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Matching of shapes bound by freeform curves

M. Ramanathan Department of Engineering Design Indian Institute of Technology Madras. Matching of shapes bound by freeform curves. Shape Matching. A problem that finds similar shape to the query one. Prominent inputs include 3D models, images, curves . Approaches used. Global properties

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Matching of shapes bound by freeform curves

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  1. M. Ramanathan Department of Engineering Design Indian Institute of Technology Madras Matching of shapes bound by freeform curves Department of Engineering Design, IIT Madras

  2. Shape Matching • A problem that finds similar shape to the query one. • Prominent inputs include 3D models, images, curves. Department of Engineering Design, IIT Madras

  3. Approaches used • Global properties • Manifold learning • Local properties such as shape diameter • For silhouettes - skeletal context, contour-based descriptor, region-based, graph-based. Department of Engineering Design, IIT Madras

  4. Skeletal-based approaches • Graph-based • Part-based • Skeletal graph, shock graph, Reeb graph Department of Engineering Design, IIT Madras

  5. Main Contribution • Alternate scheme to component-based or part-based approach typically used in skeleton-based shape matching which calls for identification of correspondences between shapes – a complex task by itself. • Statistical-based skeleton property matching has been proposed and demonstrated. • Footpoints, the corresponding points for a point on MA, appear to have been a neglected entity so far in matching, have been employed to define one of the shape functions. Department of Engineering Design, IIT Madras

  6. Definition of Medial Axis (MA) • MA is the locus of points inside domain D which lie at the centers of all closed discs (or balls in three dimensions) which are maximal (contained in D but is not a proper subset of any other disc (or ball)) in D, together with the limit points of this locus. • The radius function of the MA of D is a continuous, real-valued function defined on M(D) whose value at each point on the MA is equal to the radius of the associated maximal disc or ball. Department of Engineering Design, IIT Madras

  7. Examples of MA Department of Engineering Design, IIT Madras

  8. Properties of MA • Symmetry information • One to one correspondence • Rigid-body transformation • Homotopy • Deriving Shape functions Department of Engineering Design, IIT Madras

  9. Algorithm for shape matching Department of Engineering Design, IIT Madras

  10. Shape functions and signature • Shape function derived from MA are • Distance between footpoints (DF) • Radius function at a point on MA (RF) • Curvature at a point on MA (CF) • Shape signature – normalized value of the shape functions, 64-bin histogram • Broad idea is to replace the graph-based approach with statistics-based one. Department of Engineering Design, IIT Madras

  11. Distance function (DF) Department of Engineering Design, IIT Madras

  12. Radius function (RF) Department of Engineering Design, IIT Madras

  13. Curvature function (CF) Department of Engineering Design, IIT Madras

  14. RF and CF Department of Engineering Design, IIT Madras

  15. Similarity Measurement • Given two shape signatures, its similarity can be computed using distance measures such as χ2, Minkowski’s LN, Mahalanobis. • For its simplicity, L2 has been employed. Department of Engineering Design, IIT Madras

  16. Database details Department of Engineering Design, IIT Madras

  17. Models in the database Partially similar MA is vastly different for similar shape Department of Engineering Design, IIT Madras

  18. Retrieval results for DF All airplanes are retrieved in the first Row. Department of Engineering Design, IIT Madras

  19. Retrieval results for RF Gear is retrieved at least in the second Row. Department of Engineering Design, IIT Madras

  20. Retrieval results for CF All brackets are retrieved in the first Row. Department of Engineering Design, IIT Madras

  21. First ten results for DF Department of Engineering Design, IIT Madras

  22. First ten results for RF Department of Engineering Design, IIT Madras

  23. First ten results for CF Department of Engineering Design, IIT Madras

  24. First and second tier DF RF Department of Engineering Design, IIT Madras

  25. First and second tier CF Department of Engineering Design, IIT Madras

  26. Interpretation • The classes ‘airplane’, and ‘bracket’ have performed really well. • L-shaped (ell) – it suffers in DF and RF. With CF, it showed good improvements (‘ell’ contains shapes that are of non-uniformly scaled ones, which affect DF and RF, but not CF that much.) Department of Engineering Design, IIT Madras

  27. Interpretation (contd.) • The class ‘rect’ suffered in CF since it zero curvature. • The class ‘bird’ also suffers because it contains a shape with hole and also a shape that is only partially similar. However, the good point here is that, when the shape with hole is given as query, similar non-holed shape is also retrieved Department of Engineering Design, IIT Madras

  28. Robustness Retrieval results for 0.02 sample size Department of Engineering Design, IIT Madras

  29. Computation Time Department of Engineering Design, IIT Madras

  30. Comparsion • Princeton Shape Benchmark, Engineering shape Benchmark • No freeform dataset available . Closest one Kimia dataset, silhouette in the form of images T. Sebastian, P. Klein, and B. Kimia. Recognition of shapes by editing their shock graphs. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 26(5):550–571, May 2004. Department of Engineering Design, IIT Madras

  31. Comparsion(contd.) • Shape geodesics method • Uses Bull’s eye test • Top 40 most similar shapes are retrieved. • Second tier results are comparable to our method. • Inner-distance method • Retrieval results are comparable • ID requires alignment • Shapes need to be articulated variants. Department of Engineering Design, IIT Madras

  32. Strengths and Limitations • The strength of this method is, though at times the MA structure can vary significantly, similarities are captured. • The method is very fast. • Signatures are global in nature – partial shape matching not possible. • Accuracy relies on the computation of MA • Spatial distribution is not considered. Department of Engineering Design, IIT Madras

  33. Future work • Suitable weighting scheme. • Visual saliency and other measures. • Creation of freeform database. • Homotopy property of MA has to be explored. Department of Engineering Design, IIT Madras

  34. Conclusions • A statistical-based skeleton property matching has been proposed and demonstrated. • Shape functions have been derived from the MA of curved boundaries. • This has the potential to replace component-based or part-based approach typically used in skeleton-based shape matching method. Department of Engineering Design, IIT Madras

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