6 : Discussions and Conclusions

6 : Discussions and Conclusions
In this paper, we proposed a new shape decomposition method which extended
the morphological methods. It can conquer two problems for the current
morphological methods, scale invariant and noise. We have proposed a
graph Laplacian energy based hierarchy shape decomposition.We can extract
more stable graph structure by using our methods. Our next step is to use
these graph structures to do shape analysis. One possible way is to combine
the spectral graph invariants [17] for shape recognition. Recently, Trinh and
Kimia [13] has proposed a graph generative for shape through the analysis of
shock graphs. We can also extend our methods with graph generative model
for morphological decomposition.
References
1. Bai, X., Latecki, L.J., Liu, W.Y.: Skeleton pruning by contour partitioning with
discrete curve evolution. IEEE Trans. PAMI 29(3), 449–462 (2007)
2. Luo, B., Wilson, R.C., Hancock, E.R.: A spectral approach to learning structural
variations in graphs. Pattern Recognition 39, 1188–1198 (2006)
3. Chung, F.R.K.: Spectral graph theory. American Mathematical Society, Reading
(1997)
4. Cootes, T.F., Edwards, G.J., Taylor, C.J.: Active appearance models. In:
Burkhardt, H., Neumann, B. (eds.) ECCV 1998. LNCS, vol. 1407, p. 484.
Springer, Heidelberg (1998)
5. Lowe, D.: Distinctive image features from scale-invariant keypoints. International
Journal of Computer Vision 1, 91–110 (2004)
10 C. Luyuan et al.
6. Gutman, I., Zhou, B.: Laplacian energy of a graph. Linear Algebra and its
Applications 44, 29–37 (2006)
7. Kim, D.H., Yun, I.D., Lee, S.U.: A new shape decomposition scheme for graphbased
representation. Pattern Recognition 38(5), 673–689 (2005)
8. Kimia, B.B., Tannenbaum, A.R., Zucker, S.W.: Shapes, shocks, and deformations.
Int. J. Computer Vision 15, 189–224 (1995)
9. Klassen, Srivastava, A., Mio, W., Joshi, S.H.: Analysis of planar shapes using
geodesic paths on shape spaces. IEEE Transactions on Pattern Analysis and
Machine Intelligence 26, 372–383 (2004)
10. Latecki, L.J., Lakamper, R.: Convexity rule for shape decomposition based
on discrete contour evolution. Computer Vision and Image Understanding 77,
441–454 (1999)
11. Lee, C.G., Small, C.G.: Multidimensional scaling of simplex shapes. Pattern
Recognition 32, 1601–1613 (1999)
12. Murase, H., Nayar, S.K.: Illumination planning for object recognition using
parametric eigenspaces. IEEE Transactions on Pattern Analysis and Machine
Intelligence 16, 1219–1227 (1994)
13. Trinh, N., Kimia, B.B.: A symmetry-based generative model for shape. In:
International Conference on Computer Vision (2007)
14. Pitas, I., Venetsanopoulos, A.N.: Morphological shape decomposition. IEEE
Trans. Pattern Anal. Mach. Intell. 12(1), 38–45 (1990)
15. Shokoufandeh, A., Dickinson, S., Siddiqi, K., Zucker, S.: Indexing using a spectral
encoding of topological structure. In: International Conference on Computer
Vision and Pattern Recognition, pp. 491–497 (1999)
16. Torsello, A., Hancock, E.R.: A skeletal measure of 2d shape similarity. Computer
Vision and Image Understanding 95(1), 1–29 (2004)
17. Xiao, B., Hancock, E.R.: Clustering shapes using heat content invariants, pp.
1169–1172 (2005)
18. Xiao, B., Hancock, E.R.: A spectral generative model for graph structure. In:
SSPR/SPR, pp. 173–181 (2006)
19. Xiao, B., Song, Y.-Z., Hall, P.M.: Learning object classes from structure. In:
British Machine Vision Conference, Warwich, vol. 1407, pp. 207–217 (2007)