figure 3 in § 6.1.

This is consistent with the arrangement of weave density maps of Woman with a Lute (L14), Woman with a Pearl Necklace (L18), Woman Holding a Balance (L19), and Woman Writing a Letter, with Her Maid (L31) in figure 7 in § 6.1. The angle maps for the quartet arranged as in figure 8 in § 6.1 appear in figure [2]. Part of figure 2 is enlarged in figure [3] with end points of the weft snake indicator traversing both Woman with a Lute (L14) and Woman with a Pearl Necklace (L18) marked by arrowheads.

The Art of Painting (L26) is another Vermeer painting with an angle map possessing a weft snake indicator and a corresponding wiggly bundle of threads (or weft snake) crossing its X-radiograph.² This weaving fault will occur in the weft threads.³ Thus, a weft snake indicator that corresponds to a wavy bundle of threads in the X-radiograph can be used to designate the direction of the weft threads. Unfortunately, weft snake indicators do not appear in angle maps of all of Vermeer’s canvases – only fifteen out of 34. And not all artifacts that can be flagged as weft snake indicators actually reveal weft snakes. Sometimes it can be due to another type of canvas fault. One point to remember: because it is a weaving flaw, a weft snake should continue across the full width of the weft of the original canvas.

The established and preferred method of determining which thread direction is weft and which is warp relies on the presence of selvedge, which runs in the warp direction along the edges of the canvas. Because tacking edges were commonly removed when relining a painting, selvedges are now likely to be lost.⁴ This problem is not as acute for Vermeer as for most seventeenth-century artists because more than half of Vermeer’s paintings on canvas retain their original tacking edges.⁵ In a discussion of standard seventeenth-century strip widths used by Vermeer (whichrange from 67 to 118 cm), three paintings are noted as having (had) selvedges: The Procuress (L03) across the top and Young Woman with a Wine Glass (L10) and View of Delft (L12) on both the right and left sides.⁶ Selvedge remains on the left side of The Art of Painting (L26) as well.⁷ Three – The Procuress (L03), Young Woman with a Wine Glass (L10), and The Art of Painting (L26) – of these four paintings have weft snake indicators.

In the angle map of the vertical threads of The Procuress (L03) the weft snake indicator is vertical and about one-tenth of the painting’s width from the right edge. About one-third of the height up from the bottom is a crinkled horizontal crease that is weaker than the vertical artifact and crosses the entire painting. This horizontal line of angle fluctuation is a seam – not a weft snake. The presence of a seam joining two pieces of canvas is quite visible in the vertical thread density map in the upper right of figure [4]. The vertical weft snake indicator in the top portion does not cross the seambecause the bottom portion was not originally one piece with the top portion in the current configuration of the two pieces as the painting support. The vertical weft snake indicator in The Procuress (L03) is perpendicular to the direction of the selvedge along the top edge, which is in the direction of the warp. Thus, this weft snake indicator is undeniably in the weft direction, as it should be.

For Young Woman with a Wine Glass (L10) in figure [5] three horizontal weft snake indicators traverse the painting canvas between about one-third of the way down from the top and the middle of the canvas, as visible in figure [6]. A horizontal weft snake indicator appears about one-third of the way down from the top of The Art of Painting (L26). In both Young Woman with a Wine Glass (L10) and The Art of Painting (L26), the horizontal weft snake indicator is perpendicular to the vertical selvedge and therefore is in the weft direction.

1
Woman with a Lute X-radiograph (left) and Close-up (right) Revealing Wiggling Threads.

2
Thread Angle Maps of Weave-Matching Gang of Four: Woman Writing a Letter, with Her Maid, upper left, Woman with a Lute below Woman Writing a Letter, with Her Maid, Woman with a Pearl Necklace to the right of Woman with a Lute, Woman Holding a Balance below Woman with a Pearl Necklace.

3
Excerpt from figure 2 of Weft Snake Indicator Running Through Woman with a Lute and Woman with a Pearl Necklace and Marked by Arrows.

4
Weave Maps of The Procuress (from 0.5 cm evaluation squares centered on 0.25 cm grid).

A warp-weft indicator occurring infrequently in Vermeer’s paintings is a seam joining two pieces of canvas parallel to the warp thread direction. Thus, the smaller dimension of the painting is larger than the weft-width of the original canvas roll. The seam is typically made by adjoining the two pieces along their selvedges.⁸ Thus, the vertical seam in Christ in the House of Martha and Mary (L02) indicates that its vertical threads are the warp threads. Furthermore, its 160 cm height exceeds all (weft-dimension) strip widths found for Vermeer.⁹

A more common test, which can be performed on all canvases, relies on the observation that the variability in the thread count in the weft direction is more than that in the warp direction,¹⁰ which can be automated with a standard deviation calculation.¹¹ From our computation of the thread count in the hundreds of small evaluation squares covering a painting, we can compute the standard deviation of these local counts for the two thread directions. According to this test, the direction with the larger standard deviation is a candidate for the weft direction. Confidence in this designation is reduced as the separation of the two standard deviations shrinks. Furthermore, the utility of an algorithmically computed local average can be weakened when the image condition introduces interference that adds noise to the computed thread count values. The speckled appearance of the pertinent thread angle maps, for example for Woman with a Lute (L14) in figure 2 in § 6.1, is one example where the standard deviation calculation conceivably could be improved by further signal processing.

