1. Shape Matching with Occlusion in Image Databases Aristeidis Diplaros Euripides G.M. Petrakis Evangelos Milios Technical University of Crete

2. = Given a shape database, retrieve shapes which are similar to an example shape. = Shape matching is the central problem of shape retrieval. = How similar? Problem description

3. Methodology = Main idea: Merging of a "noisy" sequence of segments and matching with one or more segments of the other shape. Merging of 3 segments of the upper curve And matching with one segment of the lower curve

4. = B-spline approximation. = Curvature: = Inflections points are given by k(u)=0. = Segments with k>0 are convex (C). = Segments with k<0 are concave (V). = The shape is transformed to a sequence of segments VCVC.

5. Shape A Dynamic Programming Table i 2 1 1 2 3 Shape B j = transitions = matching of segments. = simple or compound transitions.

6. Shape Á i 2 1 1 2 3 Shape  j = No matching of C with V. = CVC...C -> C and VCV...V-> V. = Only half of the cells are filled with values.

7. = Matching cases

8. = The DP table consists of three distinct areas: = Initialization area (the first row) - filled with : = Termination area (the last row) – all complete paths end at cells in this area. = Computation area (the remaining rows)

9. = For each "accessible" cell we calculate the matching cost as: = Where: = Constant ë: = small ë favours merging. = large ë prevents merging.

10. = Three features are calculated for each segment: = l = arc length. = S = area between the chord and the arc. = ₩ = the angle traversed by the tangent to the segment.

11. Experimental results " Two datasets: " 1000 closed shaped " 1500 open shapes " 20 queries. " Precision / recall diagrams. " Human relevance judgments. " Demonstrate the superiority of our method over traditional shape matching method based on Fourier and Moments

12. Example

13. Closed dataset

14. Open dataset

15. Conclusions = Our approach handles occluded, noisy or deformed shapes and is independent of translation, scale, rotation, starting point selection and symmetric transformations of shapes. = Our evaluation indicates that our approach is well suited to shape matching and retrieval.