**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.

**Publication:**

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