Abstract
In this paper we propose a surface reconstruction method for highly noisy and non-uniform data based on minimal surface model and tensor voting method. To deal with ill-posedness, noise and/or other uncertainties in the data we processes the raw data first using tensor voting before we do surface reconstruction. The tensor voting procedure allows more global and robust communications among the data to extract coherent geometric features and saliency independent of the surface reconstruction. These extracted information will be used to preprocess the data and to guide the final surface reconstruction. Numerically the level set method is used for surface reconstruction. Our method can handle complicated topology as well as highly noisy and/or non-uniform data set. Moreover, improvements of efficiency in implementing the tensor voting method are also proposed. We demonstrate the ability of our method using synthetic and real data.
H. Zhao is partially supported by ONR, DARPA and Sloan Fellowship. M. Jiang is partially supported by the National Basic Research Program of China under Grant 2003CB716101, National Science Foundation of China under Grants 60325101, 60272018 and 60372024, and Engineering Research Institute, Peking University. S. Zhou and T. Zhou are partially supported by the National Basic Research Program of China under Grant 2003CB716101, National Science Foundation of China under Grant 60372024, and Engineering Research Institute, Peking University.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Rogers, D.F.: An introduction to NURBS: with historical perspective. Morgan Kaufmann Publishers Inc., San Francisco (2001)
Amenta, N., Bern, M.: Surface reconstruction by voronoi filtering. Discrete and Comput. Geometry 22, 481–504 (1999)
Edelsbrunner, H.: Shape reconstruction with delaunay complex. In: Lucchesi, C.L., Moura, A.V. (eds.) LATIN 1998. LNCS, vol. 1380, pp. 119–132. Springer, Heidelberg (1998)
Boissonnat, J.D.: Geometric structures for three dimensional shape reconstruction. ACM Trans. Graphics 3, 266–286 (1984)
Amenta, N., Bern, M., Eppstein, D.: The crust and the -skeleton: Combinational curve reconstruction. In: 14th ACM Symposium on Computational Geometry (1998)
Amenta, N., Bern, M., Kamvysselis, M.: A new voronoi-based surface reconstruction algorithm. In: SIGGRAPH 1998: Proceedings of the 25th annual conference on Computer graphics and interactive techniques, pp. 415–421. ACM Press, New York (1998)
Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Surface reconstruction from unorganized points. In: SIGGRAPH 1992: Proceedings of the 19th annual conference on Computer graphics and interactive techniques, pp. 71–78. ACM Press, New York (1992)
Bajaj, C.L., Bernardini, F., Xu, G.: Automatic reconstruction of surfaces and scalar fields from 3rd scans. In: SIGGRAPH 1995: Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, pp. 109–118. ACM Press, New York (1995)
Curless, B., Levoy, M.: A volumetric method for building complex models from range images. In: SIGGRAPH 1996: Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, pp. 303–312. ACM Press, New York (1996)
Hilton, A., Stoddart, A.J., Illingworth, J., Windeatt, T.: Implicit surface-based geometric fusion. Comput. Vis. Image Underst. 69(3), 273–291 (1998)
Bloomenthal, J., Wyvill, B. (eds.): Introduction to Implicit Surfaces. Morgan Kaufmann Publishers Inc., San Francisco (1997)
Whitaker, R.: A level set approach to 3D reconstruction from range data. International journal of Computer Vision (1997)
Zhao, H.-K., Osher, S., Merriman, B., Kang, M.: Implicit and non-parametric shape reconstruction from unorganized data using a variational level set method. Computer Vision and Image Understanding 80, 295–319 (2000)
Zhao, H., Osher, S., Fedkiw, R.: Fast surface reconstruction using the level set method. In: VLSM 2001: Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM 2001), Washington, DC, USA, p. 194. IEEE Computer Society, Los Alamitos (2001)
Carr, J.C., Beatson, R.K., Cherrie, J.B., Mitchell, T.J., Fright, W.R., McCallum, B.C., Evans, T.R.: Reconstruction and representation of 3d objects with radial basis functions. In: SIGGRAPH 2001: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, pp. 67–76. ACM Press, New York (2001)
Medioni, G., Lee, M.-S., Tang, C.-K.: A computational framework for segmentation and grouping. Elsevier, Amsterdam (2000)
Zhao, H.: Fast sweeping method for Eikonal equations. Mathematics of Computation (2004)
Zhao, H., Osher, S., Fedkiw, R.: Fast surface reconstruction and deformation using the level set method. In: Proceedings of IEEE Workshop on Variational and Level Set Methods in Computer Vision, Vancouver (July 2001)
Osher, S., Fedkiw, R.: Level set methods and dynamic implicit surfaces. Springer, New York (2002)
Zhao, H.-K., Chan, T., Merriman, B., Osher, S.: A variational level set approach to multiphase motion. J. Comput. Phys. 127, 179–195 (1996)
Jia, J., Tang, C.-K.: Inference of segmented color and texture description by tensor voting, June 2004, vol. 26, pp. 771–786 (2004)
Tong, W.-S., Tang, C.-K., Mordohai, P., Medioni, G.: First order augmentation to tensor voting for boundary inference and multiscale analysis in 3d. IEEE Trans. Pattern Anal. Mach. Intell. 26(5), 594–611 (2004)
Tang, C.-K., Medioni, G.: Inference of integrated surface, curve, and junction descriptions from sparse 3rd data. IEEE Trans. Pattern Anal. Mach. Intell. 20(11), 1206–1223 (1998)
Peng, D., Merriman, B., Osher, S., Zhao, H., Kang, M.: A PDE based fast local level set method. J. Comput. Phys. 155, 410–438 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lu, D., Zhao, H., Jiang, M., Zhou, S., Zhou, T. (2005). A Surface Reconstruction Method for Highly Noisy Point Clouds. In: Paragios, N., Faugeras, O., Chan, T., Schnörr, C. (eds) Variational, Geometric, and Level Set Methods in Computer Vision. VLSM 2005. Lecture Notes in Computer Science, vol 3752. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11567646_24
Download citation
DOI: https://doi.org/10.1007/11567646_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29348-4
Online ISBN: 978-3-540-32109-5
eBook Packages: Computer ScienceComputer Science (R0)