Hierarchical Organization of Shapes for Efficient Retrieval

1
Hierarchical Organization of Shapes for Efficient
Retrieval

• Victoria Choi
• EN161 Final Project Mid-Presentation
• November 22, 2004

2
Overview of Project

• Organize shapes in a data structure for search
  efficiency
• Cluster shapes in minimum variance clusters
  randomly (implemented)
• Build tree structure from calculating mean shape
  of each cluster

3
Change of plans

• The paper uses geodesic distances to determine
  minimum variance during the clustering and
  Karcher means
• Nhons project is on geodesic distances and
  averaging using Karcher means
• Focus on clustering and building tree structure
  using distances available in the lab and then
  compare

4
Algorithm Clustering

• Minimum-Variance Clustering
• Goal minimise average distance-square Q within
  clusters
• Utilises Markov chain Monte Carlo (MCMC) search
  process
• Start with calculating distances among all shape
  (already available)
• 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

5
Algorithm Clustering

• What is Q?
• Cost function associated with moving one element
  from one cluster to another
• In other words, the average distance-squared
  within the cluster

6
Algorithm Clustering

• Moving shapes
• Select a shape randomly and re-assign it to
  another cluster with probability P if the shape
  is not a singleton

7
Algorithm Clustering

• Swapping shapes
• Select two shapes from two different clusters
  randomly and swap them with probability P
• Q(1) and Q(2) are the Q-values of the original
  configuration and the new configuration

8
Random Clustering

9
After 10000 iterations

• cluster 1
• apple01bat05, bat06, cattle05, cattle06
• cluster 2
• bird03, bird08, bird09, cattle01, lmfish05,
  lmfish09, truck03, truck05, truck10, watch01
• cluster 3
• apple04, apple05, apple09, apple10, truck04,
  truck07, truck08
• cluster 4
• bird02, lmfish02, lmfish03, lmfish06, lmfish08,
  pocket01, truck02, truck06
• cluster 5
• key02, key03, key04, key05, key08, key08, key09,
  key10, lmfish01, lmfish04, lmfish07, lmfish10,
  truck09, watch02, watch03, watch05, watch06,
  watch07, watch08, watch09, watch10
• cluster 6
• rat02, rat03, rat04, rat05, rat06, rat07, rat08,
  rat09, rat10, truck01
• cluster 7
• cattle02, cattle03, cattle04, cattle07, cattle08,
  cattle09, cattle10, key01
• cluster 8
• apple06, bird04, bird05, bird06, bird07
• cluster 9
• apple02, apple03, apple07, apple08, bat01, key05,
  key06, key07, pocket02, pocket03, pocket04,
  pocket05, pocket06, pocket07, pocket08, pocket09,
  pocket10, rat01
• cluster 10

10
Whats Next?

• Improve algorithm by testing with different
  number of clusters and iterations
• Play around with definition of P
• Generate tree by implementing shape averaging
• Test and compare results with using geodesic
  distances and Karcher means