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In this paper, we derive new shape descriptors based on a directional characterization. The main idea is to study the behavior of the shape neighborhood under family of transformations. We obtain a description invariant with respect to rotation, reflection, translation and scaling. We consider family of volume-preserving transformations. Our descriptor is based on the volume of the neighbourhood of transformed image. A well-defined metric is then proposed on the associated feature space. We show the continuity of this metric. Some results on shape retrieval are provided on Kimia 216 and part of MPEG-7 CE-Shape-1 databases to show the accuracy of the proposed shape metric.

Shape Descriptor Based on the Volume of Transformed Image Boundary