Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> A new approach is presented for elastic registration of medical images, and is applied to magnetic resonance images of the brain. Experimental results demonstrate remarkably high accuracy in superposition of images from different subjects, thus enabling very precise localization of morphological characteristics in population studies. There are two major novelties in the proposed algorithm. First, it uses an attribute vector, i.e. a set of geometric moment invariants that is defined on each voxel in an image, to reflect the underlying anatomy at different scales. The attribute vector, if rich enough, can distinguish between different parts of an image, which helps establish anatomical correspondences in the deformation procedure. This is a fundamental deviation of our method, referred to as HAMMER, from other volumetric deformation methods, which are typically based on maximizing image similarity. Second, in order to avoid being trapped by local minima, i.e. suboptimal poor matches, HAMMER uses a successive approximation of the energy function being optimized by lower dimensional energy functions, which are constructed to have significantly fewer local minima. This is achieved by hierarchically selecting features that have distinct attribute vectors, thus drastically reducing ambiguity in finding correspondence. A number of experiments in this paper have demonstrated excellent performance. <s> BIB001 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> In this work, we present a method for the integration of fea- ture and intensity information for non rigid registration. Our method is based on a free-form deformation model, and uses a normalized mu- tual information intensity similarity metric to match intensities and the robust point matching framework to estimate feature (point) correspon- dences. The intensity and feature components of the registration are posed in a single energy functional with associated weights. We com- pare our method to both point-based and intensity-based registrations. In particular, we evaluate registration accuracy as measured by point landmark distances and image intensity similarity on a set of seventeen normal subjects. These results suggest that the integration of intensity and point-based registration is highly effective in yielding more accurate registrations. <s> BIB002 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> In this article we merge point feature and intensity-based registration in a single algorithm to tackle the problem of multiple brain registration. Because of the high variability of the shape of the cortex across individuals, there exist geometrical ambiguities in the registration process that an intensity measure alone is unable to solve. This problem can be tackled using anatomical knowledge. First, we automatically segment and label the whole set of the cortical sulci, with a non-parametric approach that enables the capture of their highly variable shape and topology. Then, we develop a registration energy that merges intensity and feature point matching. Its minimization leads to a linear combination of a dense smooth vector field and radial basis functions. We use and process differently the bottom line of the sulci from its upper border, whose localization is even more variable across individuals. We show that the additional sulcal energy improves the registration of the cortical sulci, while still keeping the transformation smooth and one-to-one. <s> BIB003 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> Two new consistent image registration algorithms are presented: one is based on matching corresponding landmarks and the other is based on matching both landmark and intensity information. The consistent landmark and intensity registration algorithm produces good correspondences between images near landmark locations by matching corresponding landmarks and away from landmark locations by matching the image intensities. In contrast to similar unidirectional algorithms, these new consistent algorithms jointly estimate the forward and reverse transformation between two images while minimizing the inverse consistency error-the error between the forward (reverse) transformation and the inverse of the the reverse (forward) transformation. This reduces the ambiguous correspondence between the forward and reverse transformations associated with large inverse consistency errors. In both algorithms a thin-plate spline (TPS) model is used to regularize the estimated transformations. Two-dimensional (2-D) examples are presented that show the inverse consistency error produced by the traditional unidirectional landmark TPS algorithm can be relatively large and that this error is minimized using the consistent landmark algorithm. Results using 2-D magnetic resonance imaging data are presented that demonstrate that using landmark and intensity information together produce better correspondence between medical images than using either landmarks or intensity information alone. <s> BIB004 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> This paper presents a method of deformable registration of cortical structures across individuals, using hybrid volumetric and surface warping. The proposed method uses two steps. In