Abstract
This paper addresses the problem of reconstructing implicit function from point clouds with noise and outliers acquired with 3D scanners. We introduce a filtering operator based on mean shift scheme, which shift each point to local maximum of kernel density function, resulting in suppression of noise with different amplitudes and removal of outliers. The “clean” data points are then divided into subdomains using an adaptive octree subdivision method, and a local radial basis function is constructed at each octree leaf cell. Finally, we blend these local shape functions together with partition of unity to approximate the entire global domain. Numerical experiments demonstrate robust and high quality performance of the proposed method in processing a great variety of 3D reconstruction from point clouds containing noise and outliers.
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Weiss, V., Andor, L., Renner, G., Varady, T.: Advanced Surface Fitting Techniques. Computer Aided Geometric Design 1, 19–42 (2002)
Iglesias, A., Echevarría, G., Gálvez, A.: Functional Networks for B-spline Surface Reconstruction. Future Generation Computer Systems 8, 1337–1353 (2004)
Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., Silva, C.T.: Point Set Surfaces. In: Proceedings of IEEE Visualization, San Diego, CA, USA, pp. 21–28 (2001)
Amenta, N., Kil, Y.J.: Defining Point-Set Surfaces. ACM Transactions on Graphics 3, 264–270 (2004)
Levin, D.: Mesh-Independent Surface Interpolation. In: Geometric Modeling for Scientific Visualization, pp. 37–49. Springer, Heidelberg (2003)
Fleishman, S., Cohen-Or, D., Silva, C.T.: Robust Moving Least-Squares Fitting with Sharp Features. ACM Transactions on Graphics 3, 544–552 (2005)
Savchenko, V.V., Pasko, A., Okunev, O.G., Kunii, T.L.: Function Representation of Solids Reconstructed from Scattered Surface Points and Contours. Computer Graphics Forum 4, 181–188 (1995)
Turk, G., O’Brien, J.: Variational Implicit Surfaces. Technical Report GIT-GVU-99-15, Georgia Institute of Technology (1998)
Wendland, H.: Piecewise Polynomial, Positive Definite and Compactly Supported Radial Functions of Minimal Degree. Advances in Computational Mathematics, 389–396 (1995)
Morse, B.S., Yoo, T.S., Rheingans, P., Chen, D.T., Subramanian, K.R.: Interpolating Implicit Surfaces from Scattered Surface Data Using Compactly Supported Radial Basis Functions. In: Proceedings of Shape Modeling International, Genoa, Italy, pp. 89–98 (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: Proceedings of ACM Siggraph 2001, Los Angeles, CA, USA, pp. 67–76 (2001)
Beatson, R.K.: Fast Evaluation of Radial Basis Functions: Methods for Two-Dimensional Polyharmonic Splines. IMA Journal of Numerical Analysis 3, 343–372 (1997)
Wu, X., Wang, M.Y., Xia, Q.: Implicit Fitting and Smoothing Using Radial Basis Functions with Partition of Unity. In: Proceedings of 9th International Computer-Aided-Design and Computer Graphics Conference, Hong Kong, China, pp. 351–360 (2005)
Ohtake, Y., Belyaev, A., Seidel, H.P.: Multi-scale Approach to 3D Scattered Data Interpolation with Compactly Supported Basis Functions. In: Proceedings of Shape Modeling International, Seoul, Korea, pp. 153–161 (2003)
Tobor, I., Reuter, P., Schlick, C.: Multi-scale Reconstruction of Implicit Surfaces with Attributes from Large Unorganized Point Sets. In: Proceedings of Shape Modeling International, Genova, Italy, pp. 19–30 (2004)
Comaniciu, D., Meer, P.: Mean Shift: A Robust Approach toward Feature Space Analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence 5, 603–619 (2002)
Cheng, Y.Z.: Mean Shift, Mode Seeking, and Clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence 8, 790–799 (1995)
Ohtake, Y., Belyaev, A., Alexa, M., Turk, G., Seidel, H.P.: Multi-level Partition of Unity Implicits. ACM Transactions on Graphics 3, 463–470 (2003)
Taubin, G.: Estimation of Planar Curves, Surfaces and Nonplanar Space Curves Defined by Implicit Equations, with Applications to Edge and Range Image Segmentation. IEEE Transaction on Pattern Analysis and Machine Intelligence 11, 1115–1138 (1991)
Boubekeur, T., Heidrich, W., Granier, X., Schlick, C.: Volume-Surface Trees. Computer Graphics Forum 3, 399–406 (2006)
Schall, O., Belyaev, A., Seidel, H.-P.: Robust Filtering of Noisy Scattered Point Data. In: IEEE Symposium on Point-Based Graphics, Stony Brook, New York, USA, pp. 71–77 (2005)
Rusinkiewicz, S., Levoy, M.: Qsplat: A Multiresolution Point Rendering System for Large Meshes. In: Proceedings of ACM Siggraph 2000, New Orleans, Louisiana, USA, pp. 343–352 (2000)
Lorensen, W.E., Cline, H.F.: Marching Cubes: A High Resolution 3D Surface Construction Algorithm. Computer Graphics 4, 163–169 (1987)
Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., Stuetzle, W.: Surface Reconstruction from Unorganized Points. In: Proceedings of ACM Siggraph’92, Chicago, Illinois, USA, pp. 71–78 (1992)
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Yang, J., Wang, Z., Zhu, C., Peng, Q. (2007). Implicit Surface Reconstruction from Scattered Point Data with Noise. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds) Computational Science – ICCS 2007. ICCS 2007. Lecture Notes in Computer Science, vol 4488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72586-2_8
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DOI: https://doi.org/10.1007/978-3-540-72586-2_8
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