Point Cloud Denoising via Moving RPCA

We present an algorithm for the restoration of noisy point cloud data, termed Moving Robust Principal Components Analysis (MRPCA). We model the point cloud as a collection of overlapping two‐dimensional subspaces, and propose a model that encourages collaboration between overlapping neighbourhoods. Similar to state‐of‐the‐art sparse modelling‐based image denoising, the estimated point positions are computed by local averaging. In addition, the proposed approach models grossly corrupted observations explicitly, does not require oriented normals, and takes into account both local and global structure. Sharp features are preserved via a weighted ℓ1 minimization, where the weights measure the similarity between normal vectors in a local neighbourhood. The proposed algorithm is compared against existing point cloud denoising methods, obtaining competitive results.

[1]  Yi Ma,et al.  Robust principal component analysis? , 2009, JACM.

[2]  Daniel Cohen-Or,et al.  Consolidation of unorganized point clouds for surface reconstruction , 2009, ACM Trans. Graph..

[3]  Ravi Krishna Kolluri,et al.  Provably good moving least squares , 2005, SIGGRAPH Courses.

[4]  Emmanuel J. Candès,et al.  Exact Matrix Completion via Convex Optimization , 2009, Found. Comput. Math..

[5]  Daniel Cohen-Or,et al.  ℓ1-Sparse reconstruction of sharp point set surfaces , 2010, TOGS.

[6]  Wenping Wang,et al.  Denoising point sets via L0 minimization , 2015, Comput. Aided Geom. Des..

[7]  Nina Amenta,et al.  Defining point-set surfaces , 2004, ACM Trans. Graph..

[8]  Emmanuel J. Candès,et al.  The Power of Convex Relaxation: Near-Optimal Matrix Completion , 2009, IEEE Transactions on Information Theory.

[9]  Jianfei Cai,et al.  Robust surface reconstruction via dictionary learning , 2014, ACM Trans. Graph..

[10]  Gonzalo Mateos,et al.  Robust PCA as Bilinear Decomposition With Outlier-Sparsity Regularization , 2011, IEEE Transactions on Signal Processing.

[11]  Julie Digne,et al.  Similarity based filtering of point clouds , 2012, 2012 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops.

[12]  Tamy Boubekeur,et al.  Non Local Point Set Surfaces , 2012, 2012 Second International Conference on 3D Imaging, Modeling, Processing, Visualization & Transmission.

[13]  Alessandro Foi,et al.  Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering , 2007, IEEE Transactions on Image Processing.

[14]  Markus H. Gross,et al.  Feature Preserving Point Set Surfaces based on Non‐Linear Kernel Regression , 2009, Comput. Graph. Forum.

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

[16]  Michael Elad,et al.  Sparse and Redundant Representations - From Theory to Applications in Signal and Image Processing , 2010 .

[17]  Daniel Cohen-Or,et al.  Parameterization-free projection for geometry reconstruction , 2007, ACM Trans. Graph..

[18]  Michael Wimmer,et al.  Continuous projection for fast L1 reconstruction , 2014, ACM Trans. Graph..

[19]  D. Cohen-Or,et al.  Robust moving least-squares fitting with sharp features , 2005, ACM Trans. Graph..

[20]  Guillermo Sapiro,et al.  Online dictionary learning for sparse coding , 2009, ICML '09.

[21]  Daniel Cohen-Or,et al.  Edge-aware point set resampling , 2013, ACM Trans. Graph..

[22]  Jian Liu,et al.  Point cloud normal estimation via low-rank subspace clustering , 2013, Comput. Graph..

[23]  Marc Alexa,et al.  Point set surfaces , 2001, Proceedings Visualization, 2001. VIS '01..

[24]  François Goulette,et al.  POINT CLOUD NON LOCAL DENOISING USING LOCAL SURFACE DESCRIPTOR SIMILARITY , 2010 .

[25]  Marc Alexa,et al.  Interpolatory point set surfaces—convexity and Hermite data , 2009, TOGS.

[26]  Markus H. Gross,et al.  Algebraic point set surfaces , 2007, ACM Trans. Graph..

[27]  Stephen P. Boyd,et al.  Graph Implementations for Nonsmooth Convex Programs , 2008, Recent Advances in Learning and Control.

[28]  Ligang Liu,et al.  Survey on sparsity in geometric modeling and processing , 2015, Graph. Model..

[29]  Ron Kimmel,et al.  Patch‐Collaborative Spectral Point‐Cloud Denoising , 2013, Comput. Graph. Forum.

[30]  Jean-Michel Morel,et al.  A non-local algorithm for image denoising , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[31]  张振跃,et al.  Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment , 2004 .

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

[33]  Emmanuel J. Candès,et al.  Exact Matrix Completion via Convex Optimization , 2008, Found. Comput. Math..

[34]  Michael Elad,et al.  Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries , 2006, IEEE Transactions on Image Processing.