Joshi, Shantanu; Srivastava, Anuj; Mio, Washington; Liu, Xiuwen Hierarchical organization of shapes for efficient retrieval. (English) Zbl 1098.68785 Pajdla, Tomáš (ed.) et al., Computer vision – ECCV 2004. 8th European conference on computer vision, Prague, Czech Republic, May 11–14, 2004. Proceedings, Part III. Berlin: Springer (ISBN 3-540-21982-X/pbk). Lecture Notes in Computer Science 3023, 570-581 (2004). Summary: This paper presents a geometric approach to perform: (i) hierarchical clustering of imaged objects according to the shapes of their boundaries, and (ii) testing of observed shapes for classification. An intrinsic metric on nonlinear, infinite-dimensional shape space, obtained using geodesic lengths, is used for clustering. This analysis is landmark free, does not require embedding shapes in \(\mathbb{R}^2\), and uses ordinary differential equations for flows (as opposed to partial differential equations). Intrinsic analysis also leads to well defined shape statistics such as means and covariances, and is computationally efficient. Clustering is performed in a hierarchical fashion. At any level of hierarchy clusters are generated using a minimum dispersion criterion and an MCMC-type search algorithm. Cluster means become elements to be clustered at the next level. Gaussian models on tangent spaces are used to pose binary or multiple hypothesis tests for classifying observed shapes. Hierarchical clustering and shape testing combine to form an efficient tool for shape retrieval from a large database of shapes. For databases with \(n\) shapes, the searches are performed using \(\log(n)\) tests on average. Examples are presented for demonstrating these tools using shapes from Kimia shape database and the Surrey fish database.For the entire collection see [Zbl 1050.68004]. Cited in 1 Document MSC: 68T45 Machine vision and scene understanding PDFBibTeX XMLCite \textit{S. Joshi} et al., Lect. Notes Comput. Sci. 3023, 570--581 (2004; Zbl 1098.68785) Full Text: DOI