A novel approach to polygonal approximation of digital curves
Journal of Visual Communication and Image Representation
Fast, accurate and convergent tangent estimation on digital contours
Image and Vision Computing
Optimized polygonal approximation by dominant point deletion
Pattern Recognition
Dominant point detection by reverse polygonization of digital curves
Image and Vision Computing
Polygonal approximation of digital planar curves through break point suppression
Pattern Recognition
Analysis and comparative evaluation of discrete tangent estimators
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Mathematical and Computer Modelling: An International Journal
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This paper introduces a new theory for the tangential deflection and curvature of plane discrete curves. Our theory applies to discrete data in either rectangular boundary coordinate or chain coded formats: its rationale is drawn from the statistical and geometric properties associated with the eigenvalue-eigenvector structure of sample covariance matrices. Specifically, we prove that the nonzero entry of the commutator of a piar of scatter matrices constructed from discrete arcs is related to the angle between their eigenspaces. And further, we show that this entry is-in certain limiting cases-also proportional to the analytical curvature of the plane curve from which the discrete data are drawn. These results lend a sound theoretical basis to the notions of discrete curvature and tangential deflection; and moreover, they provide a means for computationally efficient implementation of algorithms which use these ideas in various image processing contexts. As a concrete example, we develop the commutator vertex detection (CVD) algorithm, which identifies the location of vertices in shape data based on excessive cummulative tangential deflection; and we compare its performance to several well established corner detectors that utilize the alternative strategy of finding (approximate) curvature extrema.