Implementation of Direct Optimization Techniques for Deformable Image Registration

Student: Patrick Wucherer
Advisor: Nassir Navab
Supervision by: Darko Zikic

Abstract

In this report we discuss two different direct approaches for solving the optimization problem of the deformable registration in 2D. The aim is, to minimize the nonlinear least squares cost function. The first part of the function is the sum of squared differences and the second part is a component for penalizing the function, if the displacement field is not smooth. We tried to solve this problem with direct techniques, so we first discretize the cost function and then solve it with the Gradient Descent and the Gauss-Newton minimization method. We compare the two methods by applying them to synthetic images, to show their different convergence. We conclude, that the Gauss-Newton method should be preferred, because of the faster convergence, not only in respect to the number of iterations, but also in respect to time in our implementation.

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