Automatic Scale Selection for Analyzing 3-D Point Clouds



The neighborhood size (the scale) used for computing features (e.g., the surface normal) is estimated based on the data distribution.
A standard task involved in computing local features from 3-D point clouds is to estimate some geometric quantity from the distribution of points in a neighborhood around each data point. The geometric quantities may be statistics of the point distribution derived from the scatter matrix or differential features such as normals, curvatures, or tangent plane depending on the task.

The problem is to select automatically the optimal size of the neighborhood (the "scale") over which the computation should be carried out. Too coarse  a scale blurs out important details; too fine a scale emphsizes  the noise in the data. This is akin the well-studied problem of selecting the natural scale in images, with the key difference that the data (the 3-D points) is no longer sampled on a regular grid; it may have arbitrary distribution and density.

This project investigates a class of approaches in which the "optimal" scale is estimated by iterating between computing the feature, estimating its uncertainty, and refining the neighborhood size accordingly. These ideas have been applied to the robust estimation of surface features (e.g., normals), and to the estimation of  differential characteristics of 3-D curves (tangent,, curvature, torsion) from irregular 3-D samples. 

The tools have been applied to terrain classification and 3-D environment modeling for unmanned ground vehicles. Similar ideas have been used to the estimation of the optimal scale in images to ensure invariance to complex transformations such as scene illumination.


Ranjith Unnikrishnan and  Martial Hebert, Denoising Manifold and Non-Manifold Point Clouds. British Machine Vision Conference, September, 2007.

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

Jean-Francois Lalonde , Ranjith UnnikrishnanNicolas Vandapel, Martial Hebert, Scale Selection for the Analysis of Point-Sampled 3-D Surfaces. Fifth International Conference on 3-D Digital Imaging and Modeling (3DIM 2005), June, 2005.

Ranjith Unnikrishnan and Martial Hebert, Extracting Scale and Illuminant Invariant Regions through Color. 17th British Machine Vision Conference (BMVC), Sept, 2006.


This research is supported by:

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