On the convergence of planar curves under smoothing
IEEE Transactions on Image Processing
Curvature product corner detection in direct curvature scale space
International Journal of Computational Vision and Robotics
Original Articles: Time-scale energy based analysis of contours of real-world shapes
Mathematics and Computers in Simulation
Multiscale Corner Detection in Planar Shapes
Journal of Mathematical Imaging and Vision
Shape retrieval based on parabolically fitted curvature scale-space maps
IScIDE'12 Proceedings of the third Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
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The curvature scale-space (CSS) technique is suitable for extracting curvature features from objects with noisy boundaries. To detect corner points in a multiscale framework, Rattarangsi and Chin investigated the scale-space behavior of planar-curve corners. Unfortunately, their investigation was based on an incorrect assumption, viz., that planar curves have no shrinkage under evolution. In the present paper, this mistake is corrected. First, it is demonstrated that a planar curve may shrink nonuniformly as it evolves across increasing scales. Then, by taking into account the shrinkage effect of evolved curves, the CSS trajectory maps of various corner models are investigated and their properties are summarized. The scale-space trajectory of a corner may either persist, vanish, merge with a neighboring trajectory, or split into several trajectories. The scale-space trajectories of adjacent corners may attract each other when the corners have the same concavity, or repel each other when the corners have opposite concavities. Finally, we present a standard curvature measure for computing the CSS maps of digital curves, with which it is shown that planar-curve corners have consistent scale-space behavior in the digital case as in the continuous case.