On Nonrigid Shape Similarity and Correspondence

An important operation in geometry processing is finding the correspondences between pairs of shapes. The Gromov-Hausdorff distance, a measure of dissimilarity between metric spaces, has been found to be highly useful for nonrigid shape comparison. Here, we explore the applicability of related shape similarity measures to the problem of shape correspondence, adopting spectral type distances. We propose to evaluate the spectral kernel distance, the spectral embedding distance and the novel spectral quasi-conformal distance, comparing the manifolds from different viewpoints. By matching the shapes in the spectral domain, important attributes of surface structure are being aligned. For the purpose of testing our ideas, we introduce a fully automatic framework for finding intrinsic correspondence between two shapes. The proposed method achieves state-of-the-art results on the Princeton isometric shape matching protocol applied, as usual, to the TOSCA and SCAPE benchmarks

Word Image Matching Based on Hausdorff Distances

Hausdorff distance (HD) and its modifications provides one of the best approaches for matching of binary images. This paper proposes a formalism generalizing almost all of these HD based methods. Numerical experiments for searching words in binary text images are carried out with old Bulgarian typewritten text, printed Bulgarian Chrestomathy from 1884 and Slavonic manuscript from 1574

Hausdorff distances for searching in binary text images

Hausdorff distance (HD) seems the most efficient instrument for measuring how far two compact non-empty subsets of a metric space are from each other. This paper considers the possibilities provided by HD and some of its modifications used recently by many authors for resemblance between binary text images. Summarizing part of the existing word image matching methods, relied on HD, we investigate a new similar parameterized method which contains almost all of them as particular cases. Numerical experiments for searching words in binary text images are carried out with 333 pages of old Bulgarian typewritten text, 200 printed pages of Bulgarian Chrestomathy from year 1884, and 200 handwritten pages of Slavonic manuscript from year 1574. They outline how the parameters must be set in order to use the advantages of the proposed method for the purposes of word matching in scanned document images

Text Search in Document Images Based on Hausdorff Distance Measures

The Hausdorff type distances between the sets of points on the plane are the commonly used similarity measures for binary images. In this work we present several such measures in a unified manner and introduce a new, naturally arisen variant of Hausdorff distance. The matching performance of all similarity measures is compared by computer experiments, using real word images from a scanned book