• Shock-graph matching for some shapes
• Robustness to transformation
• Boundary perturbations
• Articulation and deformation of parts
• Viewpoint variation
• Segmentation errors
• Partial occlusion
• Indexing results
• Shape database
• MPEG-7 database
• Fish database

Shock-Graph Matching Results

• Shock-graph matching  gives intuitive correspondences for a variety of shapes

Robustness to Visual Transformations

• The medial axis is sensitive to boundary perturbations, which introduce spurious edges in the graph

• Typically tackled by regularization during the detection process or post-detection

• Here regularization is an integral part of the recognition process

• The shock graph inherently segments a shape into parts  and captures the hierarchical relationship between them

• Hence it is robust to changes which may occur in some of the parts

• Most viewpoint changes cause the spatial location and shape of parts to change; handled by deform edit

• At certain views,  there is a appearance/disappearance of a part; handled by the splice edit

• A change in aspect is handled by the contract edit

• Shadows and highlights often lead to segmentation errors in figure-ground segregation

• Occluder blends with the shape

• Occluder blends with the background

• Extra objects; (rider on horse)

Indexing into shape databases

• Shape database

The first database (99 shapes) has nine categories (fish, rabbit, airplane, ``greeble'', tool, hand, doll, four-legged animal, and sea-animal) eleven shapes in each category

Acknowledgements: Mike Tarr, Farzin Mokhtarian, Stan Sclaroff

• Each shape is matched against all other shapes

• Top 15 matches for a few shapes ordered by edit distance

• Results quantified in terms of top 10 matches from same category
 

	1	2	3	4	5	6	7	8	9	10
%	100	100	100	99	99	99	97	96	95	87

• Top three matches are always correct
Top
• MPEG-7 test database: selected 216 shapes from eighteen categories with twelve shapes each

• Top 15 matches for a few shapes ordered by edit distance

• Results are quantified in terms of top 11 matches being in the same category

• Top three matches are always correct

• Fish database (F. Mokhtarian)

• 105 fish outlines, 90 in core database, 15 queries

• Each query shape is matched against all shapes in the database

• Results show that shock graph matching can make fine distinctions