Least-Squares Transformations between Point-Sets

  • Kalle Rutanen
  • Germán Gómez-Herrero
  • Sirkka-Liisa Eriksson
  • Karen Egiazarian
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7944)


This paper derives formulas for least-squares transformations between point-sets in ℝ d . We consider affine transformations, with optional constraints for linearity, scaling, and orientation. We base the derivations hierarchically on reductions, and use trace manipulation to achieve short derivations. For the unconstrained problems, we provide a new formula which maximizes the orthogonality of the transform matrix.


least-squares transformation point-set rank-deficient 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Kalle Rutanen
    • 1
  • Germán Gómez-Herrero
    • 2
  • Sirkka-Liisa Eriksson
    • 1
  • Karen Egiazarian
    • 3
  1. 1.Department of MathematicsTampere University of TechnologyFinland
  2. 2.Netherlands Institute for NeuroscienceNetherlands
  3. 3.Department of Signal ProcessingTampere University of TechnologyFinland

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