On the psychophysics of the shape triangle

We earlier introduced an approach to categorical shape description based on the singularities (shocks) of curve evolution equations. We now consider t he simplest compositions of shocks, and show that they lead to three classe s of parametrically ordered shape sequences, organized along the sides of a shape triangle. By conducting several psychophysical experiments we demons trate that shock-based descriptions are predictive of performance in shape perception. Most significantly, the experiments reveal a fundamental differ ence between perceptual effects dominated by when shocks form with respect to one another, versus those dominated by where they form. The shock-based theory provides a foundation for unifying tasks as diverse as shape bisecti on, recognition, and categorization. (C) 2001 Elsevier Science Ltd. All rig hts reserved.