Optimal similarity registration of volumetric images

This paper proposes a novel approach to optimally solve volumetric registration problems. The proposed framework exploits parametric dictionaries for sparse volumetric representations, ℓ¹ 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.