1. Mesh modeling and processing M. Ramanathan STTP CAD 2011Mesh modeling and processing

2. Mesh model Consists of only {V, E, F} Boundary meshes – represent 2D surfaces embed in 3D STTP CAD 2011Mesh modeling and processing

3. Characteristics Simple/Concise representation Aids faster visualization and exchange of data No geometry/topology information available Created using scanning or modeling softwares STTP CAD 2011Mesh modeling and processing

4. Mesh processing Mesh segmentation/decomposition Mesh model/shape matching Correspondence of mesh models STTP CAD 2011Mesh modeling and processing

5. Mesh segmentation Decomposing a mesh into meaningful components Part-type and surface-type are two prominent approaches STTP CAD 2011Mesh modeling and processing

6. Approaches for mesh segmentation Region growing Hierarchical clustering Iterative clustering Spectral analysis Implicit methods STTP CAD 2011Mesh modeling and processing

7. Mesh attributes STTP CAD 2011Mesh modeling and processing Minimum curvatureAverage geodesic distance Local shape diameter Difference between Normal directions

8. Region Growing Algorithm Initialize a priority queue Q of elements Loop until all elements are clustered Choose a seed element and insert to Q Create a cluster C from seed Loop until Q is empty –Get the next element s from Q –If s can be clustered into C Cluster s into C Insert s neighbours to Q Merge small clusters into neighbouring ones STTP CAD 2011Mesh modeling and processing

9. Clustering algorithm using prominent cross-sections compute local cross-sections spread over the mesh model can be defined as a cross-section of a local sweep passing through that point. STTP CAD 2011Mesh modeling and processing

10. Sectional Gauss map STTP CAD 2011Mesh modeling and processing

11. Algorithm to compute PCS STTP CAD 2011Mesh modeling and processing

12. PCS for different models STTP CAD 2011Mesh modeling and processing

13. Segmentation STTP CAD 2011Mesh modeling and processing

14. Segmentation of CAD models STTP CAD 2011Mesh modeling and processing (a) Fuzzy clustering (b) Feature point (c) Blowing bubbles (d) Plumber (e) Fitting primitives

15. Problem of matching Matching is the process of determining how similar two shapes are. STTP CAD 2011Mesh modeling and processing

16. Simple Definition Retrieve visually similar objects from a database using query object. … User Interface Query Object Database … Output

17. Taxonomy of shape matching methods STTP CAD 2011Mesh modeling and processing

18. D2 Shape distribution STTP CAD 2011Mesh modeling and processing D2 shape distributions of five tanks (gray curves) and six cars (black curves)

19. Skeletal graph matching STTP CAD 2011Mesh modeling and processing Skeletal graph matching with colors showing the node-to-node correspondence based uponthe topology and radial distance about the edge

20. View-based similarity STTP CAD 2011Mesh modeling and processing Extraction of the lightfield descriptor for a chair model

21. Local diameter function STTP CAD 2011Mesh modeling and processing

22. DF, CDF and CF STTP CAD 2011Mesh modeling and processing DF – Diameter function, CF – Centricity function CDF – Combined function

23. Temperature distribution descriptor STTP CAD 2011Mesh modeling and processing

24. Spectral embedding STTP CAD 2011Mesh modeling and processing Compute the affinity matrix and its Eigen decomposition A = VDV T.. D is a diagonal matrix with eigenvalues e1,e2, …, en, along the diagonal and V = [v1|... |vn] is an n × n matrix with v1,..., vn the corresponding eigenvectors.

25. Database – Accumulation of models Princeton shape benchmark (PSB) – 3D graphical models Engineering shape benchmark (ESB) – 3D CAD models McGill Database – 3D Articulated models STTP CAD 2011Mesh modeling and processing

26. Visualizing the results STTP CAD 2011Mesh modeling and processing

27. Quantitative analysis First-tier and second-tier values are defined as percentage of models in the query’s class that appear in top K matches, where K is dependent on the size of the query’s class. The higher values of these statistics indicate better retrieval results. Precision–recall (PR) curves. Precision is the ratio of the relevant models retrieved to the retrieval size. Recall is the fraction of the relevant models retrieved for a given retrieval size. STTP CAD 2011Mesh modeling and processing

28. Correspondence problem The problem can be generally stated as: given input shapes S1;S2; : : : ;SN, find a meaningful relation (or mapping) between their elements. STTP CAD 2011Mesh modeling and processing

29. Partial correspondence STTP CAD 2011Mesh modeling and processing

30. References R. Gal, A. Shamir, and D. Cohen-Or. Pose-oblivious shape signature. IEEE Transactions on Visualization and Computer Graphics, 13(2):261–271, Mar./Apr. 2007. N. Iyer, S. Jayanti, K. Lou, Y. Kalyanaraman, and K. Ramani. Three-dimensional shape searching: state-of-the-art review and future trends. Computer-Aided Design, 37(5):509– 530, 2005. V. Jain and H. Zhang. A spectral approach to shape-based retrieval of articulated 3d models. Comput. Aided Des., 39(5):398–407, 2007. R. Osada, T. Funkhouser, B. Chazelle, and D. Dobkin. Shape distributions. ACM Trans. Graph., 21(4):807–832, 2002. P. Shilane, P. Min, M. Kazhdan, and T. Funkhouser. The princeton shape benchmark. In Shape Modeling International, June 2004. J. Tangelder and R. Veltkamp. A survey of content based 3D shape retrieval methods. In SMI ’04: Proceedings of the Shape Modeling International, pages 145–156, June 2004. R. Veltkamp. Shrec home page. http://www.aimatshape.net/event/SHREChttp://www.aimatshape.net/event/SHREC Ariel Shamir. A survey on mesh segmentation techniques. Computer Graphics Forum, 27 (6), pp. 1539-1556,2008. Oliver van Kaick, Hao Zhang, Ghassan Hamarneh, Daniel Cohen-Or, A survey on shape correspondence Subramani S., Ramanathan M., Yagnanarayanan K., Sundar M, Manish, Ramani K, and Hoffmann C. M., "PCS - Prominent cross-section for mesh models", Computer Aided Design and Applications (CADA), Volume 7, Number 4, Pages 601-620, 2010. STTP CAD 2011Mesh modeling and processing