Tianqiang Liu will present his research seminar/general exam on Tuesday May 8 at
2PM in Room 401 (note room!). The members of his committee are: Tom Funkhouser
(advisor), Szymon Rusinkiewicz, and Moses Charikar. Everyone is invited to attend
his talk and those faculty wishing to remain for the oral exam following are welcome
to do so. His abstract and reading list follow below.

Abstract:

In this project, we propose an automatic algorithm for finding a correspondence map between two 3D surfaces. The key insight is that global reflective symmetry axes are stable, recognizable, semantic features of most real-world surfaces. Thus, it is possible to find a useful map between two surfaces by first extracting symmetry axis curves, aligning the extracted curves, and then extrapolating correspondences found on the curves to both surfaces. The main advantages of this approach are efficiency and robustness: the difficult problem of finding a surface map is reduced to three significantly easier problems: symmetry detection, curve alignment, and correspondence extrapolation, each of which has a robust, polynomial-time solution (e.g. optimal alignment of 1D curves is possible with dynamic programming). We investigate of this approach on a wide range of examples, including both intrinsically symmetric surfaces and polygon soups, and find that it is superior to previous methods in cases where two surfaces have different overall shapes but similar reflective symmetry axes, a common case in computer graphics.

Reading list:

1. VAN KAICK, O., ZHANG, H., HAMARNEH, G., AND COHEN- OR, D. 2010. A survey on shape correspondence. Eurographics State-of-the-Art report.

2. BRONSTEIN, A. M., BRONSTEIN, M. M., AND KIMMEL, R. 2006. Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. PNAS

3 . KIM, V. G., LIPMAN, Y., AND FUNKHOUSER, T. 2011. Blended intrinsic maps. ACM Transactions on Graphics (Proc of SIGGRAPH 2011).

4. MARZAL, A., AND PALAZO ́ N, V. 2005. Dynamic time warping of cyclic strings for shape matching. Pattern Recognition and Image Analysis,

5. SCHREINER, J., ASIRVATHAM, A., PRAUN, E., AND HOPPE, H. 2004. Inter-surface mapping. ACM Transactions on Graphics (Proc of SIGGRAPH 2004).

6. XU, K., ZHANG, H., TAGLIASACCHI, A., LIU, L., LI, G., MENG, M., AND XIONG, Y. 2009. Partial intrinsic reflectional symmetry of 3d shapes. ACM Transactions on Graphics

7. ZHANG, H., SHEFFER, A., COHEN-OR, D., ZHOU, Q., VAN KAICK, O., AND TAGLIASACCHI, A. 2008. Deformation driven shape correspondence. Computer Graphics Forum, vol. 27, Wiley Online Library, 1431–1439.

8. PODOLAK, J., SHILANE, P., GOLOVINSKIY, A., RUSINKIEWICZ, S., AND FUNKHOUSER, T. 2006. A planar-reflective symmetry transform for 3d shapes, ACM Transactions on Graphics (Proc of SIGGRAPH 2006)

9. PRAUN, E., SWELDENS, W., AND SCHRO ̈ DER, P. 2001. Consistent mesh parameterizations. ACM Transactions on Graphics (Proc of SIGGRAPH 2001).

10. HILAGA, M., SHINAGAWA, Y., KOHMURA, T., AND KUNII, T. 2001. Topology matching for fully automatic similarity estimation of 3d shapes. Proceedings of the 28th annual conference on Computer graphics and interactive techniques, ACM, 203– 212.

11. SUNDAR, H., SILVER, D., GAGVANI, N., AND DICKINSON, S. 2003. Skeleton based shape matching and retrieval. In Shape Modeling International, 2003, IEEE, 130–139.

12. DONALD D. HEARN, M. PAULINE BAKER, Computer Graphics with Open GL (4th Edition):