Hierarchical Organization of Shapes for Efficient Retrieval

1
Hierarchical Organization of Shapes for Efficient
Retrieval

• Victoria Choi
• EN161 Project Final Presentation
• December 17, 2004

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Project Goal

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

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Algorithm Clustering

• Variance (average distance-squared within a
  cluster)
• Moving Shapes
• Swapping Shapes

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Algorithm Tree Generation

• Generate nodes for level above by calculating a
  unique mean shape
• Cluster nodes with a predefined number of
  clusters
• Repeat until there is only one cluster on the
  level and calculate the mean shape as the head
  node

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More on Clustering

• Number of clusters is crucial to
  performance/speed
• More clusters if clusters are not clearly defined
  by distances
• Cooling Schedule
• Not important for original implementation
  (calculating probabilities for all possible
  choices and choosing the maximum)
• Crucial for latter implementation (generate
  random probability and execute action if
  probability calculated is greater)
• Both implementations give comparable results

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For 10 clusters

• bat09, bird01, bird02, bird07, truck01, truck03,
  truck04, truck10
• bird05, bird06, cattle04, cattle05
• bird03, bird04, bird08, bird09, bird10, truck06
• key01, key04, key07, key08, lmfish06, lmfish09,
  truck08, truck09, watch01, watch02, watch03,
  watch04, watch05, watch06, watch07, watch08,
  watch09, watch10
• rat01, rat02, rat03, rat04, rat05, rat06, rat07,
  rat08, rat09, rat10
• key02, key03, key05, key06, key09, key10,
  pocket01, pocket02, pocket03, pocket04, pocket05,
  pocket06, pocket07, pocket08, pocket10
• bat01, bat02, bat03, bat04, bat05, bat06, bat07,
  bat08, bat10
• apple01, apple02, apple03, apple04, apple05,
  apple06, apple07, apple08, apple09, apple10,
  pocket09
• cattle01, cattle02, cattle03, cattle06, cattle07,
  cattle08, cattle09, cattle10
• lmfish01, lmfish02, lmfish03, lmfish04, lmfish05,
  lmfish07, lmfish08, lmfish10, truck02, truck05

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For 18 clusters

• key03, key05, key06, key09, key10, lmfish06,
  lmfish09, watch05, watch07
• lmfish03, truck02, truck03, truck04, truck06,
  truck08
• cattle01, cattle02, cattle03
• bird07, bird08, bird09, bird10
• cattle06, cattle07, cattle08, cattle09, cattle10
• rat03, rat04, rat05, rat06, rat09
• bird01, bird02
• key01, key04, key07, key08, watch01, watch02,
  watch03, watch05, watch06, watch08, watch09,
  watch10
• key02, pocket01, pocket02, pocket03, pocket04,
  pocket05, pocket06, pocket07, pocket08, pocket09,
  pocket10
• rat01, rat02, rat07, rat08, rat10
• apple05, apple08, apple09
• apple01, apple02, apple03, apple04, apple06,
  apple07, apple10
• bird03, bird04, bird05, bird06
• cattle04, cattle05
• bat01, bat02, bat03, bat06, bat06, bat07, bat09,
  bat10
• lmfish01, lmfish02, lmfish05, lmfish07, lmfish08,
  lmfish10
• bat04, bat05, bat08
• lmfish04, truck01, truck05, truck07, truck09,
  truck10

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For 20 clusters

• apple03, apple04, apple05, apple10
• key08, lmfish09, watch01, watch02, watch03,
  watch05, watch06, watch07, watch08, watch09,
  watch10
• bat01, bat06, bat07, bat09, bat10
• bat02, bat03, bird09
• rat01, rat02, rat08
• cattle01, cattle02, cattle03
• lmfish01, lmfish02, lmfish05, lmfish08, lmfish10
• bird01, truck01, truck03
• bat04, bat05, bat08
• rat05, rat06, rat09
• cattle04, cattle05
• rat03, rat04, rat07, rat10
• cattle06, cattle07, cattle08, cattle09, cattle10
• truck02, truck04, truck05, truck06, truck07,
  truck08, truck09, truck10
• lmfish03, lmfish04, lmfish06, lmfish07, watch04
• key01, key02, key03, key04, key05, key06, key07,
  key09, key10
• apple01, pocket01, pocket02, pocket03, pocket04,
  pocket05, pocket06, pocket07, pocket08, pocket09,
  pocket10
• apple02, apple06, apple07, apple08, apple09
• bird02, bird07, bird08, bird10

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Problem with Clustering

• key08, lmfish09, watch01, watch02, watch03,
  watch05, watch06, watch07, watch08, watch09,
  watch10
• Need more distinguished distances

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Geodesic Distances 10 clusters

• B2, I3
• D3, I1, I2, I4, I5
• C2, C3, D1
• A3, C1, F1, F2, F3
• G1, G3, G4, G5, H1, H2, H3, H4, H5
• C4, C5, D2
• B1, D5
• E2, E3, E4, E5, F4, F5
• D4, G2
• A1, A2, A4, A5, B3, B4, B5, E1

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Geodesic Distances 18 clusters

• D1, D4
• E1, F4, F5
• G2
• E2, E3, E4
• C1, C2
• C3
• I3
• G5, H3, H4, H5
• B2, D3
• I1, I2, I4, I5
• E5, F1, F2, F3
• B1
• C5
• C4, D2
• A2, A3, B4, B5
• A1, A4, A5, B3
• G1, G3, G4, H1, H2
• D5

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Even more problematic

• Results worse than with the other set of
  distances
• Distances definition between sets not distinct
  enough
• Large errors in geodesic distance calculation

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Tree Generation

• No Karcher mean averaging function
• Large errors in geodesic distances would make
  Karcher mean function error-prone
• To visualize the tree generation algorithm, we
  use a 2-D plot
• Each point on the plot would represent a shape
  with the distances from other points the
  distances from other shapes
• Assumption distance calculation and mean shape
  generation algorithms that works really well

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Starting with 5 clusters
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Building the tree
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Searching for a Node
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With 10 clusters
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Optimal Cluster Number

• The number of clusters at each level is
  important.
• At each level, the more clusters, the more
  accurate the algorithm will be
• But this will also increase the number of levels,
  thus sacrificing speed
• Currently dividing the number of clusters by 2 to
  get the number for the above level

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Improvements

• Develop algorithms which provide a sound
  implementation of shape distance, mean shape
  calculations and shape matching
• Calculate optimal cluster number for each level
• Faster implementation (??)

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Thank you for your time!

• Questions?
• Comments?