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Taekyu Kwon, Yunfeng Li, Michael Scheessele, Aaron Michaux, Zygmunt Pizlo; Spatially-global interpolation of closed curves. Journal of Vision 2014;14(10):68. doi: https://doi.org/10.1167/14.10.68.
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© ARVO (1962-2015); The Authors (2016-present)
Most previous methods focused on spatially local interpolation using rules such as proximity, co-linearity, co-circularity and relatability. We propose a spatially global model based on finding the shortest path in the log-polar representation of the image which is a good approximation to the topographical map of the retina in the area V1. The shortest path in a log-polar representation corresponds to a smooth, convex and closed curve in the retinal image. As such, our method implements two fundamental rules of Gestalt perceptual organization: closure and good continuation. The subject was shown a fragmented convex polygon (target) embedded in noise consisting of 300 line segments. A random polygon was generated as a convex hull of 10 randomly generated points. To minimize spatially local cues, the pairwise distances of the contour fragments in the target were randomized. Furthermore, the orientation of each contour fragment of the target was randomly perturbed by +/- 10 to 30 deg. Two subjects were asked to reconstruct the target by clicking the mouse on the line segments perceived as forming the target. The model was applied to the same stimuli. Both the subject and the model started the reconstruction at a line segment that was longer than other line segments. The subjects reconstructed the targets very reliably and the model produced closed contours that matched the ground truth quite well. We conclude that the human visual system uses both spatially global and spatially local interpolation mechanisms. We view the task of contour interpolation as a combinatorial correspondence problem, which is analogous to other computationally hard correspondence problems in vision such as stereo, motion, recognition and symmetry. The plausibility of the shortest path model is supported by existing results showing that humans produce near-optimal solutions to shortest path and traveling salesman problems in linear time.
Meeting abstract presented at VSS 2014
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