The extraction of shape primitives such as lines and curves from images is an important problem in the research of visual perception. The mechanism of grouping edge components of image into curves has been extensively explored in previous studies on perceptual organization. Co-circularity is a tendency of edge pixels to lie on a curve with regular curvature, or a circular arc. Field et al. proposed association field , a visual cortex model that explains the perceptual organization based on co-circularity. Conventional biological models of curve extraction [2, 3, 4] are based on association field. However, they have shown limited ability to discriminate strict circular arcs from long and salient curves since association field is not tuned to specific curvature. We propose a novel visual cortex model that groups the detected edge pixels into circular arcs. The core of the proposed method is to overcome the limitation of association field in detecting circular arcs by adding delicate inhibitions and co-linearity constraints. An oscillatory network  with the proposed neural connectivity groups edge pixels on a circular arc by synchronization of neural oscillation. The proposed network is robust against clutters and partial damage of edge pixels in real images. In addition, slight modifications to the network enable to perceive random curves and straight lines. This work provides a computational model on how the interaction between low-level image elements builds up meaningful high level image representations in visual perception.
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