the first step, a HAMMER-based volumetric registration algorithm warps the model surface to the individual’s space. In the second step, an attribute-based surface registration method further refines the results of the volumetric warping. An attribute vector is defined for each vertex on the cortical surface, and used to capture the local and global geometric features of the surface patch. The attribute vector is designed to be as distinctive as possible, so that each vertex on the model surface can find its correspondence on the individual surface. Experimental results on synthesized and real brain data are provided to demonstrate the performance of the proposed method in registering cortical structures across individuals. <s> BIB005 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> We investigate the introduction of cortical constraints for non rigid intersubject brain registration. We extract sulcal patterns with the active ribbon method, presented by Le Goualher et al. (1997). An energy based registration method (Hellier et al., 2001), which will be called photometric registration method in this paper, makes it possible to incorporate the matching of cortical sulci. The local sparse similarity and the photometric similarity are, thus, expressed in a unified framework. We show the benefits of cortical constraints on a database of 18 subjects, with global and local assessment of the registration. This new registration scheme has also been evaluated on functional magnetoencephalography data. We show that the anatomically constrained registration leads to a substantial reduction of the intersubject functional variability. <s> BIB006 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> This paper examine the Euler-Lagrange equations for the solution of the large deformation diffeomorphic metric mapping problem studied in Dupuis et al. (1998) and Trouve (1995) in which two images I 0, I 1 are given and connected via the diffeomorphic change of coordinates I 0???1=I 1 where ?=?1 is the end point at t= 1 of curve ? t , t?[0, 1] satisfying .? t =v t (? t ), t? [0,1] with ?0=id. The variational problem takes the form ::: ::: $$\mathop {\arg {\text{m}}in}\limits_{\upsilon :\dot \phi _t = \upsilon _t \left( {\dot \phi } \right)} \left( {\int_0^1 {\left\| {\upsilon _t } \right\|} ^2 {\text{d}}t + \left\| {I_0 \circ \phi _1^{ - 1} - I_1 } \right\|_{L^2 }^2 } \right),$$ ::: ::: where ?v t? V is an appropriate Sobolev norm on the velocity field v t(·), and the second term enforces matching of the images with ?·?L 2 representing the squared-error norm. ::: ::: In this paper we derive the Euler-Lagrange equations characterizing the minimizing vector fields v t, t?[0, 1] assuming sufficient smoothness of the norm to guarantee existence of solutions in the space of diffeomorphisms. We describe the implementation of the Euler equations using semi-lagrangian method of computing particle flows and show the solutions for various examples. As well, we compute the metric distance on several anatomical configurations as measured by ?0 1?v t? V dt on the geodesic shortest paths. <s> BIB007 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> A key technique for protein analysis is the geometric alignment of gel electrophoresis images. While in previous work either intensity- or landmark-based approaches have been used for the registration of electrophoresis images, we here introduce a scheme incorporating both intensity and landmark information. With this approach, point landmarks are localized using a model fitting scheme and this geometric information is combined with intensity information for elastic image registration. By experiments on the basis of electrophoresis images of different levels of complexity, we demonstrate that the intensity information alone is generally not sufficient to accurately register corresponding images. However, it turns out that the incorporation of landmarks significantly improves the registration accuracy. This is supported by quantitative results. <s> BIB008 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> We develop a novel Lagrangian reference frame diffeomorphic image and landmark registration method. The algorithm uses the fixed Langrangian reference frame to define the map between coordinate systems, but also generates and stores the inverse map from the Eulerian to the Lagrangian frame. Computing both maps allows facile computation of both Eulerian and Langrangian quantities. We apply this algorithm to estimating a putative evolutionary change of coordinates between a population of chimpanzee and human cortices. Inter-species functional homologues fix the map explicitly, where they are known, while image similarities guide the alignment elsewhere. This map allows detailed study of the volumetric change between chimp and human cortex. Instead of basing the inter-species study on a single species atlas, we diffeomorphically connect the mean shape and intensity templates for each group. The human statistics then map diffeomorphically into the space of the chimpanzee cortex providing a comparison between species. The population statistics show a significant doubling of the relative prefrontal lobe size in humans, as compared to chimpanzees. <s> BIB009 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> This