Abstract
This work addresses the problem of surface reconstruction from unorganized points and normals that are acquired from laser scanning of 3D objects. We propose a novel technique for implicit surface reconstruction that effectively combines the trend setting method known as Multi-level Partition of the Unity (MPU) with the Gaussian Process Regression. The reconstructed implicit surface is obtained by subdividing the domain into a set of smaller sub-domains using the MPU algorithm, in each sub-domain a Gaussian Process Regression is carried out that provides accurate local approximations which are blended to obtain a global representation corresponding to the reconstructed implicit surface. The proposed algorithm is able to deal efficiently with point clouds presenting several features such as complex topology and geometry, missing regions and very low sampling rate. Moreover, we conduct some experiments with several acquired data and perform some comparisons with state of the art techniques showing competitive results.
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References
Amenta, N., Bern, M.: Surface reconstruction by voronoi filtering. Discrete and Computational Geometry 22, 481–504 (1999)
Amenta, N., Choi, S., Kollury, R.: The power crust, unions of balls, and the medial axis transform. Computational Geometry 19, 103–108 (2000)
Boissonat, J.D., Cazals, F.: Smooth surface reconstruction via natural neighbour interpolation of distance functions. Computational Geometry 22, 185–203 (2002)
Dey, T.K.: Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (2007)
Mederos, B., Amenta, N., Velho, L., de Figueredo, L.H.: Surface reconstruction for noisy point clouds. In: Symposium on Geometry Processing, pp. 53–62 (2005)
Carr, J.C., Beatson, R.K., Cherrie, J.B., Mitchell, J.T., Right, W.R., McCallum, C.B., Evans, R.T.: Reconstruction and representation of 3D objects with radial basis functions. In: ACM SIGGRAPH 2001, pp. 67–76. ACM Press (2001)
Turk, G., O’brien, J.F.: Modelling with implicit surfaces that interpolate. ACM Transactions on Graphics 21, 855–873 (2002)
Levin, D.: Mesh-independent surface interpolation (2003)
Adamson, A., Alexa, M.: Approximating and intersecting surfaces from points. In: Symposium on Geometry Processing, pp. 230–239 (2003)
Kollury, R.K.: Provably good moving least squares. ACM Transactions on Algorithms 4, 106–112 (2008)
Guennebaud, S., Gross, M.: Algebraic point set surfaces. ACM Transaction on Graphics 26, 1–23 (2010)
Kazhdan, M.M., Bolitho, M., Hoppe, H.: Poisson surface reconstruction. In: Symposium on Geometry Processing, pp. 61–70 (2006)
Kazdan, M.M.: Reconstruction of solid models from oriented point sets. In: Symposium on Geometry Processing, pp. 73–82 (2005)
Manson, P.G., Schaeffer, S.: Streaming surface reconstruction using wavelets. Computer Graphics Forum 27, 1411–1420 (2008)
Ohtake, Y., Belyaev, A., Alexa, M., Turk, G., Seidel, H.P.: Multi-level partition of unity implicits. In: ACM SIGGRAPH, pp. 27–31. ACM Press (2003)
Ohtake, Y., Belyaev, A., Seidel, H.P.: Sparse surface reconstruction with adaptive partition of unity and radial basis function. In: Graphical Models, pp. 150–165 (2005)
Rasmussen, C.E., Williams, C.: Gaussian Processes for Machine Learning. MIT Press (2006)
Smith, M., Posner, I., Newman, P.: Efficient non-parametric surface representations using active sampling for push broom laser data. In: Robotics: Science and Systems Conference (2010)
Gerardo-Castro, M.P., Peynot, T., Ramos, F.: Laser-radar data fusion with gaussian process implicit surfaces. In: The 9th International Conference on Field and Service Robotics, vol. 105, pp. 289–302 (2015)
Dragiev, S., Toussaint, M., Gienger, M.: Gaussian process implicit surfaces for shape estimation and grasping. In: IEEE International Conference on Robotics and Automation, ICRA 2011, pp. 9–13 (2011)
Williams, O., Fitzgibbon, A.: Gaussian process implicit surfaces. In: Gaussian Process in Practice (2007)
Taylor, J.S., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press (2004)
Lewiner, T., Lopes, H., Vieira, A.W., Tavares, G.: Efficient implementation of marching cubes’ cases with topological guarantees. Journal of Graphics Tools 8, 1–15 (2003)
Berger, M., Levine, J.A., Nonato, L.G., Taubin, G., Silva, C.T.: A benchmark for surface reconstruction. ACM Transactions on Graphics (2013)
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López, M.G., Mederos, B., Dalmau, O. (2014). GP-MPU Method for Implicit Surface Reconstruction. In: Gelbukh, A., Espinoza, F.C., Galicia-Haro, S.N. (eds) Human-Inspired Computing and Its Applications. MICAI 2014. Lecture Notes in Computer Science(), vol 8856. Springer, Cham. https://doi.org/10.1007/978-3-319-13647-9_25
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DOI: https://doi.org/10.1007/978-3-319-13647-9_25
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13646-2
Online ISBN: 978-3-319-13647-9
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