Least-Squares Fitting of Two 3-D Point Sets

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

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)698-700
Number of pages3
JournalIEEE transactions on pattern analysis and machine intelligence
Issue number5
StatePublished - Sep 1987
Externally publishedYes


  • 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


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