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Globally optimal volume registration using DC programming

by E. Kokiopoulou and D. Kressner and N. Paragios and P. Frossard

(Report number 2009-38)

Abstract
This paper proposes a novel approach to optimally solve rigid registration problems among volumetric images. The proposed framework exploits sparse geometric expansions for volumetric representations and DC (Difference of Convex functions) programming. We apply the SAD (sum of absolute differences) criterion to the sparse representation of the reference volume and we derive a DC decomposition of this criterion with respect to the transformation parameters. This permits to employ a cutting plane algorithm for determining the optimal relative transformation parameters of the query volume. It further enjoys theoretical guarantees 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 large potential of the proposed method.

Keywords:

@Techreport{KKPF09_419,
  author = {E. Kokiopoulou and D. Kressner and N. Paragios and P. Frossard},
  title = {Globally optimal volume registration using DC programming},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2009-38},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2009/2009-38.pdf },
  year = {2009}
}

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