paper proposes a new interactive hybrid non-rigid registration framework that combines any intensity-based algorithm with a feature-based component, using an iterative dual energy minimization. The resulting transformation combines both intensity-based and feature-based deformation fields. The feature matching exploits user-placed landmark pairs, and based on saliency and similarity measures, optimizes the correspondences in the neighborhood of each landmark. A dense feature-based deformation field is then generated using a thin-plate spline interpolation. Additionally, the framework allows user interactivity for live guidance of the algorithm in case of errors or inaccuracies. We present three experimental results of our hybrid approach on lung, pelvis and brain datasets, and show that in each case, the registration benefited from the hybrid approach as opposed to its intensity component alone. <s> BIB010 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> An image registration technique is presented for the registration of medical images using a hybrid combination of coarse-scale landmark and B-splines deformable registration techniques. The technique is particularly effective for registration problems in which the images to be registered contain large localized deformations. A brief overview of landmark and deformable registration techniques is presented. The hierarchical multiscale image decomposition of E. Tadmor, S. Nezzar, and L. Vese, A multiscale image representation using hierarchical (BV;L(2)) decompositions, Multiscale Modeling and Simulations, vol. 2, no. 4, pp. 554{579, 2004, is reviewed, and an image registration algorithm is developed based on combining the multiscale decomposition with landmark and deformable techniques. Successful registration of medical images is achieved by first obtaining a hierarchical multiscale decomposition of the images and then using landmark-based registration to register the resulting coarse scales. Corresponding bony structure landmarks are easily identified in the coarse scales, which contain only the large shapes and main features of the image. This registration is then fine tuned by using the resulting transformation as the starting point to deformably register the original images with each other using an iterated multiscale B-splines deformable registration technique. The accuracy and efficiency of the hybrid technique is demonstrated with several image registration case studies in two and three dimensions. Additionally, the hybrid technique is shown to be very robust with respect to the location of landmarks and presence of noise. <s> BIB011 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> This paper describes DARTEL, which is an algorithm for diffeomorphic image registration. It is implemented for both 2D and 3D image registration and has been formulated to include an option for estimating inverse consistent deformations. Nonlinear registration is considered as a local optimisation problem, which is solved using a Levenberg-Marquardt strategy. The necessary matrix solutions are obtained in reasonable time using a multigrid method. A constant Eulerian velocity framework is used, which allows a rapid scaling and squaring method to be used in the computations. DARTEL has been applied to intersubject registration of 471 whole brain images, and the resulting deformations were evaluated in terms of how well they encode the shape information necessary to separate male and female subjects and to predict the ages of the subjects. <s> BIB012 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> The aim of this paper is to develop a registration methodology in order to combine anatomical and functional information provided by thoracic/abdominal computed tomography (CT) and whole-body positron emission tomography (PET) images. The proposed procedure is based on the incorporation of prior anatomical information in an intensity-based nonrigid registration algorithm. This incorporation is achieved in an explicit way, initializing the intensity-based registration stage with the solution obtained by a nonrigid registration of corresponding anatomical structures. A segmentation algorithm based on a hierarchically ordered set of anatomy-specific rules is used to obtain anatomical structures in CT and emission PET scans. Nonrigid deformations are modeled in both registration stages by means of free-form deformations, the optimization of the control points being achieved by means of an original vector field-based approach instead of the classical gradient-based techniques, considerably reducing the computational time of the structure registration stage. We have applied the proposed methodology to 38 sets of images (33 provided by standalone machines and five by hybrid systems) and an assessment protocol has been developed to furnish a qualitative evaluation of the algorithm performance <s> BIB013 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> We introduce a new hybrid approach for spline-based elastic image registration using both point landmarks and intensity information. As underlying deformation model we use Gaussian elastic body splines (GEBS), which are solutions of the Navier equation of linear elasticity under Gaussian forces. We also incorporate landmark localization