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Surface parameterizations are widely applied in computer graphics, medicalimaging and transformation optics. In this paper, we rigorously derive thegradient vector and Hessian matrix of the discrete conformal energy forspherical conformal parameterizations of simply connected closed surfaces ofgenus-$0$. In addition, we give the sparsity structure of the Hessian matrix,which leads to a robust Hessian-based trust region algorithm for thecomputation of spherical conformal maps. Numerical experiments demonstrate thelocal quadratic convergence of the proposed algorithm with low conformaldistortions. We subsequently propose an application of our method to surfaceregistrations that still maintains local quadratic convergence.

A Robust Hessian-based Trust Region Algorithm for Spherical Conformal Parameterizations