Abstract
In the physical environment familiar size is an effective depth cue because the distance from the eye to an object equals the ratio of its physical size to its angular extent in the visual field. Such simple geometrical relations do not apply to pictorial space, since the eye itself is not in pictorial space, and consequently the notion “distance from the eye” is meaningless. Nevertheless, relative size in the picture plane is often used by visual artists to suggest depth differences. The depth domain has no natural origin, nor a natural unit; thus only ratios of depth differences could have an invariant significance. We investigate whether the pictorial relative size cue yields coherent depth structures in pictorial spaces. Specifically, we measure the depth differences for all pairs of points in a 20-point configuration in pictorial space, and we account for these observations through 19 independent parameters (the depths of the points modulo an arbitrary offset), with no meaningful residuals. We discuss a simple formal framework that allows one to handle individual differences. We also compare the depth scale obtained by way of this method with depth scales obtained in totally different ways, finding generally good agreement.
Highlights
“Familiar size” is perhaps the best known depth cue (Berkeley 1709)
The size ratios are converted into 190 depth differences, and a standard procedure is run to find the 20 depth values, always under the constraint that the average depth equals zero
From the 20 depth values we find 190 “explained” depth differences, and the standard deviation of the mismatches from the observed depth difference values is taken as a measure of the coherence of the result
Summary
“Familiar size” is perhaps the best known depth cue (Berkeley 1709). It is the basis of stadimetry,(1) which has been—and occasionally still is—of military importance in range estimates for gunnery. When the absolute size (as in the case of people) is not available, one may still use the size cue whenever multiple instances of some kind of object are simultaneously detected. In this case the size cue yields ratios of distances It suffices that the objects are merely statistically similar, common instances are trees or barns in a landscape. An interesting example is Thebaid, attributed to Gherardo Starnina, painted in 1410 In such pictures things do not change in pictorial size as they recede, with castles in the foreground smaller than huts in the background, people larger than bridges, etc (see Figure 1a). Such pictures still have a well developed pictorial space due to other cues. These are instances where the size cue remains ineffective
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