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Shape Correspondence through Landmark Sliding

Shape Correspondence through Landmark Sliding. Anup Kedia. Introduction. Shape Landmarks. Contd. Landmark Sliding Shape Correspondence Result. Need. Statistical Shape Analysis Accuracy. Different types of Shapes. Supports closed, open, self-crossing and multiple shapes. Input.

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Shape Correspondence through Landmark Sliding

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  1. Shape Correspondence through Landmark Sliding Anup Kedia Anup Kedia

  2. Introduction • Shape • Landmarks

  3. Contd.. • Landmark Sliding • Shape Correspondence • Result

  4. Need • Statistical Shape Analysis • Accuracy

  5. Different types of Shapes • Supports closed, open, self-crossing and multiple shapes.

  6. Input • Landmarks of template shape • Landmarks of target shape • The shape is open or closed

  7. Contd.. • The parameters are is the curve length from u(0) to u(t) s|L is the curve length from v(0) to v(s) a|b  modulus operation GOAL : To find s = {s0 , s1 , … sn-1 } such that the shape ‘V’ (target) from it corresponds well to the template shape.

  8. Problem • How to represent the shape? • We use Catmull Rom Splines since • They are smooth • They interpolate the landmarks.

  9. Problem • How to represent and initialize the landmarks? We manually label the landmarks s.t • The no. of landmarks are same • The starting pt. is approximately the same. i.e , we roughly correspond the landmarks manually.

  10. Contd..

  11. Problem • If a landmark moves beyond its neighbours? We add a constraint

  12. Goal • We try to minimize the cost function, Ø(s) = d(U,V) + λR(s) d(U,V) -> landmark based shape difference R(s) -> representation Error λ -> Regularization Factor

  13. Contd.. L  Thin Plate matrix λ= 10-3 in our experiments

  14. Experiment

  15. Open Shapes • For open curves, we • Fix the end points • Remove segment between the first and last point while calculating R(s).

  16. Experiment for open shapes

  17. Multiple Curves • ‘L’ is calculated taking all the curves. • R(s) is calculated seperately for each curve.

  18. Experiment for multiple curves

  19. Multiple Shape Correspondence • We have a set of samples We have to find an average shape to which all the shapes corresponds well. • We do it by • Taking average of all the shapes using procustes analysis • Slide the shapes w.r.t to the average shape • Repeat the above process.

  20. Experiment

  21. Conclusion • Works for all types of shapes • It considers both global shape deformation and local geometric features unlike the previous methods.

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