Abstract
This paper studies shape representation of general 3D objects. In particular, it proposes a conformal representation for genus-zero mesh objects, by using the discrete conformal mapping technique. It also proposes a new method to reconstruct the original shape from its conformal representation. In order to simplify and robustify the computation, we made several improvements to the above two procedures. The modifications include planar graph drawing initialization, Moebius factorization and spring-embedding-based reconstruction, etc. Though being mostly incremental, these modifications do provide significant improvements on previous methods. Possible applications include 3D geometry compression and object classification/recognition, etc.
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References
Taubin, G., Rossignac, J.: Geometric Compression Through Topological Surgery. ACM Transactions on Graphics 17(2), 84–115 (1998)
Faugeras, O.: Stratification of 3-D vision: projective, affine, and metric representations. JOSA-A (1995)
Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004)
Burkhardt, H., Reisert, M., Li, H.: Invariant for Discrete Structures-An Extension of Haar invariant over Dirac Delta Functions. In: Pattern Recognition Symposium, DAGM 2004, Germany (2004)
Gu, X., Wang, Y., Chan, T.F., Thompson, P.M., Yau, S.: Genus Zero Surface Conformal Mapping and Its Application to Brain Surface Mapping. IEEE T-Medical Imaging 23(8) (August 2004)
Floater, M.S., Hormann, K.: Surface Parameterization: a Tutorial and Survey. In: Advances in Multiresolution for Geometric Modelling, pp. 157–186. Springer, Heidelberg (2005)
Shum, H., Hebert, M., Ikeuchi, K.: On 3D Shape Similarity. In: IEEE-CVPR 1996 (1996)
Li, H., Hartley, R.I.: A new 3D Fourier descriptor for describing arbitrary genus-0 mesh objects. RSISE/NICTA Technique Report (2005)
Gotsman, C., Gu, X., Sheffer, A.: Fundamentals of Spherical Parameterization for 3D Meshes. ACM Transactions on Graphics (TOG) 22(3), 358–363 (2003)
Gu, X., Yau, S.: Surface Classification Using Conformal Structures. In: Proc ICCV 2003 (2003)
Gu, X., Wang, Y., Yau, S.: Geometry compression using Riemannian structure. Communication in information systems 3(3), 171–182 (2004)
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Li, H., Hartley, R., Burkhardt, H. (2005). Discrete Conformal Shape Representation and Reconstruction of 3D Mesh Objects. In: Roli, F., Vitulano, S. (eds) Image Analysis and Processing – ICIAP 2005. ICIAP 2005. Lecture Notes in Computer Science, vol 3617. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11553595_66
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DOI: https://doi.org/10.1007/11553595_66
Publisher Name: Springer, Berlin, Heidelberg
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