Flexible Multi-scale Image Alignment Using B-Spline Reparametrization
We present a new flexible alignment method to align two images. By minimizing an energy functional measuring the difference between the initial image and the target image, an L 2-gradient flow is derived for determining a map between the images. The flow is integrated by a finite element method in the spatial direction and an explicit Euler scheme in the temporal direction. Multi-resolution representations are used for achieving efficient multi-scale alignment. The experimental results show that the proposed method is effective, robust and capable of capturing the variation of the initial and target images, from large scale to small. We show that the map of two images in the alignment model is injective and surjective under appropriate conditions, and the solution of the alignment model exists. The results on the existence and uniqueness of the solution for the ordinary differential equation derived from the finite element discretization of our flexible alignment model are established.
KeywordsTarget Image Gaussian Filter Ordinary Differential Equation Finite Element Discretization Normalize Cross Correlation
This work is supported in part by NSFC key project under the grant 10990013, NSFC Funds for Creative Research Groups of China (grant No. 11021101) and NSFC project under the grant 81173663.
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