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multi-modal images

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Abstract — Multimodal image registration significantly benefits from previous denoising and structure segmentation and vice versa. In particular combined information of different image modalities makes segmentation significantly more robust. Indeed, fundamental tasks in image processing are highly interdependent. A variational approach is presented, which combines the detection of corresponding edges, an edge preserving denoising and the morphological registration via a non-rigid deformation for a pair of images with structural correspondence. The morphology of an image function is split into a singular part consisting of the edge set and a regular part represented by the field of normals on the ensemble of level sets. A Mumford-Shah type free discontinuity problem is applied to treat the singular morphology and the matching of corresponding edges under the deformation. The matching of the regular morphology is quantified by a second contribution which compares deformed normals and normals at deformed positions. Finally, a nonlinear elastic energy controls the deformation itself and ensures smoothness and injectivity. A multi scale approach that is based on a phase field approximation leads to an effective and efficient algorithm. Numerical experiments underline the robustness of the presented approach and show applications on medical images.

Abstract. A physically motivated approach is presented to compute a shape average of a given number of shapes. An elastic deformation is assigned to each shape. The shape average is then described as the common image under all elastic deformations of the given shapes, which minimizes the total elastic energy stored in these deformations. The underlying nonlinear elastic energy measures the local change of length, area, and volume. It is invariant under rigid body motions, and isometries are local minimizers. The model is relaxed involving a further energy which measures how well the elastic deformation image of a particular shape matches the average shape, and a suitable shape prior can be considered for the shape average. Shapes are represented via their edge sets, which also allows for an application to averaging image morphologies described via ensembles of edge sets. To make the approach computationally tractable, sharp edges are approximated via phase fields, and a corresponding variational phase field model is derived. Finite elements are applied for the spatial discretization, and a multi-scale alternating minimization approach allows the efficient computation of shape averages in 2D and 3D. Various applications, e. g. averaging the shape of feet or human organs, underline the qualitative properties of the presented approach.

Summary. The application of the theory of deformable templates to the study of the action of a group of diffeomorphisms on deformable objects provides a powerful framework to compute dense one-to-one matchings on d-dimensional domains. In this paper, we derive the geodesic equations that govern the time evolution of an optimal matching in the case of the action on 2D curves with various driving matching terms, and provide a Hamiltonian formulation in which the initial momentum is represented by an L 2 vector field on the boundary of the template. Key words: Infinite-dimensional Riemannian manifolds, Hamiltonian systems, shape representation and recognition.

Abstract. In this paper, we present a new non-parametric combined segmentation and registration method. The problem is cast as an optimization one, combining a matching criterion based on the active contour without edges [4] for segmentation, and a nonlinear-elasticity-based smoother on the displacement vector field. This modeling is twofold: first, registration is jointly performed with segmentation since guided by the segmentation process; it means that the algorithm produces both a smooth mapping between the two shapes and the segmentation of the object contained in the reference image. Secondly, the use of a nonlinearelasticity-type regularizer allows large deformations to occur, which makes the model comparable in this point with the viscous fluid registration method [7]. Several applications are proposed to demonstrate the potential of this method to both segmentation of one single image and to registration between two images. 1

Abstract—This paper presents a new algorithm based on the Mumford–Shah model for simultaneously detecting the edge features of two images and jointly estimating a consistent set of transformations to match them. Compared to the current asymmetric methods in the literature, this fully symmetric method allows one to determine one-to-one correspondences between the edge features of two images. The entire variational model is realized in a multiscale framework of the finite element approximation. The optimization process is guided by an estimation minimization-type algorithm and an adaptive generalized gradient flow to guarantee a fast and smooth relaxation. The algorithm is tested on T1 and T2 magnetic resonance image data to study the parameter setting. We also present promising results of four applications of the proposed algorithm: interobject monomodal registration, retinal image registration, matching digital photographs of neurosurgery with its volume data, and motion estimation for frame interpolation. Index Terms—Image registration, edge detection, Mumford– Shah (MS) model. Fig. 1. Nonsymmetric MS model for edge matching. and are the given reference and template images. and are the restored, piecewise smooth functions of image and image. is the combined discontinuity set of both images. Function represents the spatial transformation from image to image. I.

Abstract. In some registration applications additional user knowledge is available, which can improve and accelerate the registration process, especially for non-rigid registration. This is particularly important in the transfer of pre-operative plans to the operating room, e.g. for navigation. In case of tubular structures, such as vessels, a geometric representation can be extracted via segmentation and skeletonization. We present a new class of distance measures based on global filter kernels to compare such models efficiently with image data. The approach is validated in a non-rigid registration application with Powerdoppler ultrasound data. 1

Mathematical methods for time series analysis and digital image processing