Scale Selection for Geometric Fitting in Noisy Point Clouds


From a 3-D point cloud (right), points are manually extracted and represented as a graph (center). Our approach estimates the tangents of the curve at each point using scale-adaptive PCA (right).

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Abstract

In recent years, there has been a resurgence in the use of raw point cloud data as the geometric primitive of choice for several modeling tasks such as rendering, editing and compression. Algorithms using this representation often require reliable additional information such as the curve tangent or surface normal at each point. Estimation of these quantities requires the selection of an appropriate scale of analysis to accommodate sensor noise, density variation and sparsity in the data. To this goal, we present a new class of locally semi-parametric estimators that allows analysis of accuracy with finite samples, as well as explicitly addresses the problem of selecting optimal support volume for local fitting. Experiments on synthetic and real data validate the behavior predicted by the model, and show competitive performance and improved stability over leading alternatives that require a preset scale.

IJCGA'10 Citation

Ranjith Unnikrishnan, Jean-François Lalonde, Nicolas Vandapel and Martial Hebert. Scale Selection for Geometric Fitting in Noisy Point Clouds. International Journal of Computational Geometry and Applications, 20(5):543--575, 2010. [PDF], [BibTeX]

3DPVT 2006

Parts of this work previously appeared in 3DPVT'06.

Conference paper

Ranjith Unnikrishnan, Jean-François Lalonde, Nicolas Vandapel and Martial Hebert. Scale Selection for the Analysis of Point-Sampled Curves. Third International Symposium on 3D Processing, Visualization and Transmission (3DPVT 2006), 2006. [PDF], [BibTeX]

Technical report

Ranjith Unnikrishnan, Jean-François Lalonde, Nicolas Vandapel and Martial Hebert. Scale Selection for the Analysis of Point-Sampled Curves: Extended report. tech. report CMU-RI-TR-06-25, Robotics Institute, Carnegie Mellon University, June, 2006. [PDF], [BibTeX]

3DIM 2005

Parts of this work previously appeared in 3DIM'05.

Conference paper

Jean-François Lalonde, Ranjith Unnikrishnan, Nicolas Vandapel and Martial Hebert. Scale Selection for Classification of Point-sampled 3-D Surfaces. Fifth International Conference on 3-D Digital Imaging and Modeling (3DIM), June 2005. [PDF], [BibTeX]

Technical report

Jean-François Lalonde, Ranjith Unnikrishnan, Nicolas Vandapel and Martial Hebert. Scale Selection for the Analysis of Point-Sampled Curves: Extended report. tech. report CMU-RI-TR-05-01, Robotics Institute, Carnegie Mellon University, June, 2005. [PDF], [BibTeX]

Talk

Download the slides from the talk presented at 3DIM'05 in the following formats:

[MS Powerpoint, 8.5MB], original version.
[PDF, 2.2MB], export from Powerpoint.

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