Least-Squares Fitting of Two 3-D Point Sets
IEEE Transactions on Pattern Analysis and Machine Intelligence
Least-Squares Estimation of Transformation Parameters Between Two Point Patterns
IEEE Transactions on Pattern Analysis and Machine Intelligence
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Geometric computation for machine vision
Geometric computation for machine vision
In Defense of the Eight-Point Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
Group Theoretical Methods in Image Understanding
Group Theoretical Methods in Image Understanding
Analysis of 3-D Rotation Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
On Weighting and Choosing Constraints for Optimally Reconstructing the Geometry of Image Triplets
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part II
Bundle Adjustment - A Modern Synthesis
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
First Order Error Propagation of the Procrustes Method for 3D Attitude Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stochastically optimal epipole estimation in omnidirectional images with geometric algebra
RobVis'08 Proceedings of the 2nd international conference on Robot vision
Geometry and kinematics with uncertain data
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
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Because 3-D data are acquired using 3-D sensing such as stereo vision and laser range finders, they have inhomogeneous and anisotropic noise. This paper studies optimal computation of the similarity (rotation, translation, and scale change) of such 3-D data. We first describe two well known methods for this: the Gauss-Newton and the Gauss-Helmert methods, which are often regarded as different techniques. We then point out that they have similar mathematical structures and combine them to define a hybrid, which we call the modified Gauss-Helmert method. Doing stereo vision simulation, we demonstrate that the proposed method is superior to either of the two methods in convergence performance. Finally, we show an application to real GPS geodetic data and point out that the widely used homogeneous and isotropic noise model is insufficient. We also discuss some numerical issues about GPS data.