uncertainties represented by weight matrices to cope with anisotropic errors. The hybrid registration approach is formulated as an energy-minimizing functional that incorporates landmark and intensity information as well as a regularization based on GEBS. Since the approach is based on a physical deformation model, cross-effects in elastic deformations can be taken into account. We demonstrate the applicability of our scheme based on MR images of the brain. It turns out that the new scheme achieves more accurate results compared to a pure landmark-based as well as a pure intensity-based scheme. <s> BIB014 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> In order to compare anatomical and functional brain imaging data across subjects, the images must first be registered to a common coordinate system in which anatomical features are aligned. Intensity-based volume registration methods can align subcortical structures well, but the variability in sulcal folding patterns typically results in misalignment of the cortical surface. Conversely, surface-based registration using sulcal features can produce excellent cortical alignment but the mapping between brains is restricted to the cortical surface. Here we describe a method for volumetric registration that also produces an accurate one-to-one point correspondence between cortical surfaces. This is achieved by first parameterizing and aligning the cortical surfaces using sulcal landmarks. We then use a constrained harmonic mapping to extend this surface correspondence to the entire cortical volume. Finally, this mapping is refined using an intensity-based warp. We demonstrate the utility of the method by applying it to T1-weighted magnetic resonance images (MRIs). We evaluate the performance of our proposed method relative to existing methods that use only intensity information; for this comparison we compute the intersubject alignment of expert-labeled subcortical structures after registration. <s> BIB015 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> We propose an efficient non-parametric diffeomorphic image registration algorithm based on Thirion's demons algorithm. In the first part of this paper, we show that Thirion's demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. We provide strong theoretical roots to the different variants of Thirion's demons algorithm. This analysis predicts a theoretical advantage for the symmetric forces variant of the demons algorithm. We show on controlled experiments that this advantage is confirmed in practice and yields a faster convergence. In the second part of this paper, we adapt the optimization procedure underlying the demons algorithm to a space of diffeomorphic transformations. In contrast to many diffeomorphic registration algorithms, our solution is computationally efficient since in practice it only replaces an addition of displacement fields by a few compositions. Our experiments show that in addition to being diffeomorphic, our algorithm provides results that are similar to the ones from the demons algorithm but with transformations that are much smoother and closer to the gold standard, available in controlled experiments, in terms of Jacobians. <s> BIB016 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> Modern morphometric studies use non-linear image registration to compare anatomies and perform group analysis. Recently, log-Euclidean approaches have contributed to promote the use of such computational anatomy tools by permitting simple computations of statistics on a rather large class of invertible spatial transformations. In this work, we propose a non-linear registration algorithm perfectly fit for log-Euclidean statistics on diffeomorphisms. Our algorithm works completely in the log-domain, i.e. it uses a stationary velocity field. This implies that we guarantee the invertibility of the deformation and have access to the true inverse transformation. This also means that our output can be directly used for log-Euclidean statistics without relying on the heavy computation of the log of the spatial transformation. As it is often desirable, our algorithm is symmetric with respect to the order of the input images. Furthermore, we use an alternate optimization approach related to Thirion's demons algorithm to provide a fast non-linear registration algorithm. First results show that our algorithm outperforms both the demons algorithm and the recently proposed diffeomorphic demons algorithm in terms of accuracy of the transformation while remaining computationally efficient. <s> BIB017 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> In this paper, we propose a novel method for the registration of volumetric images of the brain that optimizes the alignment of both cortical and subcortical structures. In order to achieve this, relevant geometrical information is extracted from a surface-based morph and diffused into the volume using the Navier operator of elasticity, resulting in a volumetric warp that aligns cortical folding patterns. This warp field is then refined with an intensity driven optical flow procedure that registers noncortical regions, while preserving the cortical alignment. The result is a combined surface and volume morph (CVS) that accurately registers both cortical and subcortical