A news item caught my attention a short while ago with the headline “Did da Vinci create a 3D ‘Mona Lisa?'” It reports the discovery by Claus-Christian Carbon and Vera Hesslinger that a version of the Mona Lisa (alias La Gioconda) at the Prado in Madrid shows its subject from a slightly different angle than the better-known version at the Louvre in Paris. That finding suggests in turn that the two versions could have been created simultaneously by a pair artists working side by side, perhaps Leonardo da Vinci and one of his students. In an article entitled “Da Vinci’s Mona Lisa entering the next dimension” (here’s a link, with supporting material here), Carbon and Hesslinger state that “the two Giocondas together might represent the first stereoscopic image in world history.” Indeed, they speculate that the paintings may even have been intended to function as a stereoscopic pair, considering Leonardo’s documented interest in the phenomenon of binocular vision.
In addition to various intriguing descriptions, diagrams, and anaglyphs, Carbon and Hesslinger have treated us to a tweened animated GIF of the two Mona Lisas based on something called the “Fast Matlab Stereo Matching Algorithm by Wim Abbeloos.” This graphic illustration in particular attracted my attention because of my broader interest in the use of tweened animations to display historical stereoscopic images (see here and here). The actual tweening in Carbon and Hesslinger’s GIF is quite sophisticated—well beyond anything I know how to achieve myself. But at the same time, I’m not sure their animation explores the perspectival relationship between the two Giocondas as effectively as it could.
One issue is the focus of the animation—that is, the choice of corresponding points in the pair of images that are held stationary while other points are allowed to shift relative to them. Carbon and Hesslinger opt to focus simultaneously on the hands and face, the two elements that together also form the centerpiece of their analysis. From this, the impression I get personally is one of the subject inflating and deflating, while only the sitter’s hands and the arm of the chair present a plausible 3D effect. Meanwhile, the rendering of intermediary positions of other elements is problematic—note in particular the discontinuous “jump” in the treatment of the cloth running from the subject’s left shoulder down towards her lap. I’m afraid that people who casually judge the merits of Carbon and Hesslinger’s claim on the basis of looking at their animation, rather than on the rest of their carefully articulated analysis, might not be convinced.
But I find that changing the focus of the animation can enhance the resulting impression of depth and motion. Here, for example, is an animation I produced by taking the pair of side-by-side images presented by Carbon and Hesslinger “as is” (no rotation, no adjustment of scale) and focusing on the cloth over the subject’s left shoulder:
This animation admittedly lacks the technical sophistication and analytical framework of Carbon and Hesslinger’s animation, but for the image as a whole—as opposed to just the hands—I believe it yields a superior impression of three-dimensionality and horizontal shift of perspective (if that’s what we’re looking for). I’ve tried some alternative focus points, but I think this one may give the best illusion of depth we can achieve—that is, if we keep both images at their original size.
I’m inclined to believe the claim that the two paintings were created from two different vantage points, or at least that this is true of the underlying cartoons. That in itself would be a remarkable finding. However, I’m less won over by the hypothesis that the two paintings were intended as a stereoscopic pair. Carbon and Hesslinger have calculated angles for the horizontal discrepancies relevant to stereoscopy and have drawn up a nice schematic of the studio showing reconstructed horizontal positions for the subject and artists within it. But the news report about the discovery quotes an observation by cognitive psychologist Martin Arguin that disparities between the two versions of the figure are “largely oriented vertically, and not horizontally as would be required to replicate the left and right eye views.” Carbon and Hesslinger acknowledge this point, suggesting that the vertical disparities might have been an “unwanted spin-off from the specific positions the painters took.” But there’s another hypothesis that would explain both the vertical and horizontal disparities: namely, that the two versions were produced from different positions for some reason that had nothing to do with stereoscopic aspirations. Posing for a portrait was probably rather tedious and inconvenient; making a subsequent duplicate of a single portrait necessarily introduced a generation loss in the copy. Taking two portraits at once would thus have had a certain practical benefit. Or perhaps Leonardo wanted to try out a couple different perspectives and ended up liking both of them. Either way, it’s easy to imagine why the two portraits would have needed to be made at slightly different spots within his studio, and the spots are as likely to have varied vertically as they are to have varied horizontally.
And then there’s the background. As Carbon and Hesslinger acknowledge in “Da Vinci’s Mona Lisa entering the next dimension,” it was the rediscovery of the long-obscured background in the Prado version that drew attention to that version of the painting in the first place. In another article entitled “On the Nature of the Background Behind Mona Lisa,” they report that the background of the Prado version is “zoomed in” relative to the background of the Louvre version by a factor of just over 10% but is “statistically not different with regard to shape”—that is, “except for a deviation concerning the upper left part of the mountainside.” In other words, they assert that the two versions of the background don’t display any difference in perspective such as we’d expect of a real landscape; instead, one background is simply painted larger than the other. In their own animated GIF, the backdrop expands and contracts; but here’s an alternative animation I created in which the two versions of the backdrop are shown scaled to the same size (as nearly as I could manage, using the bases of the posts on the loggia as the point of reference) and the figure is allowed to change size relative to it:
Based on their bi-dimensional regression analysis, Carbon and Hesslinger conclude that the background was likely “a plane landscape motif painted on canvas” which might have hung behind the sitter in Leonardo’s studio, and not an actual landscape present behind the sitter. At one point they suggest that the artist of the Prado version “must have stood closer to the motif-canvas than did Leonardo” in order to account for the zooming in, while at another point they suggest that the outlines of the background were added separately, “using a different technique” than was used for the sitter.
