Least-Squares Fitting of Two 3-D Point Sets

K. S. Arun; T. S. Huang; S. D. Blostein

doi:10.1109/TPAMI.1987.4767965

Least-Squares Fitting of Two 3-D Point Sets

K. S. Arun, T. S. Huang, S. D. Blostein

Research output: Contribution to journal › Article › peer-review

Abstract

Two point sets { p_i } and { p’_i }; i = 1, 2, … … …, N are related by p’_i= Rp_i+ T + N_i, where R is a rotation matrix, T a translation vector, and N_i a noise vector. Given {p_i} and { p’_i }, we present an algorithm for finding the least-squares solution of R and T, which is based on the singular value decomposition (SVD) of a 3 × 3 matrix. This new algorithm is compared to two earlier algorithms with respect to computer time requirements.

Original language	English (US)
Pages (from-to)	698-700
Number of pages	3
Journal	IEEE transactions on pattern analysis and machine intelligence
Volume	PAMI-9
Issue number	5
DOIs	https://doi.org/10.1109/TPAMI.1987.4767965
State	Published - Sep 1987
Externally published	Yes

Keywords

Computer vision
least-squares
motion estimation
quaternion
singular value decomposition

ASJC Scopus subject areas

Software
Computer Vision and Pattern Recognition
Computational Theory and Mathematics
Artificial Intelligence
Applied Mathematics

Online availability

10.1109/TPAMI.1987.4767965

Library availability

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AU - Arun, K. S.

AU - Huang, T. S.

AU - Blostein, S. D.

PY - 1987/9

Y1 - 1987/9

N2 - Two point sets { pi } and { p’i }; i = 1, 2, … … …, N are related by p’i= Rpi+ T + Ni, where R is a rotation matrix, T a translation vector, and Ni a noise vector. Given {pi} and { p’i }, we present an algorithm for finding the least-squares solution of R and T, which is based on the singular value decomposition (SVD) of a 3 × 3 matrix. This new algorithm is compared to two earlier algorithms with respect to computer time requirements.

AB - Two point sets { pi } and { p’i }; i = 1, 2, … … …, N are related by p’i= Rpi+ T + Ni, where R is a rotation matrix, T a translation vector, and Ni a noise vector. Given {pi} and { p’i }, we present an algorithm for finding the least-squares solution of R and T, which is based on the singular value decomposition (SVD) of a 3 × 3 matrix. This new algorithm is compared to two earlier algorithms with respect to computer time requirements.

KW - Computer vision

KW - least-squares

KW - motion estimation

KW - quaternion

KW - singular value decomposition

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Least-Squares Fitting of Two 3-D Point Sets

Abstract

Keywords

ASJC Scopus subject areas

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