Parts of Visual Objects: An Experimental Test of the Minima Rule

Abstract

Three experiments were conducted to test Hoffman and Richards's (1984) hypothesis that, for purposes of visual recognition, the human visual system divides three-dimensional shapes into parts at negative minima of curvature. In the first two experiments, subjects observed a simulated object (surface of revolution) rotating about a vertical axis, followed by a display of four alternative parts. They were asked to select a part that was from the object. Two of the four parts were divided at negative minima of curvature and two at positive maxima. When both a minima part and a maxima part from the object were presented on each trial (experiment 1), most of the correct responses were minima parts (101 versus 55). When only one part from the object--either a minima part or a maxima part--was shown on each trial (experiment 2), accuracy on trials with correct minima parts and correct maxima parts did not differ significantly. However, some subjects indicated that they reversed figure and ground, thereby changing maxima parts into minima parts. In experiment 3, subjects marked apparent part boundaries. 81% of these marks indicated minima parts, 10% of the marks indicated maxima parts, and 9% of the marks were at other positions. These results provide converging evidence, from two different methods, which supports Hoffman and Richard's minima rule.

Discrimination of 3-D shape and 3-D curvature from motion in active vision

“…Computing a ratio of two curvatures in different directions and then comparing it with another ratio at a different time is a rather complex task for the visual system, but we cannot discard this hypothesis on the basis of the results of the present experiment. In fact, there have been reports that the human visual system is quite able to use complex geometric quantities such as lines of minimal curvature in constructing global shape (Braunstein, Hoffman, & Saidpour, 1989). The present experiment indicates that principal curvatures could be used in the perception of local shape.…”

Selective attention to the parts of an object

“…On the one hand, because the attributes may be coded with respect to the part or object (e.g., the gap is coded to the left or right of the crossbar), selection could occur from a late, object-based representation (or structural description) that codes parts relative to an object's geometry in a non-PART-BASED ATTENTION 307 spatial format. On the other hand, selection could be mediated through an array format (or spatiotopic) representation, in which the parts are coded in terms of their spatial locations; the parts could be delimited from one another by stimulus level cues, such as concave cusps or minima of curvature (Braunstein, Hoffman, & Saidpour, 1989;Gibson, 1994;Hoffman & Richards, 1984;Hoffman & Singh, 1997;Stevens & Brooks, 1988). The representation that is selected from is likely to be influenced by many factors, including the task that subjects perform (Vecera & Farah, 1994), so an "either-or" answer may not be possible.…”

Processing convexity and concavity along a 2-D contour: figure–ground, structural shape, and attention

“…The sequence was the reverse of the memory task used by Braunstein et al (1989). Instead of seeing the object and then one part that may have come from it, observers first saw a segment and then had to decide whether the segment was present in the silhouette.…”

“…Many empirical studies have tested this proposal or, at least, interpreted their findings in the light of the minima rule. Braunstein, Hoffman, and Saidpour (1989) presented participants with a surface defined by dots and rotating about a vertical axis. This was followed by a display of four alternative parts.…”