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Hierarchical Organization of Shapes for Efficient Retrieval

Hierarchical Organization of Shapes for Efficient Retrieval. Victoria Choi EN161 Final Project Initial Presentation November 5, 2004. Overview. Motivation Algorithm Results Action Plan Sources. Motivation. Characterization of complex objects using their contours

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Hierarchical Organization of Shapes for Efficient Retrieval

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  1. Hierarchical Organization of Shapes for Efficient Retrieval Victoria Choi EN161 Final Project Initial Presentation November 5, 2004

  2. Overview • Motivation • Algorithm • Results • Action Plan • Sources

  3. Motivation • Characterization of complex objects using their contours • Common approaches study objects using discrete collection of points (e.g. ‘landmark-based’ analysis), mapping or functions • Increase efficiency by improving database searches in systems with shape-based queries

  4. Motivation

  5. Algorithm: Background • Geodesic paths between shapes • Utilises minimum energy to bend one shape into another • Cluster shapes according to minimum pairwise geodesic distances • Generate tree using Karcher mean

  6. Algorithm: Clustering • Minimum-Variance Clustering • Goal: minimise average distance-square Q within clusters • Utilises Markov chain Monte Carlo (MCMC) search process • Start with calculating pairwise geodesic distances among all shape • Randomly distribute shapes in clusters • With equal probability: • (1) move a shape or • (2) swap two shapes • Repeat above step for a predefined number of iterations

  7. Algorithm: Clustering

  8. Algorithm:Tree-generation • Objects are organized according to coarser differences at top levels and finer differences at lower levels • Bottom-up construction • Start with all shapes at lowest level • After clustering, compute a mean shape for each cluster and cluster them at the upper level • Repeat until the top of the tree is reached • Karcher mean is utilised to compute mean shapes

  9. Algorithm:Tree-generation

  10. Results of Shape Retrieval

  11. Project Plan • now-11/12: confirm database and other information availability, gather necessary resources, implement clustering algorithm • 11/12-11/19: implement tree-generation algorithm • 11/19-11/23: implement shape retrieval algorithm • 11/23-end: testing/debugging, presentation preparation

  12. Sources • Hierarchical Organization of Shapes for Efficient Retrieval –- Joshi, Srivastava, Mio, and Liu • Statistical Shape Analysis: Clustering, Learning and Testing –- Srivastava, Joshi, Mio, and Liu (extension of above paper) • Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces – Klassen, Srivastava, Mio, and Joshi

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