But the above animation nudges me towards a different view. The background doesn’t simply “expand” at a constant rate from the Louvre version to the Prado version; if it did, all its parts ought to appear reasonably stationary when the two versions are adjusted to the same scale and superimposed. But the depictions of the cloth over the sitter’s left shoulder imply that the vantage point of the Louvre version was somewhat higher and more forward than the vantage point of the Prado version. The sill of the loggia, the angle of the bases of its columns, and the landscape stretching back at least as far as the water (whether “real” or painted on a canvas) can all be seen shifting spatially in ways that appear impressionistically to match that same displacement. Try to focus your attention simultaneously on the left shoulder cloth, the sill of the loggia, and the nearest portion of landscape, and see if these don’t feel as though they’re moving coherently together. They do for me. Perhaps someone else can pursue this point with more theoretical rigor than I have to see if a plausible set of vertical and horizontal coordinates and angles can be worked out for it.
I agree with Carbon and Hesslinger that the upper left mountainside stands out as an anomaly; in fact, the more distant background in general seems out of sync with the rest of the scene in my animation. Significantly, this anomalous part of the landscape is more or less the same part of it that is missing from the Isleworth Mona Lisa—yet another version of the painting, seemingly unfinished, with a somewhat controversial relationship to the Louvre version (see the website of the Mona Lisa Foundation for some of the arguments). So there’s other circumstantial evidence that only the part of the background that can be seen moving consistently with the sitter in my animation is “original” in some sense, although the actual landscape shown in the Isleworth version doesn’t line up well with the Louvre and Prado versions. Perhaps the anomaly reflects a mismatch between the actual vertical displacement of a background or backdrop during the original sitting and Leonardo’s sense of where he wanted the horizon to appear in the finished paintings.
Whether any portion of the backgrounds of the Louvre and Prado Mona Lisas represents a real landscape present during the sitting or not, one thing that’s clear is that these two backgrounds weren’t contrived to sustain a conventional stereoscopic effect when viewed in tandem. Note that details in the background are deflected up and down in my animation, and not left to right. The horizontal disparities are apparently minimal, while the vertical disparities are quite pronounced—and, I believe, perspectivally consistent with the vertical disparities seen in the depictions of the figure itself. Overall, the treatment of the background seems incompatible with an intentional stereoscopic experiment, but not with two portraits taken simultaneously in the interest of efficiency, or for some other reason.
In fact, the discrepancies between the two paintings as a whole seem fully consistent with someone leaning forward and backward, or standing up and sitting down. If I had to venture a hypothesis of my own about the two images based solely on these animation experiments rather than on bi-dimensional regression analysis, I’d suggest they were made from two vantage points that differed mostly in height and proximity to the sitter. So, for instance, Leonardo might have had two panels mounted one above the other, such that he had to stand on a stepstool, lean forward, and look downward when working on the top one. The resulting change in angle could, I suspect, account for the “stereoscopic” characteristics Carbon and Hesslinger detected in the hands.
In “Da Vinci’s Mona Lisa entering the next dimension,” Carbon and Hesslinger briefly and dismissively mention another alleged case of early stereoscopy, albeit not quite as early as the Mona Lisa: i.e., “the Chimenti sketches once misunderstood as being stereoscopic.” Jacopo Chimenti (ca. 1551-1640) drew two sketches of a man holding a plumb line which sparked a controversy back in the 1860s when it was claimed that they produced a stereoscopic effect when properly viewed together and must have been created with that use in mind. The article which Carbon and Hesslinger cite in connection with the Chimenti sketches—Nicholas J. Wade, “The Chimenti Controversy,” Perception 32 (2003): 185-200—is often perceived as having debunked that claim (or, really, as having pointed out that it had already been debunked in the 1860s). The basis for the debunking was, first, that although parts of the paired images appeared legitimately stereoscopic, they weren’t consistently stereoscopic, as shown by the presence of measurable vertical disparities alongside the expected horizontal ones; and, second, that any two attempts to copy the same image twice by hand will yield a slight “pseudoscopic” impression of three-dimensional relief if viewed in a stereoscope. Here’s an animation I’ve based on a photograph of the Chimenti sketches reprinted in Wade’s article, adjusting the two images so that the subject is shown at the same scale in both:
The effect of relief may be very imperfect, but at the same time it strikes me as too well coordinated to be the result of sheer chance in an attempt to make two copies of the same drawing. Indeed, the authority to whom Wade gives the final word in his article—Hermann von Helmholtz—wrote:
The two pictures of the man were certainly made from different positions, but I must admit that it seems to me very unlikely that Chimenti intended them for a stereoscopic experiment, because the stool, the dividers, and the plumb line, which could easily have been drawn correctly, are treated as unessentials and all drawn so irregularly and so differently that they cannot be combined. Had the artist desired to test a theory, it is more likely that he would have drawn the easy things correctly and the difficult parts, such as the man, more inaccurately.
I suspect that the Louvre and Prado Mona Lisas and the two Chimenti sketches may have a lot in common. Each pair of images appears to have been made of the same subject, but from different vantage points. Both pairs can be combined today to yield illusions of spatial depth. Neither pair of images was probably intended for that purpose, and neither gives a straightforward stereoscopic impression. But in my opinion that doesn’t make the effect any less interesting or impressive.
Update, June 3, 2015: Here’s a new and improved animation I created from the Louvre and Prado Mona Lisas using the morphing techniques described here.