articleTop 10% cited

Least-Squares Fitting of Two 3-D Point Sets

IEEE Transactions on Pattern Analysis and Machine Intelligence · 1987 · Vol. PAMI-9(5) · pp. 698–700

K.S. Arun✉(University of Illinois Urbana-Champaign)Thomas S. Huang(University of Illinois Urbana-Champaign)Steven D. Blostein(University of Illinois Urbana-Champaign)

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Abstract

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.

Advanced Vision and Imaging Robotics and Sensor-Based Localization Image and Object Detection TechniquesSingular value decompositionMathematicsAlgorithmTranslation (biology)Noise (video)CombinatoricsLeast-squares function approximationMatrix (chemical analysis)Singular valueRotation (mathematics)

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