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Symmetry Axis

Symmetry Axis. Occlusion. Articulation. Stretching. Stretching. Symmetry Axis. Shape. Shape Axis (SA). SA-Tree. Shape Representation via Self-Similarity work of Liu, Kohn and Geiger. A variational shape representation model based on self-similarity of shapes.

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Symmetry Axis

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  1. Symmetry Axis Occlusion Articulation Stretching Stretching Symmetry Axis Computer Vision

  2. Shape Shape Axis (SA) SA-Tree Computer Vision

  3. Shape Representation via Self-Similarity work of Liu, Kohn and Geiger • A variational shape representation model based on self-similarity of shapes. • For each shape contour, first compute its shape axis then derive a unique shape-axis-tree (SA-tree) or shape-axis-forest (SA-forest) representation. Shape Contour Shape Axis (SA) SA-Tree Computer Vision

  4. counterclockwise clockwise The Insight • Use two different parameterizations to compute the represention of a shape. • Construct a cost functional to measure the goodness of a match between the two parameterizations. • The cost functional is decided by the self-similarity criteria. • Useful self-similarity criteria include symmetry, parallelism (translation), convexity and distance. Computer Vision

  5. Parameterized Shapes • Two different parameterizations: counterclockwise clockwise with • When the curve is closed we have Computer Vision

  6. Co-Circularity Cost Functional/Energy Density Computer Vision

  7. Cost Functional/Energy Density • Structural properties • Symmetric • Geometrical properties • Translation invariant • Rotation invariant • Self-Similarity properties Computer Vision

  8. A Dynamic Programming Solution Computer Vision

  9. A Dynamic Programming Solution Computer Vision

  10. Shape Shape Axis SA-Tree Experimental Results for Closed Shapes Computer Vision

  11. Shape Shape Axis (SA) SA-Tree Experimental Results for Open Shapes Computer Vision

  12. Experimental Results for Open Shapes Shape Axis (SA) SA-Forest Computer Vision

  13. Matching Trees with deletions and merges for articulation and occlusions Computer Vision

  14. Convexity v.s. Symmetry White Convex Region Black Convex Region Computer Vision

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