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Recognition of Shapes by Editing Shock Graphs Thomas B. Sebastian Philip N.Klein Benjamin B. Kimia Div. Of Engineering Brown University Dept. of Computer Science Brown University Div. Of Engineering Brown University Presented by Yuan Chen, Oct. 18, 2004 Outline Shock Graph Key ideas Partitioning the Shape Space Deformation Path Edit Distance Algorithm Results Shock Graph Medial axis: locus of centers of maximal circles that are bitangent to shape boundary. Shock Graph -- A variant of the medial axis -- With direction of flow -- Shock segment: medial axis segment with monotonic flow; a more refined partition of medial axis. Shock Graph Image courtesy of Thomas B. Sebastian et al, 2001. Shock Transitions • Boundaries between shape cells ( collection of shapes with same shock graph topology). Image courtesy of Thomas B. Sebastian et al, 2003. Key Ideas All shapes with the same shock graph topology are equivalent --- shape space partitioned All deformations with the same sequence of shock graph transitions are equivalent. The globally optimal transition sequence can be found in polynomial time. Partitioning the shape space Shape space is collection of all shapes. -- Shape is a point -- Shape deformation sequence is a path. -- Cost of optimal deformation sequence is distance from A to B. Image courtesy of Thomas B. Sebastian et al, 2001. Deformation Path Sequence of shock graph transitions. Shock graph transitions are formally classified and the complete list is known: Image courtesy of Thomas B. Sebastian et al, 2001. Deformation Path A shape deformation bundle is the set of deformation paths passing through the same set of shape cells. --- Discretization. Image courtesy of Thomas B. Sebastian et al, 2001. Deformation Path Avoid complexity-increasing deformation paths. Image courtesy of Thomas B. Sebastian et al, 2001. Edit Distance Algorithm Apply the edit distance approach to find the optimal path among all possibilities. – polynomial time. Image courtesy of Thomas B. Sebastian et al, 2001. Four Groups of Edit Operations Slice: Contract: Merge: deletes a shock branch and merges the remaining two. deletes a shock branch between degree-three nodes. combines two branches at a degree-two node. Deform: relates two shapes in the same shape cell. Images courtesy of Thomas B. Sebastian et al, 2001. Assigning costs to edit operations Derive the cost of the deform edit: Sum over local shape differences – differences between matching shock segment attributes. Other edit costs are considered to be limiting cases of a deform cost. Deform cost between shock segments Length differences of the boundary segments Curvature differences of boundary segments Difference in width of shape Difference in relative orientation of boundary segments Results The performance of shock-graph matching in the presence of commonly occurring visual transformations: ------- boundary perturbations articulation and deformation of parts shadow and highlights viewpoint variation scale partial occlusion Indexing results Boundary perturbations Shock computation is sensitive to boundary perturbations. But the cost of a splice in this case is very low. Articulations and deformation of parts Robust in the presence of articulation and deformation of part of the shape. Shadow and Highlights Shadow -- tend not to affect the shock graph topology Highlight – tend to be small Viewpoint variation Smooth changes are handled by deform edit Abrupt changes are handled by splices or contract edit Scale Can’t be handled. -- The shock-graph topology is not changed by scale. -- But the shock edge comparison is not scale invariant!! Partial Occlusion Small partial occlusion can be handled. Indexing results Handle small database very well: 9x11 and 8x12 To deal with large database: -- improve the efficiency of matching -- reduce the computational burden in the indexing scheme Thank You !