Corner detection in curvilinear dot grouping.
Corners, or discontinuities in orientation, are one of the most salient and useful properties of contours. But how sensitive are we in detecting them, and what does this sensitivity imply about the processes by which corners can be detected. In this paper we address both of these questions, starting with the observation that changing the sampling phase of a curve changes the geometry of its discrete trace, or the set of discrete (retinotopic) points onto which the curve projects. This motivates our stimuli--dotted curves--and our experimental design: if curves are represented by dots, the placement of the dots effects whether or not corners are perceived. Specifically, we present quantitative data on sensitivity to discontinuities as a function of dot phase, and address its theoretical explanation within a two-stage model of orientation selection. Curvature plays a key role in this model, and, finally, the model and experimental data are brought together by showing that a very coarse approximation to change in curvature (or differences in local curvature estimates) is sufficient to account for the psychophysical data on sensitivity to discontinuities.