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Main Ideas

• The Shape Space: The collection of all shapes with the neighborhood topology determined by some class of local deformations.
   
• Two shapes can be related by an arbitrary defomation which continuously morphs the initial shape A until it eventually equals the second shape B.

• The distance between two shapes is defined as the cost of the optimal path.
   
• Deformation sequence is represented by a sequence of shock graphs.
   
• Need to account for the instabilities in the shock representation.
   

• Shape cell is the collection of shapes with the same shock graph topology.

• A transition takes the shape to a neighboring shape cell.
   
• A path between two shapes typically pass through many shape cells.
   
• Deformation path bundle is the set of paths that pass through the same shape cells.

Edit distance to find the optimal sequence in polynomial time. 

Example edit sequences

• Fish-to-fish

   
  

• Dog-to-cat

  

• Plane-to-plane

  

Matching Results

Matching in the presence of visual transformations

Database results

Database I (9 categories, 11 shapes)

Database II  (18 categories, 12 shapes)

Indexing using user sketches

Perceptual Grouping

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Last update: Oct. 23, 2001