In this paper, we analyze and test three theories of 3-D shape perception: (1) Helmholtizian theory, which assumes that perception of the shape of an object involves reconstructing Euclidean structure of the object (up to size scaling) from the object's retinal image after taking into account the object's orientation relative to the observer, (2) Gibsonian theory, which assumes that shape perception involves invariants (projective or affine) computed directly from the object's retinal image, and (3) perspective invariants theory, which assumes that shape perception involves a new kind of invariants of perspective transformation. Predictions of these three theories were tested in four experiments. In the first experiment, we showed that reliable discrimination between a perspective and nonperspective image of a random polygon is possible even when information only about the contour of the image is present. In the second experiment, we showed that discrimination performance did not benefit from the presence of a textured surface, providing information about the 3-D orientation of the polygon, and that the subjects could not reliably discriminate between the 3-D orientation of textured surface and that of a shape. In the third experiment, we compared discrimination for solid shapes that either had flat contours (cuboids) or did not have visible flat contours (cylinders). The discrimination was very reliable in the case of cuboids but not in the case of cylinders. In the fourth experiment, we tested the effectiveness of planar motion in perception of distances and showed that the discrimination threshold was large and similar to thresholds when other cues to 3-D orientation were used. All these results support perspective invariants as a model of 3-D shape perception.
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[Show abstract][Hide abstract] ABSTRACT: When a planar shape is viewed obliquely, it is deformed by a perspective deformation. If the visual system were to pick up
geometrical invariants from such projections, these would necessarily be invariant under the wider class of projective transformations.
To what extent can the visual system tell the difference between perspective and nonperspective but still projective deformations
of shapes? To investigate this, observers were asked to indicate which of two test patterns most resembled a standard pattern.
The test patterns were related to the standard pattern by a perspective or projective transformation, or they were completely
unrelated. Performance was slightly better in a matching task with perspective and unrelated test patterns (92.6%) than in
a projective-random matching task (88.8%). In a direct comparison, participants had a small preference (58.5%) for the perspectively
related patterns over the projectively related ones. Preferences were based on the values of the transformation parameters
(slant and shear). Hence, perspective and projective transformations yielded perceptual differences, but they were not treated
in a categorically different manner by the human visual system.
[Show abstract][Hide abstract] ABSTRACT: In this paper we propose a new theory of the Gestalt law of good continuation. In this theory perceptual processes are modeled by an exponential pyramid algorithm. To test the new theory we performed three experiments. The subject's task was to detect a target (a set of dots arranged along a straight or curved line) among background dots. Detectability was high when: (a) the target was long; (b) the density of target dots relative to the density of background dots was large; (c) the local change of angle was small along the entire line; (d) local properties of the target were known to the subject. These results are consistent with our new model and they contradict prior models.
[Show abstract][Hide abstract] ABSTRACT: A group model of mental transformations based on the geometric model of P. B. Yale (1968, Geometry and symmetry, Holden-Day, San Francisco) was constructed for form recognition. The model consisted of nine characteristic subgroups of the similarity group in Euclidean space. With these subgroups, six series were formed, representing six visual paths for form recognition. Each series involved five characteristic subgroups. Six subframes were associated with nine characteristic subgroups in the model. These subframes were shape (angle measure), the sense, size (volume), verticality, uprightness, and position. The model was validated by an experiment, using reaction time as the behavior index. Since shape is the common invariant property of all subgroups of the similarity group, angle measure was not included in ordering of subframes. The findings show that the preservation of uprightness of a form provides the best condition for form recognition, followed by the preservation of sense and verticality of a form. While the effect of position is not strong, size has the weakest influence on space form recognition. Copyright 1999 Academic Press.
No preview · Article · Oct 1999 · Journal of Mathematical Psychology