Matrix analysis
Motion and Structure From Two Perspective Views: Algorithms, Error Analysis, and Error Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
6D SLAM—3D mapping outdoor environments: Research Articles
Journal of Field Robotics
CAD-based range sensor placement for optimum 3D data acquisition
3DIM'99 Proceedings of the 2nd international conference on 3-D digital imaging and modeling
Fast 3D mapping by matching planes extracted from range sensor point-clouds
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
The ESA Lunar Robotics Challenge: Simulating operations at the lunar south pole
Journal of Field Robotics
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In this work, we utilize a recently studied more accurate range noise model for 3D sensors to derive from scratch the expressions for the optimum plane which best fits a point-cloud and for the combined covariance matrix of the plane's parameters. The parameters in question are the plane's normal and its distance to the origin. The range standard-deviation model used by us is a quadratic function of the true range and is a function of the incidence angle as well. We show that for this model, the maximum-likelihood plane is biased, whereas the least-squares plane is not. The plane-parameters' covariance matrix for the least-squares plane is shown to possess a number of desirable properties, e.g., the optimal solution forms its null-space and its components are functions of easily understood terms like the planar-patch's center and scatter. We verify our covariance expression with that obtained by the eigenvector perturbation method. We further compare our method to that of renormalization with respect to the theoretically best covariance matrix in simulation. The application of our approach to real-time range-image registration and plane fusion is shown by an example using a commercially available 3D range sensor. Results show that our method has good accuracy, is fast to compute, and is easy to interpret intuitively.