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      Adaptive FEM-based nonrigid image registration using truncated hierarchical B-splines

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          Abstract

          We present an efficient approach of Finite Element Method (FEM)-based nonrigid image registration, in which the spatial transformation is constructed using truncated hierarchical B-splines (THB-splines). The image registration framework minimizes an energy functional using an FEM-based method and thus involves solving a large system of linear equations. This framework is carried out on a set of successively refined grids. However, due to the increased number of control points during subdivision, large linear systems are generated which are generally demanding to solve. Instead of using uniform subdivision, an adaptive local refinement scheme is carried out, only refining the areas of large change in deformation of the image. By incorporating the key advantages of THB-spline basis functions such as linear independence, partition of unity and reduced overlap into the FEM-based framework, we improve the matrix sparsity and computational efficiency. The performance of the proposed method is demonstrated on 2D synthetic and medical images.

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          A survey of medical image registration.

          The purpose of this paper is to present a survey of recent (published in 1993 or later) publications concerning medical image registration techniques. These publications will be classified according to a model based on nine salient criteria, the main dichotomy of which is extrinsic versus intrinsic methods. The statistics of the classification show definite trends in the evolving registration techniques, which will be discussed. At this moment, the bulk of interesting intrinsic methods is based on either segmented points or surfaces, or on techniques endeavouring to use the full information content of the images involved.
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            THB-splines: The truncated basis for hierarchical splines

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              Discrete B-splines and subdivision techniques in computer-aided geometric design and computer graphics

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                Author and article information

                Journal
                2017-03-17
                Article
                10.1016/j.camwa.2016.05.020
                1703.05963
                6ad7c97f-68d3-46b7-8b69-c8a3da1b7bdf

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Computers & Mathematics with Applications, Volume 72, Issue 8, October 2016, Pages 2028-2040
                math.NA

                Numerical & Computational mathematics
                Numerical & Computational mathematics

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