Similarity measures and comparison metrics for image shapes
Yu. V. Vizilter, Sergey Yu. Zheltov · Journal of Computer and Systems Sciences International · 2014
The problem of defining the procedure of morphological comparison of mosaic shapes consistent with the Pyt’ev morphological image-to-shape comparison is discussed. Four different techniques for constructing such a procedure are studied, which are based on the search for critical points of the morphological correlation coefficient, on the analysis of properties of superposition of projectors onto shapes, on the estimation of the angle aperture between shapes considered as subspaces of the space of images, and on the Hausdorff metric between shape manifolds projected onto a unit hypersphere. For all the techniques, measures of similarity or dissimilarity of mosaic shapes are obtained independently. The similarity measures based on the first two approaches (morphological shape correlation coefficients) turned out to be identical, while the two other techniques resulted in the dissimilarity measures that are related to the morphological correlation shape coefficient with one-to-one dependences.