Hansen, Michael Sass1; Thorup, Signe Strann3; Warfield, Simon K.4
1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Image Analysis and Computer Graphics, Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark4 Harvard Medical School
Image registration based on geodesic flows has gained much popularity in recent years. We describe a novel parametrization of the velocity field in a stationary flow equation. We show that the method offers both precision, flexibility, and simplicity of evaluation. With our representation, which is very similar to existing methods, we show that we can find an analytical solution. This solution converges exponentially to the true solution, and the gradients may be determined similarly. We compare to existing prominent methods; the log-euclidean polyaffine framework, and the DARTEL implementation of geodesic shooting for computational anatomy. We avoid to do warp field convolution by interpolation in a dense field, we can easily calculate warp derivatives in a reference frame of choice, and we can consequently avoid interpolation in the image space altogether.
2012 Ieee Workshop on Mathematical Methods in Biomedical Image Analysis (mmbia), 2012
convergence of numerical methods; convolution; differential geometry; flow; image registration; interpolation; medical image processing
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2012 IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA), 2012