regions, establishing a single coordinate system suitable for the entire brain. <s> BIB018 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> We introduce a new hybrid approach for spline-based elastic registration of multimodal medical images. The approach uses point landmarks as well as intensity information based on local analytic measures for joint entropy and mutual information. The information-theoretic similarity measures are computationally efficient and can be optimized independently for each voxel. We have applied our approach to synthetic images, brain phantom images, as well as clinically relevant multimodal medical images. We also compared our measures with previous measures. <s> BIB019 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> Volumetric registration of brain MR images presents a challenging problem due to the wide variety of sulcal folding patterns. We present a novel volumetric registration method based on an intermediate parameter space in which the shape differences are normalized. First, we generate a 3D harmonic map of each brain volume to unit ball which is used as an intermediate space. Cortical surface features and volumetric intensity are then used to find a simultaneous surface and volume registration. We present a finite element method for the registration by using a tetrahedral volumetric mesh for registering the interior volumetric information and the corresponding triangulated mesh at the surface points. This framework aligns the convoluted sulcal folding patterns as well as the subcortical structures by allowing simultaneous flow of surface and volumes for registration. We describe the methodology and FEM implementation and then evaluate the method in terms of the overlap between segmented structures in coregistered brains. <s> BIB020 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> We present the Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizors for the modified Demons objective function can be efficiently approximated on the sphere using iterative smoothing. Based on one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast. The Spherical Demons algorithm can also be modified to register a given spherical image to a probabilistic atlas. We demonstrate two variants of the algorithm corresponding to warping the atlas or warping the subject. Registration of a cortical surface mesh to an atlas mesh, both with more than 160 k nodes requires less than 5 min when warping the atlas and less than 3 min when warping the subject on a Xeon 3.2 GHz single processor machine. This is comparable to the fastest nondiffeomorphic landmark-free surface registration algorithms. Furthermore, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different applications that use registration to transfer segmentation labels onto a new image 1) parcellation of in vivo cortical surfaces and 2) Brodmann area localization in ex vivo cortical surfaces. <s> BIB021 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> In this paper we present a novel hybrid approach for multimodal medical image registration based on diffeomorphic demons. Diffeomorphic demons have proven to be a robust and efficient way for intensity-based image registration. A very recent extension even allows to use mutual information (MI) as a similarity measure to registration multimodal images. However, due to the intensity correspondence uncertainty existing in some anatomical parts, it is difficult for a purely intensity-based algorithm to solve the registration problem. Therefore, we propose to combine the resulting transformations from both intensity-based and landmark-based methods for multimodal non-rigid registration based on diffeomorphic demons. Several experiments on different types of MR images were conducted, for which we show that a better anatomical correspondence between the images can be obtained using the hybrid approach than using either intensity information or landmarks alone. <s> BIB022 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> In this paper we propose a variational approach for multimodal image registration based on the diffeomorphic demons algorithm. Diffeomorphic demons has proven to be a robust and efficient way for intensity-based image registration. However, the main drawback is that it cannot deal with multiple modalities. We propose to replace the standard demons similarity metric (image intensity differences) by point-wise mutual information (PMI) in the energy function. By comparing the accuracy between our PMI based diffeomorphic demons and the B-Spline based free-form deformation approach (FFD) on simulated deformations, we show the proposed algorithm performs significantly better. <s> BIB023 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> In this paper, we introduce a novel approach to bridge the gap between the landmark-based and the iconic-based voxel-wise registration methods. The registration problem is formulated with the use of Markov Random Field theory resulting in a discrete objective function consisting of thee parts. The first part of the energy accounts for the iconic-based volumetric registration problem while the second one for establishing geometrically meaningful correspondences by optimizing over a set of automatically generated mutually salient candidate pairs of