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Anthony D. D'Antona, Wilson S. Geisler; Optimal Contour Interpolation Using Natural Scene Statistics. Journal of Vision 2013;13(9):1239. doi: 10.1167/13.9.1239.
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© ARVO (1962-2015); The Authors (2016-present)
Retinal images are two-dimensional projections of three-dimensional scenes, and therefore the contours of many objects in a scene are partially occluded. Contour occlusions create two difficult tasks for visual systems: 1) determining which visible contour elements belong to the same object (contour grouping and contour integration), and 2) determining the shapes of contours between visible contour elements (contour interpolation). Here, we focus on contour interpolation. Given two spatially separated contour elements with known orientations, we use the statistics of contours in natural scenes to determine the optimal estimate of the contour shape connecting these elements. Contour data was sampled from a database of natural image contours. Each contour was rotated and scaled into common coordinates, and then resampled to a fixed number of points. These standardized contours were binned by the orientations of the two end contour elements. For each bin, principle component analysis (PCA) was performed on every contour within that bin. For almost every bin, the first three principal components accounted for over 90% of the variance. All contours in a given bin were projected onto these first three components, resulting in a 3D cloud of PCA coefficients representing the shapes of all the contours in that bin. In this PCA representation, the centroid of the distribution of PCA coefficients specifies the Bayesian optimal (minimum mean squared error) estimate of contour shape. These statistics characterize the information present in natural images for determining contour shape using only local, spatially separated contour elements. Our results provide principled predictions for interpreting the results of previous contour interpolation studies and future experiments. Importantly, we find that contour shapes in natural images (excluding long contours containing sharp changes in orientation) are well characterized by only three dimensions, once the orientations at the two ends of the contour are specified.
Meeting abstract presented at VSS 2013
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