A new method of warp-weft designation is offered via weave maps with the discovery of a sufficient number of interrelated weave matches that, when combined, form a collection of rollmates. If the larger dimension of a weave matching group, such as in figure 7 in § 6.1, exceeds all reasonable strip widthsand the smaller dimension does not, the direction of the larger dimension is presumed to be the direction of the warp threads. The width of the group (around 100 cm in figure 7 in § 6.1) corresponds to a strip width of approximately 1.5 el,¹² while the height of over 160 cm of the group in figure 7 in § 6.1 exceeds all strip widths found for Vermeer’s canvases, and therefore is not considered the weft direction.¹³ Thus, the vertical direction in figure 7 in § 6.1 is deemed the warp direction.

Applying the same logic regarding size to the two tall (that is aligned vertically) weave match pairs The Geographer (L27) - The Astronomer (L28) and Young Woman Standing at a Virginal (L33) - Young Woman Seated at a Virginal (L34) is inconclusive. Interestingly, these four paintings are essentially all the same size, and the two pairs have similar average thread counts as indicated in table 1 in § 6.1 that are on the borderline of qualifying as a count match between the two pairs. With both pairs aligned as indicated in table 2 in § 6.1, their longest dimension is just over 100 cm. This is within the range of strip widths used by Vermeer ¹⁴ and corresponds to a standard width of 1.5 el.¹⁵ Therefore, vertical need not be the warp direction for these two pairs. If it were, it would be compatible with the horizontal weft snake indicators observed in Young Woman Standing at a Virginal (L33) and Young Woman Seated at a Virginal (L34). Neither The Geographer (L27) nor The Astronomer (L28) have weft snake indicators.

Table 1 lists all of the weft snake indicators observed in the angle maps of all of Vermeer’s paintings on canvas.

The standard deviations in the thread counts are also recorded. The direction of selvedge, when known, is indicated. The entry for the one painting – The Procuress (L03) – with a seam among those in table 1 includes the seam’s orientation. All other paintings exhibit no (prominent) weft snake indicators. They are deemed not present in Christ in the House of Martha and Mary (L02), A Maid Asleep (L04), The Milkmaid (L07), The Glass of Wine (L08), The Little Street (L11), View of Delft (L12), Woman at the Virginal with a Gentleman (L15), Woman Holding a Balance (L19), A Lady Writing (L20), Mistress and Maid (L21), Girl with a Pearl Earring (L22), Study of a Young Woman (L23), The Geographer (L27), The Astronomer (L28), The Lacemaker (L29), Woman Writing a Letter, with Her Maid (L31), The Guitar Player (L35), and Young Woman Seated at a Virginal (L36).

In the case of The Love Letter (L30) the angle maps suffer from too much interference to confidently locate weft snake indicators.

As noted earlier, the weft snake indicators found in The Procuress (L03) and Young Woman with a Wine Glass (L10) agree with the warp-weft implications of selvedge. By the standard deviation (std) ‘rule’ the higher std indicates the weft, which is horizontal for The Procuress (L03) and Young Woman with a Wine Glass (L10). For The Procuress (L03) this contradicts the vertical weft direction established by the existence of the horizontal selvedge. The std-selected weft direction as horizontal in Young Woman with a Wine Glass (L10) agrees with that implied by the vertical selvedge.

Table 1
Paintings with Weft Snake Indicators.

We have verified the canvas warp-weft designation of nine of Vermeer’s paintings with the use of selvedge and size examination. From selvedge information, we know that horizontal is the warp direction in The Procuress (L03) and vertical is the warp in Young Woman with a Wine Glass (L10), A View of Delft (L12), and The Art of Painting (L26). From the point of view of available strip widths found to be used by Vermeer, the size of the interrelated group in figure 6 in § 6.1, horizontal is the warp in Woman with a Lute (L14), Woman with a Pearl Necklace (L18), and Woman Holding a Balance (L19), and vertical is the warp in Woman Writing a Letter, with Her Maid (L31). Similarly, in Christ in the House of Martha and Mary (L02) vertical is the warp. Five of these nine paintings, for which the warp direction is known, have weft snake indicators, all of which are in the appropriate (weft)direction: The Procuress (L03) vertical, Young Woman with a Wine Glass (L10) horizontal, Woman with a Lute (L14) vertical, Woman with a Pearl Necklace (L18) vertical, and The Art of Painting (L26) horizontal. In four (The Procuress (L03), Woman with a Lute (L14), Woman with a Pearl Necklace (L18), and The Art of Painting (L26)) of these seven cases, the standard deviation test for warp-weft designation (with the higher std indicating weft) fails. Of the other four cases where the warp direction is known but no weft snake indicators are observed, the std method is right once Woman holding a Balance (L19), wrong twice (Christ in the House of Martha and Mary (L02) and Woman Writing a Letter, with Her Maid (L31)), and once View of Delft (L12) too close to call.

The dataset of X-radiographs of Vermeer’s paintings presents an opportunity to assess the utility of the weft snake indicators arising in thread angle maps. Do all weft snake indicators in table 4 correspond to bundles of wiggly threads? Can weft snake indicators appear in thread angle maps due to other weaving flaws than that of a pinching weft thread?¹⁶ Are weft snake indicators always right about the warp-weft designation? Is the occurrence of weft snake indicators in approximately 40% of Vermeer’s canvases typical for canvases used by artists in the Netherlands during the seventeenth century?