. This paper offers a new fast algorithm for non-rigid Viscous Fluid Registration of medical images that is at least an order of magnitude faster than the previous method by Christensen et al. [4]. The core algorithm in the fluid registration method is based on a linear elastic deformation of the velocity field of the fluid. Using the linearity of this deformation we derive a convolution filter which we use in a scalespace framework. We also demonstrate that the 'demon'-based registration method of Thirion [13] can be seen as an approximation to the fluid registration method and point to possible problems. 1 Introduction Non-rigid registration of two medical images is performed by applying global and/or local transformations to one of the images (which we will call the template T ) in such a way that it matches the other image (the study S). It is important to understand that the aim of the transformation is to map the template completely onto the study in such a way that informatio...

This paper studies a variational formulation of the image matching problem. We consider a scenario in which a canonical representative image T is to be carried via a smooth change of variable into an image which is intended to provide a good fit to the observed data. The images are all defined on a compact set G ae IR 3 . The changes of variable are determined as solutions of the nonlinear Eulerian transport equation dj(s; x) ds = v(j(s; x); s); j(ø ; x) = x; (0:1) with the location j(0; x) in the canonical image carried to the location x in the deformed image. The variational problem then takes the form arg min v kvk 2 + Z G jT ffi j(0; x) \Gamma D(x)j 2 dx ; (0:2) where kvk is an appropriate norm on the velocity field v(\Delta; \Delta), and the second term attempts to enforce fidelity to the data. In this paper we derive conditions under which the variational problem described above is well posed. The key issue is the choice of the norm. Conditions are formulated u...

This paper develops mathematical representations for neuro-anatomically significant substructures of the brain and their variability in a population. The focus of the paper is on the neuro-anatomical variation of the geometry and the "shape" of 2-dimensional surfaces in the brain. As examples, we focus on the cortical and hippocampal surfaces in an ensemble of Macaque monkeys and human MRI brains. The "shape" of the substructures are quantified via the construction of templates; the variations are represented by defining probabilistic deformations of the template. Methods for empirically estimating probability measures on these deformations are developed by representing the deformations as Gaussian random vector fields on the embedded sub-manifolds. This work was supported by NIH grants RR01380, RO1-MH52158-01A1 , ARO DAAL-03-86-K-0110, ARO DAAH049510494 and NSF grant BIR-9424264 The Gaussian random vector fields are constructed as quadratic mean limits using complete orthonormal b...

In this paper, we investigate the introduction of cortical constraints for non rigid inter-subject brain registration. We extract sulcal patterns with the active ribbon method, presented in [25]. An energy based registration method [21] makes it possible to incorporate the matching of cortical sulci, and express in a unified framework the local sparse similarity and the global "iconic" similarity. We show the objective benefits of cortical constraints on a database of 18 subjects, with global and local measures of the registration's quality.

In this paper we introduce a novel and efficient approach to dense image registration, which does not require a derivative of the employed cost function. In such a context the registration problem is formulated using a discrete Markov Random Field objective function. First, towards dimensionality reduction on the variables we assume that the dense deformation field can be expressed using a small number of control points (registration grid) and an interpolation strategy. Then, the registration cost is expressed using a discrete sum over image costs (using an arbitrary similarity measure) projected on the control points, and a smoothness term that penalizes local deviations on the deformation field according to a neighborhood system on the grid. Towards a discrete approach the search space is quantized resulting in a fully discrete model. In order to account for large deformations and produce results on a high resolution level a multi-scale incremental approach is considered where the optimal solution is iteratively updated. This is done through successive morphings of the source towards the target image. Efficient linear programming using the primal dual principles is considered to recover the lowest potential of the cost function. Very promising results using synthetic data with known deformations and real data demonstrate the potentials of our approach.

Echo-planar imaging (EPI) is a fast nuclear magnetic resonance imaging method. Unfortunately, local magnetic field inhomogeneities induced mainly by the subject 's presence cause significant geometrical distortion, predominantly along the phase-encoding direction, which must be undone to allow for meaningful further processing. So far, this aspect has been too often neglected.

Image registration techniques are used routinely in a variety of today’s medical imaging diagnosis. Since the problem is ill-posed, one may like to add additional information about distortions. This applies, for example, to the registration of contrast enhanced images, where variations of substructures are not related to patient motion but to contrast uptake. Here, one may only be interested in registrations which do not alter the volume of any substructure. In this paper we discuss image registration techniques with a focus on volume preserving constraints. These constraints can reduce the non-uniqueness of the registration problem significantly. Our implementation is based on a constrained optimization formulation. Upon discretization, we obtain a large, discrete, highly nonlinear optimization problem and the necessary conditions for the solution form a discretize nonlinear partial differential equation. To solve the problem we use a variant of Sequential Quadratic Programming method. Moreover, we present results on synthetic as well as on real life data. 1

Image registration is central to many challenges in medical imaging today. It has a vast range of applications. The purpose of this note is twofold. First, we review some of the most promising non-linear registration strategies currently used in medical imaging. We show that all these techniques may be phrased in terms of a variational problem and allow for a unified treatment. Second, we introduce, within the variational framework, a new nonlinear registration model based on a curvature type regularizer. We show that affine linear transformations belong to the kernel of this regularizer. This has the important consequence that an additional pre-registration step is no longer necessary. Furthermore, we develop a stable and fast implementation of the new scheme based on a real discrete cosine transformation. We demonstrate the advantages of the new technique for synthetic data sets and present an application of the algorithm for registering MR-mammography images.

Introduction Registration is the process of the alignment of medical image data. Nonlinear registration is the set of techniques that allow the alignment of data sets that are mismatched in a nonlinear or nonuniform manner. Such misalignment can be caused by a physical deformation process, or can be due to intrinsic shape differences. For example, deformation of the brain can occur during neurosurgery when the skull is opened and CSF drained, and when a tumour is removed. Nonlinear deformation is a characteristic of the motion of the nonrigid organs of the abdomen. Also, shape differences arise when a comparison is made between the brains of different people. Although the broad structure of the brain is similar throughout different people (and even different species), both normal anatomical variability and various disease states lead to local nonlinear shape differences. Harvard Medical School and Brigham and Women's Hospital, Department of Radiology, 75 Fra

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