points. The last part of the energy penalizes locally the difference between the dense deformation field due to the iconic-based registration and the implied displacements due to the obtained correspondences. Promising results in real MR brain data demonstrate the potentials of our approach. <s> BIB024 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> The goal of this study is to develop a matching algorithm that can handle large geometric changes in x-ray computed tomography (CT)-derived lung geometry occurring during deep breath maneuvers. These geometric relationships are further utilized to build a dynamic lung airway model for computational fluid dynamics (CFD) studies of pulmonary air flow. The proposed algorithm is based on a cubic B-spline-based hybrid registration framework that incorporates anatomic landmark information with intensity patterns. A sequence of invertible B-splines is composed in a multiresolution framework to ensure local invertibility of the large deformation transformation and a physiologically meaningful similarity measure is adopted to compensate for changes in voxel intensity due to inflation. Registrations are performed using the proposed approach to match six pairs of 3D CT human lung datasets. Results show that the proposed approach has the ability to match the intensity pattern and the anatomical landmarks, and ensure local invertibility for large deformation transformations. Statistical results also show that the proposed hybrid approach yields significantly improved results as compared with approaches using either landmarks or intensity alone. <s> BIB025 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> The alignment and normalization of individual brain structures is a prerequisite for group-level analyses of structural and functional neuroimaging data. The techniques currently available are either based on volume and/or surface attributes, with limited insight regarding the consistent alignment of anatomical landmarks across individuals. This article details a global, geometric approach that performs the alignment of the exhaustive sulcal imprints (cortical folding patterns) across individuals. This DIffeomorphic Sulcal-based COrtical (DISCO) technique proceeds to the automatic extraction, identification and simplification of sulcal features from T1-weighted Magnetic Resonance Image (MRI) series. These features are then used as control measures for fully-3-D diffeomorphic deformations. Quantitative and qualitative evaluations show that DISCO correctly aligns the sulcal folds and gray and white matter volumes across individuals. The comparison with a recent, iconic diffeomorphic approach (DARTEL) highlights how the absence of explicit cortical landmarks may lead to the misalignment of cortical sulci. We also feature DISCO in the automatic design of an empirical sulcal template from group data. We also demonstrate how DISCO can efficiently be combined with an image-based deformation (DARTEL) to further improve the consistency and accuracy of alignment performances. Finally, we illustrate how the optimized alignment of cortical folds across subjects improves sensitivity in the detection of functional activations in a group-level analysis of neuroimaging data. <s> BIB026 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> Analysis of gene expression patterns in brain images obtained from high-throughput in situ hybridization requires accurate and consistent annotations of anatomical regions/subregions. Such annotations are obtained by mapping an anatomical atlas onto the gene expression images through intensity- and/or landmark-based registration methods or deformable model-based segmentation methods. Due to the complex appearance of the gene expression images, these approaches require a pre-processing step to determine landmark correspondences in order to incorporate landmark-based geometric constraints. In this paper, we propose a novel method for landmark-constrained, intensity-based registration without determining landmark correspondences a priori. The proposed method performs dense image registration and identifies the landmark correspondences, simultaneously, using a single higher-order Markov Random Field model. In addition, a machine learning technique is used to improve the discriminating properties of local descriptors for landmark matching by projecting them in a Hamming space of lower dimension. We qualitatively show that our method achieves promising results and also compares well, quantitatively, with the expert's annotations, outperforming previous methods. <s> BIB027 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> Abstract This paper proposes a generic framework for the registration, the template estimation and the variability analysis of white matter fiber bundles extracted from diffusion images. This framework is based on the metric on currents for the comparison of fiber bundles. This metric measures anatomical differences between fiber bundles, seen as global homologous structures across subjects. It avoids the need to establish correspondences between points or between individual fibers of different bundles. It can measure differences both in terms of the geometry of the bundles (like its boundaries) and in terms of the density of fibers within the bundle. It