Features of the Representation Space for 3-D Objects

To explore the nature of the representation space of 3-D objects, we studied human performance in forced-choice classification of objects composed of four geon-like parts, emanating from a common centre. The two class prototypes were distinguished by qualitative contrasts (cross-section shape; bulge/waist), and by metric parameters (degree of bulge/waist, taper ratio). Subjects were trained to discriminate between the two prototypes (shown briefly, from a number of viewpoints, in stereo) in a 1-interval forced-choice task, until they reached a 90% correct-response performance level. In experiment 1, eleven subjects were tested on shapes obtained by varying the prototypical parameters both orthogonally (Ortho), and in parallel (Para) to the line connecting the prototypes in the parameter space. For the eight subjects who performed above chance, the error rate increased with the Ortho parameter-space displacement between the stimulus and the corresponding prototype: F_1,68=3.6, p<0.06 (the effect of the Para displacement was marginal). Clearly, the parameter-space location of the stimuli mattered more than the qualitative contrasts (which were always present). To find out whether both prototypes or just the nearest neighbour of the test shape influenced the decision, in experiment 2 eight new subjects were tested on a fixed set of shapes, while the test-stage distance between the two classes assumed one of three values (Far, Intermediate, or Near). For the six subjects who performed above chance, the error rate (on physically identical stimuli) in the Near condition was higher than in the other two conditions: F_1,89=3.7, p<0.06. The results of the two experiments contradict the prediction of theories that postulate exclusive reliance on qualitative contrasts, and support the notion of a metric representation space with the subjects' performance determined by distances to more than one reference point or prototype (cf Edelman, 1995 Minds and Machines 5 45 – 68).