Summary
Based upon the geometric approach to clustering outlined in [KSMJ04], this paper presents an application to hierarchical clustering of imaged objects according to the shapes of their boundaries. The shape-distance used in clustering is an intrinsic metric on a nonlinear, infinite-dimensional shape space, obtained using geodesic lengths defined on the manifold. This analysis is landmark free, does not require embedding shapes in ℝ2, and uses ODES for flows (as opposed to PDEs). 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 is employed to ensure near-optimal configurations. The Hierarchical clustering potentially forms an efficient (O(1og n) searches) tool for retrieval from shape databases.
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Joshi, S.H., Srivastava, A. (2006). Applications of Shape-Distance Metric to Clustering Shape-Databases. In: Hager, W.W., Huang, SJ., Pardalos, P.M., Prokopyev, O.A. (eds) Multiscale Optimization Methods and Applications. Nonconvex Optimization and Its Applications, vol 82. Springer, Boston, MA. https://doi.org/10.1007/0-387-29550-X_14
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DOI: https://doi.org/10.1007/0-387-29550-X_14
Publisher Name: Springer, Boston, MA
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