GP-MPU Method for Implicit Surface Reconstruction

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.

[1]  Sunghee Choi,et al.  The power crust, unions of balls, and the medial axis transform , 2001, Comput. Geom..

[2]  Michael M. Kazhdan,et al.  Poisson surface reconstruction , 2006, SGP '06.

[3]  Marc Alexa,et al.  Approximating and Intersecting Surfaces from Points , 2003, Symposium on Geometry Processing.

[4]  M. Gross,et al.  Algebraic point set surfaces , 2007, SIGGRAPH 2007.

[5]  Nello Cristianini,et al.  Kernel Methods for Pattern Analysis , 2003, ICTAI.

[6]  Josiah Manson,et al.  Streaming Surface Reconstruction Using Wavelets , 2008, Comput. Graph. Forum.

[7]  Long Quan,et al.  Image deblurring with blurred/noisy image pairs , 2007, SIGGRAPH 2007.

[8]  Ravi Krishna Kolluri,et al.  Provably good moving least squares , 2008, SODA '05.

[9]  Michael M. Kazhdan,et al.  Reconstruction of solid models from oriented point sets , 2005, SGP '05.

[10]  Gabriel Taubin,et al.  A benchmark for surface reconstruction , 2013, TOGS.

[11]  Hans-Peter Seidel,et al.  Multi-level partition of unity implicits , 2005, SIGGRAPH Courses.

[12]  D. Levin,et al.  Mesh-Independent Surface Interpolation , 2004 .

[13]  Marcos P. Gerardo-Castro,et al.  Laser-Radar Data Fusion with Gaussian Process Implicit Surfaces , 2013, FSR.

[14]  Marc Toussaint,et al.  Gaussian process implicit surfaces for shape estimation and grasping , 2011, 2011 IEEE International Conference on Robotics and Automation.

[15]  Luiz Velho,et al.  Surface reconstruction from noisy point clouds , 2005, SGP '05.

[16]  Andrew Fitzgibbon,et al.  Gaussian Process Implicit Surfaces , 2006 .

[17]  Richard K. Beatson,et al.  Reconstruction and representation of 3D objects with radial basis functions , 2001, SIGGRAPH.

[18]  James F. O'Brien,et al.  Modelling with implicit surfaces that interpolate , 2002, TOGS.

[19]  Paul Newman,et al.  Efficient Non-Parametric Surface Representations Using Active Sampling for Push Broom Laser Data , 2010, Robotics: Science and Systems.

[20]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[21]  John Hart,et al.  ACM Transactions on Graphics: Editorial , 2003, SIGGRAPH 2003.

[22]  Jean-Daniel Boissonnat,et al.  Smooth surface reconstruction via natural neighbour interpolation of distance functions , 2002, Comput. Geom..

[23]  Thomas Lewiner,et al.  Efficient Implementation of Marching Cubes' Cases with Topological Guarantees , 2003, J. Graphics, GPU, & Game Tools.

[24]  Hans-Peter Seidel,et al.  Sparse surface reconstruction with adaptive partition of unity and radial basis functions , 2006, Graph. Model..

[25]  Tamal K. Dey,et al.  Curve and Surface Reconstruction , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..