A Variational Approach to Nonrigid Morphological Image Registration

Abstract

A variational method for nonrigid registration of multimodal image data is presented. A suitable deformation will be determined via the minimization of a morphological, i.e., contrast invariant, matching functional along with an appropriate regularization energy. The aim is to correlate the morphologies of a template and a reference image under the deformation. Mathematically, the morphology of images can be described by the entity of level sets of the image and hence by its Gauss map. A class of morphological matching functionals is presented which measure the defect of the template Gauss map in the deformed state with respect to the deformed Gauss map of the reference image. The problem is regularized by considering a nonlinear elastic regularization energy. Existence of homeomorphic, minimizing deformation is proved under assumptions on the class of admissible deformations. With respect to actual medical applications, suitable generalizations of the matching energies and the boundary conditions are presented. Concerning the robust implementation of the approach, the problem is embedded in a multiscale context. A discretization based on multilinear finite elements is discussed, and the first numerical results are presented.

A Combined Segmentation and Registration Framework with a Nonlinear Elasticity Smoother

“…The segmentation criterion is based on the gradient vector flow [36], and a deformation field is computed via non-linear elasticity using the finite element method. For completeness, we also refer the reader to [2], [23] for a variational registration method for large deformations, to [26], for a much related work which also uses nonlinear elasticity regularization but which is implemented using the finite element method, and to [9], a related work that uses nonlinear elasticity principles but different from our proposed approach. More details of the proposed method are presented in [18].…”

Line Search Multilevel Optimization as Computational Methods for Dense Optical Flow

“…Other cases include the constancy of the gradient direction [15] or the assumption that the shapes of the image (identified as the level lines) move along the sequence [16] (this assumption has been used in [19] in the context of image registration). Higher derivative models have been studied in [43].…”

“…In [16], a model is proposed for illumination-invariant optical flow computation, previously introduced in [19] in the context of image registration. The brightness constancy assumption is replaced by the assumption that the shapes of the image move along the sequence.…”

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