Mesh modeling and processing

1. Mesh modeling and processing M. Ramanathan Mesh modeling and processing

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

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

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

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

7. Mesh attributes Minimum curvature Average geodesic distance Local shape diameter Difference between Normal directions Mesh modeling and processing

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 Mesh 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. Mesh modeling and processing

10. Sectional Gauss map Mesh modeling and processing

11. Algorithm to compute PCS Mesh modeling and processing

12. PCS for different models Mesh modeling and processing

13. Segmentation Mesh modeling and processing

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

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

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

17. Taxonomy of shape matching methods Mesh modeling and processing

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

19. Skeletal graph matching Skeletal graph matching with colors showing the node-to-node correspondence based uponthetopology and radial distance about the edge Mesh modeling and processing

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

21. Local diameter function Mesh modeling and processing

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

23. Temperature distribution descriptor Mesh modeling and processing

24. Spectral embedding Compute the affinity matrix and its Eigen decomposition A = VDVT.. 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. Mesh modeling and processing

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

26. Visualizing the results Mesh 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. Mesh 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. Mesh modeling and processing

29. Partial correspondence Mesh 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/SHREC • Ariel Shamir. A survey on mesh segmentation techniques. Computer Graphics Forum, 27 (6), pp. 1539-1556,2008. • Oliver van Kaick, HaoZhang, GhassanHamarneh, 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. Mesh modeling and processing