Georges de la Tour, Christ in the carpenter's studio

Georges de la Tour was deeply influenced by Caravaggio's pronounced chiaroscuro, or enhanced light and dark, and his Christ in the carpenter's studio in the Louvre is an excellent example of his nocturne oeuvre. The painting is so realistic to Hockney that he believes it was executed using optical projections. Because a candle does not produce enough light to yield a visible image, Hockney is led to claim that the light souce was "outside the picture," or "in place of the other figure" (i.e., in place of Christ when St. Joseph was painted and in place of St. Joseph when Christ was painted). The question is then, is the light "in place of the other figure" as claimed by Hockney, or elsewhere, specifically the location of the candle, the place Hockney explicitly rejects.

Techniques from computer vision have been applied to this question, with absolutely clear, consistent and unequivocal results.

Cast-shadow analysis

The simplest method is cast-shadow analysis. One merely draws a line from a point on a shadow through its associated point on the occluder. Extended, this line will pass through the light source.

Consider the clearest and most unambiguous cast shadow in the entire tableau: that of St. Joseph's left hand on the beam below. Incidentally, this shadow is almost the exact shape of the actual hand, is the appropriate size, is connected the same direction (to the left) and there is no other object that could possibly have cast that shadow. A straight line from that shadow, through its corresponding occluder (St. Joseph's hand) leads directly to the candle—not to Christ and certainly not "outside the picture." A whole set of such cast-shadow lines agree quite well with the candle, not with Christ. (Only one such line goes through Christ.)

Occluding-contour analysis

A sophisticated technique from computer vision determines the direction of illumination based on the subtle pattern of lightness along an outer boundary or "occluding contour" of an object. When this method was applied to the de la Tour tableau, each "half" of the painting showed the light source was very close to the candle, not "in place of the other figure.

Computer graphics modelling

Computer graphics modeling of tableaus is a powerful method for understanding an artist's working methods. Stork and Furuichi built a full model and adjusted the position of the virtual illuminant until the rendered image matched the painting as closely as possible. When the virtual illuminant was in place of the candle, the rendered image matched the painting quite well; when the light was "in place of the other figure," the rendered image differed significantly from the actual painting. These results rebutted Hockney's claim.

Analysis of lighting on planar surfaces

Stork showed how to infer the position of a point source based on the pattern of illumination over a planar surface of uniform albedo. In this way he and Kale showed that the illuminant in the de la Tour was likely near the candle, rather than "in place of the other figure," though the locations were not as close to those points as those determined by cast-shadow analysis and occluding-contour analysis.

What does this mean?

These new rigorous techniques, adapted from forensic photography, show promise for a number of problems in art history far beyond Hockney's claims. They will help scholars identify when different subjects in a tableau were executed under different studio conditions, and this, in turn, may help us determine the number of artists—the "hands"—responsible for a given painting. A different approach, based on brush stroke analysis, has helped determine the number of "hands" in the execution of The holy family by Perugino.