This paper studies the properties of a new lower bound for the natural pseudo-distance. The natural pseudo-distance is a dissimilarity measure between shapes, where a shape is viewed as a topological space endowed with a real-valued continuous function. Measuring dissimilarity amounts to minimizing the change in the functions due to the application of homeomorphisms between topological spaces, with respect to the L ∞-norm. In order to obtain the lower bound, a suitable metric between size functions, called matching distance, is introduced. It compares size functions by solving an optimal matching problem between countable point sets. The matching distance is shown to be resistant to perturbations, implying that it is always smaller than the natural pseudo-distance. We also prove that the lower bound so obtained is sharp and cannot be improved by any other distance between size functions.

/pdf/natural-pseudo-distance-and-optimal-matching-between-reduced-4cm9relcft.pdf

Natural Pseudo-Distance and Optimal Matching between Reduced Size Functions

Detection and recognition of contour parts based on shape similarity

Optimal partial shape similarity

Order independent homotopic thinning for binary and grey tone anchored skeletons

Image Analysis and Computer Vision: 1998☆

Vision Geometry VIII

Vision Geometry VII

Vision Geometry VI

Vision Geometry X

Special issue: Shape Representation and Similarity for Image Databases

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