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Large Deformation Registration via N-dimensional Quasi-conformal Maps

Project Description:

We propose a new method to obtain registration between n-dimensional manifolds with very large deformation. Given a set of landmark correspondences, our algorithm produces an optimal diffeomorphism that matches prescribed landmark constraints. The obtained registration is a n-dimensional quasi-conformal map. The basic idea of the model is to minimize an energy functional with a conformality term and a smoothness term. The conformality term allows the algorithm to produce diffeomorphisms even with very large deformation. We minimize the energy functional using alternating direction method of multipliers (ADDMM). The algorithm only involves solving an elliptic problem and a pointwise minimization problem. The time complexity and the robustness of the algorithm is independent of the number of landmark points. The boundary can be fixed or freed depends on application. Experimental results are presented.


  • Y.T. Lee, K.C. Lam, L.M. Lui, Large deformation registration via n-dimensional quasi-conformal maps, arXiv:1402.6908 (2014)