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A closed-form expression of the positional uncertainty for 3D point clouds
Kwang-Ho Bae1, David Belton, Derek D Lichti
1Department of Spatial Sciences, Curtin University of Technology, Perth, Australia. K.H.Bae@curtin.edu.au
IEEE Transactions on Pattern Analysis and Machine Intelligence
|February 21, 2009
Summary
We derived a new formula for positional uncertainty in laser range finders. This improves surface normal estimation and 3D point cloud registration by reducing errors.
Area of Science:
- Robotics and Computer Vision
- Geospatial Data Processing
- Metrology and Measurement Science
Background:
- Accurate 3D point cloud registration is crucial for many applications.
- Laser range finders are widely used for 3D data acquisition.
- Positional uncertainty and surface normal estimation errors can degrade registration accuracy.
Purpose of the Study:
- To develop a closed-form expression for positional uncertainty in time-of-flight laser range finders.
- To derive an explicit form for the angular variance of the estimated surface normal vector.
- To provide tools for precise surface normal estimation and outlier detection in 3D point cloud registration.
Main Methods:
- Derivation of a closed-form expression for positional uncertainty considering measurement errors.
- Formulation of the angular variance for the surface normal vector.
- Development of algorithms for optimal neighborhood size selection and point cloud resampling.
Main Results:
- A novel closed-form expression quantifying positional uncertainty.
- An explicit formula for the angular variance of surface normal vectors.
- Two practical algorithms demonstrating the utility of the derived expressions.
Conclusions:
- The derived expressions enhance the precision of surface normal vector estimation.
- The methods improve outlier detection and correspondence finding for 3D point cloud registration.
- The presented algorithms contribute to more robust and accurate 3D reconstruction and analysis.
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