Affine Shape Alignment Using Covariant Gaussian Densities: A Direct Solution

Csaba Domokos, Z. Kato

Research output: Contribution to journalArticle

2 Citations (Scopus)


We propose a novel approach for the estimation of 2D affine transformations aligning a planar shape and its distorted observation. The exact transformation is obtained as a least-squares solution of a linear system of equations constructed by fitting Gaussian densities to the shapes which preserve the effect of the unknown transformation. In the case of compound shapes, we also propose a robust and efficient numerical scheme achieving near real-time performance. The method has been tested on synthetic as well as on real images. Its robustness in the case of segmentation errors, missing data, and modelling error has also been demonstrated. The proposed method does not require point correspondences nor the solution of complex optimization problems, has linear time complexity and provides an exact solution regardless of the magnitude of deformation.

Original languageEnglish
Pages (from-to)385-399
Number of pages15
JournalJournal of Mathematical Imaging and Vision
Issue number3
Publication statusPublished - Jan 1 2015



  • Affine transformation
  • Covariant function
  • Gaussian distribution
  • Registration
  • Shape alignment

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Condensed Matter Physics
  • Computer Vision and Pattern Recognition
  • Geometry and Topology
  • Applied Mathematics

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