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The problems of estimating the position of an illuminant and the direction of illumination in realist paintings
have been addressed using algorithms from computer vision. These algorithms fall into two general categories: In
model-independent methods (cast-shadow analysis, occluding-contour analysis, ...), one does not need to know
or assume the three-dimensional shapes of the objects in the scene. In model-dependent methods (shape-fromshading,
full computer graphics synthesis, ...), one does need to know or assume the three-dimensional shapes.
We explore the intermediate- or weak-model condition, where the three-dimensional object rendered is so simple
one can very confidently assume its three-dimensional shape and, further, that this shape admits an analytic
derivation of the appearance model. Specifically, we can assume that floors and walls are flat and that they
are horizontal and vertical, respectively. We derived the maximum-likelihood estimator for the two-dimensional
spatial location of a point source in an image as a function of the pattern of brightness (or grayscale value) over
such a planar surface. We applied our methods to two paintings of the Baroque, paintings for which the question
of the illuminant position is of interest to art historians: Georges de la Tour's Christ in the carpenter's studio
(1645) and Caravaggio's The calling of St. Matthew (1599-1600). Our analyses show that a single point source
(somewhat near to the depicted candle) is a slightly better explanation of the pattern of brightness on the floor
in Christ than are two point sources, one in place of each of the figures. The luminance pattern on the rear wall
in The calling implies the source is local, a few meters outside the picture frame-not the infinitely distant sun.
Both results are consistent with previous rebuttals of the recent art historical claim that these paintings were
executed by means of tracing optically projected images. Our method is the first application of such weak-model
methods for inferring the location of illuminants in realist paintings and should find use in other questions in
the history of art.
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