Internal representation of two-dimensional shape.

The psychological space of shapes has been studied in many experiments. However, how shapes are represented in the brain has not been a major issue in psychological literature. Here, the characteristics of internal representation and how it was formed have been considered and an attempt has been made to explain the results of experiments in a unified manner. First, the data of similarity of alphabetic characters and random-dot patterns were reexamined. Multivariate analysis suggested that those patterns were represented by the combination of global features. Second, three-layer neural networks were trained to perform categorization or identity transformation of the same sets of patterns as used in psychological experiments, and activation patterns of the hidden units were analyzed. When the network learned categorization of the patterns, its internal representation was not similar to the representation suggested by psychological experiments. But a network which learned identity transformation of the patterns could acquire such an internal representation. The transformation performed by this kind of network is similar to principal-component analysis in that it projects the input image onto a lower-dimensional space. From these results it is proposed that two-dimensional shapes are represented in human brain by a process like principal-component analysis. This idea is compatible with the findings in neurophysiological studies about higher visual areas.