Faithful Representation of Similarities among 3d Shapes in Human Vision

The human visual system possesses an impressive ability to remember and recognize complex three-dimensional shapes. The nature of the internal representations that underlie this ability, and the degree to which they mirror geometrical reality, are controversial 1, 2, 3]. According to some theories, the computational basis for shape representation is faithful encoding of structural 4] or metric 5] properties of individual objects and object classes. Other theories stress the representation of similarities between objects, rather than the geometry of each object in isolation 6, 7, 8]. We examined the psychophysical and computational plausibility of this latter approach to representation in a series of experiments, in which human subjects were confronted with a parametrically controlled family of animal-like 3D shapes. Following the experiments, the stimuli were arranged in a 2D metric space according to their perceived similarity, using multidimensional scaling (MDS) 9]. The resulting conngurations replicated the original arrangements of the stimuli in the parameter space, in accordance with the theory of faithful representation of similarity 6, 7, 8]. The shape of each animal-like stimulus was deened by a point in a common 70-dimensional parameter space (see Figure 1). Assuming that the response times and confusion rates are related systematically to the perceptual (representation-space) distances between the stimuli 10], we recovered the structure of the perceptual space using nonmetric MDS 11], and compared it with that of the objective parameter space, to assess the degree to which the former is a faithful representation of the latter. The planar and regular shape-space conngurations formed by the stimuli (Figure 1) were chosen to facilitate this comparison. The psychophysical data were gathered using three diierent methods for estimating perceived similarity. In the pairs of pairs comparison (cpp) experiments, the subjects diierentially rated pairwise similarity when confronted with two pairs of objects, each revolving in a separate window To whom correspondence should be addressed.