S hape Matching and Classification Using Height Functions

1. Shape Matching and Classification Using Height Functions Xide Xia ENGN 2560 Advisor: Prof. Kimia Project Initial Presentation

2. Shape Matching: object recognition, character recognition, medical image and protein analysis … • Geometric Transformations (translation, rotation, scaling, etc.) • Nonlinear Deformations (noise, articulation and occlusion)

4. Steps: • 1) Shape descriptor with height functions • 2) Similarity measure using the height descriptor

5. Shape descriptor with height functions: • A sequence of equidistant sample points X: X={Xi} , i=1,2,….,N • Tangent line Li: its direction is always starting from Xi-1 to Xi+1 • Height value Hi: the symboled distance between the jth (j = 1,. . . ,N) sample point Xj and the tangent line Li is defined as a height value hi,j.

6. (the height value of the jth sample point Xj according to the reference axis Li of the point Xi)

7. Descriptor Hi： • the direction of the reference axis Li • the location of the sample point Xi on the shape contour X.

9. Smoothed height values: F is an M *N matrix with column i being the shape descriptor Fi of the sample point Xi.

10. Local nomalization: Consequently, the value of each entry in the matrix F after normalization is in the interval [-1, 1].

11. Similarity measure using the height descriptor: In shape recognition, we usually compute a shape similarity or dissimilarity (distance) to find the optimal correspondence of contour points. Dynamic Programming (DP) algorithm to find the correspondence The shape dissimilarity: the sum of the distances of the corresponding points.

12. The cost (distance) of matching p and q: • Weight coefficient • Dissimilarity between the two shapes: Given two shapes X and Y. With DP we compute an optimal correspondence x to y that the is minimal.

13. Humans are generally more sensitive to contour deformations when the complexity of the contour is lower! • Shape complexity: where std denotes the standard deviation.

14. The dissimilarity or distance between two shapes X, Y normalized by their shape complexity values: where the factor is used to avoid divide-by-zero.

15. Shape descriptor with height functions: • A sequence of equidistant sample points X • Tangent line Li • Height value Hi • Smoothed height values • Local nomalization Similarity measure using the height descriptor: • The cost (distance) of matching p and q • Weight coefficient • Dissimilarity between the two shapes • Shape complexity • Dissimilarity normalized by complexity values

16. Schedule: • 1st week: Learn the algorithm well • 2nd ~3th week: Write up the codes of the shape descriptor part • 4th ~5th week: Write up the codes of the matching part • 6th~7th week: Debug and Test in different datasets, Make Comparison with other shape matching algorithm (Shock Graphs) • 8th week: Make conclusion, Prepare for the final presentation

17. Thank you