Hierarchical Organization of Shapes for Efficient Retrieval

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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

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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

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Motivation

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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

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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

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Algorithm Clustering
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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

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Algorithm Tree-generation

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Results of Shape Retrieval

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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

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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