Estimating 3-D rigid body transformations: a comparison of four major algorithms 

@article{Eggert1997Estimating3R,
  title={Estimating 3-D rigid body transformations: a comparison of four major algorithms
},
  author={David W. Eggert and Adele Lorusso and Robert B. Fisher},
  journal={Machine Vision and Applications},
  year={1997},
  volume={9},
  pages={272-290}
}
Abstract.A common need in machine vision is to compute the 3-D rigid body transformation that aligns two sets of points for which correspondence is known. A comparative analysis is presented here of four popular and efficient algorithms, each of which computes the translational and rotational components of the transform in closed form, as the solution to a least squares formulation of the problem. They differ in terms of the transformation representation used and the mathematical derivation of… 
View on Springer
graphics.stanford.edu
846 Citations
Highly Influential Citations
27
Background Citations
206
Methods Citations
265
Results Citations
16

846 Citations

Geometrical analysis of motion parameters from two sets of range image data
  • Yonghuai LiuM. Rodrigues
  • Computer Science
    IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028)
  • 1999
TLDR
A novel approach to calibrate motion parameters based on the explicit use of distance between feature points and angle information is presented and Experimental results have shown that the proposed algorithm is in general superior or similar to the constraint least squares based algorithm.
Fast Rigid 3D Registration Solution: A Simple Method Free of SVD and Eigen-Decomposition
TLDR
A novel solution is obtained to solve the rigid 3D registration problem, motivated by previous eigen-decomposition approaches, that does not require sophisticated matrix operations e.g. singular value decomposition or eigenvalue decomposition and can be computed within several iterations.
Fast and Globally Optimal Rigid Registration of 3D Point Sets by Transformation Decomposition
TLDR
An efficient algorithm for rigid registration of 3D point sets is implemented using the idea of translation invariant vectors and a new data structure, named 3D Integral Volume, to accelerate the bound evaluation in both BnB algorithms.
A dual quaternion-based, closed-form pairwise registration algorithm for point clouds
Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes
TLDR
This work provides a convergence analysis for widely used registration algorithms such as ICP, using either closest points or tangent planes at closest points and for a recently developed approach based on quadratic approximants of the squared distance function.
Fast Updates for Least‐Squares Rotational Alignment
TLDR
This work proposes a method based on the Cayley transformations that allows better local quadratic approximation compared to the Taylor approximation of the exponential map and results in both faster convergence as well as more stable approximation when compared to other iterative approaches.
Rigid 3-D Registration: A Simple Method Free of SVD and Eigendecomposition
  • Jin Wu
  • Computer Science
    IEEE Transactions on Instrumentation and Measurement
  • 2020
TLDR
A novel solution is obtained to solve the rigid 3-D registration problem, motivated by previous eigendecomposition approaches, and it is proven that the optimal rotation matrix can be directly computed for cases without the need for a quaternion.
Approximating Displacements in R by Rotations in R and its Application to Pointcloud Registration
No proper norm exists to measure the distance between two object poses essentially because a general pose is defined by a rotation and a translation, and thus it involves magnitudes with different…
Rigid registration of different poses of animated shapes
TLDR
A method to select a region of interest (ROI) which has a perfect alignment over the two poses (up to a rigid movement) and a simplified version of the Largest Common Point-set problem with a-priori knowledge about point correspondence is solved.
A Variational Approach to Registration with Local Exponential Coordinates
We identify a novel parameterization for the group of finite rotations (SO3), consisting of an atlas of exponential maps defined over local tangent planes, for the purpose of computing isometric…
...
...

References

SHOWING 1-10 OF 16 REFERENCES
A Comparison of Four Algorithms for Estimating 3-D Rigid Transformations
TLDR
A comparative analysis of four popular and efficient algorithms for 3-D rigid transformation computation, using respectively: singular value decomposition of a matrix, orthonormal matrices, unit quaternions and dual quaternion.
Closed-form solution of absolute orientation using orthonormal matrices
Finding the relationship between two coordinate systems by using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. The solution has…
Closed-form solution of absolute orientation using unit quaternions
TLDR
A closed-form solution to the least-squares problem for three or more paints is presented, simplified by use of unit quaternions to represent rotation.
A new closed-form solution for absolute orientation
  • Zhengyan WangA. Jepson
  • Mathematics
    1994 Proceedings of IEEE Conference on Computer Vision and Pattern Recognition
  • 1994
TLDR
The approach is based on the linear subspace method, which allows separate linear equations to be extracted for the displacement and rotation, suitable for real-time implementations, and leads to a simple algorithm for the determination of both the 3D transformation and error estimates for the estimated 3D displacement.
Least-Squares Estimation of Transformation Parameters Between Two Point Patterns
  • S. Umeyama
  • Computer Science, Mathematics
    IEEE Trans. Pattern Anal. Mach. Intell.
  • 1991
TLDR
The proposed theorem is a strict solution of the problem, and it always gives the correct transformation parameters even when the data is corrupted.
Estimating 3-D location parameters using dual number quaternions
Estimation of motion from a pair of range images: A review
On the Estimation of Rigid Body Rotation from Noisy Data
We derive an exact solution to the problem of estimating the rotation of a rigid body from noisy 3D image data. Our approach is based on total least squares (TLS), but unlike previous work involving…
Numerical Recipes in C: The Art of Sci-entific Computing
TLDR
This is the revised and greatly expanded Second Edition of the hugely popular Numerical Recipes, with over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines.
Matrix Eigensystem Routines — EISPACK Guide
TLDR
The Eispack subroutines and the handbook algol procedures are compared to show the similarities and the differences in execution times and documentation are compared.
...
...