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Optimal similarity registration of volumetric images

by E. Kokiopoulou and D. Kressner and M. Zervos and N. Paragios

(Report number 2011-18)

Abstract
This paper proposes a novel approach to optimally solve volumetric registration problems. The proposed framework exploits parametric dictionaries for sparse volumetric representations, $\ell^1$ dissimilarities and DC (Difference of Convex functions) decomposition. The SAD (sum of absolute differences) criterion is applied to the sparse representation of the reference volume and a DC decomposition of this criterion with respect to the transformation parameters is derived. This permits to employ a cutting plane algorithm for determining the optimal relative transformation parameters of the query volume. It further provides a guarantee for the global optimality of the obtained solution, which -- to the best of our knowledge -- is not offered by any other existing approach. A numerical validation demonstrates the effectiveness and the large potential of the proposed method.

Keywords:

@Techreport{KKZP11_142,
  author = {E. Kokiopoulou and D. Kressner and M. Zervos and N. Paragios},
  title = {Optimal similarity registration of volumetric images},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2011-18},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-18.pdf },
  year = {2011}
}

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