Computer Vision, Graphics, and Image Processing
Symmetry-curvature duality
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Cited by (100)
Characterizing projective geometry of binocular visual space by Möbius transformation
2019, Journal of Mathematical PsychologyCitation Excerpt :Affine geometry defines the parallelism of contours (or segments of contour) of an object viewed under different perspective conditions. Leyton (1987b), based on his earlier work on local symmetric axis (the symmetry-curvature duality theorem, Leyton, 1987a), proposed a description by Lie group action on the object’s symmetric axis as a general way of achieving different shapes corresponding to the same object. He demonstrated how a combination of simple “stretch”, “shear”, and “rotation” operations (which themselves form appropriate subgroups) will result in the positive general linear transformation group acting on the object plane, with the parameters of the subgroups completely characterizing the shape of the object under affine transformations (but not involving mirror reflection).
Skeletonization and its applications - a review
2017, Skeletonization: Theory, Methods and ApplicationsNoise-resistant Digital Euclidean Connected Skeleton for graph-based shape matching
2015, Journal of Visual Communication and Image RepresentationCitation Excerpt :Moreover, to obtain effective and pertinent matchings in the context of reals objects, it is necessary to construct skeletons robust to noise. Note that this last property is rarely satisfied by the algorithms of the literature, for which the slightest deformation of the border usually generates a branch [4]. Let us consider now skeletonization algorithms.
On the generation and pruning of skeletons using generalized Voronoi diagrams
2012, Pattern Recognition LettersMedial axis transform of a planar domain with infinite curvature boundary points
2012, Computer Aided Geometric Design