From Curvature to Contour: Hierarchical Representations of Contour Shapes in Terms of Constant Curvature Segments

Introduction: We can discriminate a stunning variety of shapes. How does the visual system encode these different shapes? We investigated the hypothesis that the visual system forms hierarchically structured representations of contour shapes, based on primitives that represent segments of constant curvature (CC). This hypothesis implies that (i) in representing a contour, encoding of CC segments is obligatory; (ii) variation in CC segments will induce perceptible differences between contours; and (iii) CC segments can be organized perceptually into higher-order parts. Experiments: In Experiment 1, we displayed contours made from two curvatures and two colors. The transition point for color was near to, but offset from, the transition point for curvature. We then presented the contour again, sometimes shifting the color transition point. When asked whether the coloring was different, participants were much less sensitive to shifts that aligned the color transition with the task-irrelevant curvature transition than to equivalent shifts that increased misalignment. In Experiment 2, we compared participants’ ability to discriminate between a contour fragment made of multiple curvatures and one made of one curvature. Sensitivity was considerably higher when multi-curvature contours were predicted to be represented with multiple CC segments than with a single CC segment. In Experiment 3, we tested a hypothesis that CC segments with the same curvature polarity are represented as higher-order “parts” of a contour. Following Palmer (1977), we tested participants’ ability to say whether a contour fragment was part of a shape. Participants were significantly faster when the fragment was from a polarity-matched contour region. Performance using polarity-matched fragments was comparable to performance using segments between curvature minima. Conclusion: These experiments suggest that CC segments are obligatorily encoded in contour representation (Exp.1), that contour discrimination depends on encoded CC segments (Exp.2), and that CC segments organize together into higher-order units (Exp.3).