is robust to fiber interruptions and reconnections. In addition, a recently introduced sparse approximation algorithm allows us to give an interpretable representation of the fiber bundles and their variations in the framework of currents. First, we used this metric to drive the registration between two sets of homologous fiber bundles of two different subjects. A dense deformation of the underlying white matter is estimated, which is constrained by the bundles seen as global anatomical landmarks. By contrast, the alignment obtained from image registration is driven only by the local gradient of the image. Second, we propose a generative statistical model for the analysis of a collection of homologous bundles. This model consistently estimates prototype fiber bundles (called template), which capture the anatomical invariants in the population, a set of deformations, which align the geometry of the template to that of each subject and a set of residual perturbations. The statistical analysis of both the deformations and the residuals describe the anatomical variability in terms of geometry (stretching, torque, etc.) and “texture” (fiber density, etc.). Third, this statistical modeling allows us to simulate new synthetic bundles according to the estimated variability. This gives a way to interpret the anatomical features that the model detects consistently across the subjects. This may be used to better understand the bias introduced by the fiber extraction methods and eventually to give anatomical characterization of the normal or pathological variability of fiber bundles. <s> BIB028 </s> Deformable Medical Image Registration: A Survey <s> 1) Additional Information Used Independently: <s> Traditional intensity-based registration methods are often insufficient for tumour tracking in time-series ultrasound, where the low signal-to-noise ratio significantly degrades the quality of the output images, and topological changes may occur as the anatomical structures slide in and out of the focus plane. To overcome these issues, we propose a hybrid feature-based Log-Demons registration method. The novelty of our approach lies in estimating a hybrid update deformation field from demons forces that carry voxel-based local information and regional spatial correspondences yielded by a block-matching scheme within the diffeomorphic Log-Demons framework. Instead of relying on intensities alone to drive the registration, we use multichannel Log-Demons, with channels representing features like intensity, local phase and phase congruency. Results on clinical data show that our method successfully registers various patient-specific cases, where the tumours are of variable visibility, and in the presence of shadows and topological changes. <s> BIB029
In the first subclass, each type of information is taken into account in a separate and sequential way. Registration is decomposed into two independent steps, each one acting on a different type of information. Typically, geometric registration precedes, resulting in a rough alignment of the two images. Subsequently, iconic registration is performed to refine the result. a) Exploiting Landmarks Information: Johnson and Christensen initialized their consistent intensity algorithm with the result of a consistent landmark approach in BIB004 . The landmark and intensity registration were solved independently in an iterative way until a criterion on the number of iterations was met. Paquin et al. proposed a multiscale approach for hybrid image registration BIB011 . The authors identified bony structure landmarks and used them to coarsely align the images. In the finer levels, intensity-based deformable registration was performed. Yin et al. BIB025 inferred the optimal displacements of a cubic -spline FFD model by alternately minimizing the sum of squared intensity differences and the distance between corresponding landmarks. b) Exploiting Surface Information: Liu et al. BIB005 proposed a hybrid algorithm that combined surface and volume information to register cortical structures. The algorithm was initialized with the result of a volumetric approach BIB001 and was subsequently refined using a surface warping method. Postelnicu et al. BIB018 started from the geometric registration, propagated the result to the whole volume using a biophysical model of the brain and refined it with a nonlinear optical flow registration algorithm. Gibson et al.  presented an approach where brain images are initially registered using an intensity-based method BIB007 and the result is refined by cortical surface registration BIB021 . Auzias et al. investigated the use of the diffeomorphic sulcal-based cortical registration (DISCO) BIB026 in collaboration with an intensity method (DARTEL BIB012 ). The methods were used in a sequential manner. c) Exploiting Segmented Structures Information: Camara et al. BIB013 presented an approach where the result of the registration of segmented structures is refined by iconic registration. 2) Additional Information Used as Constraint: Using one type of information independently of the other to initialize the following step usually results in an increase of the robustness of the registration procedure. However, there is no guarantee that the correspondences that were established during the previous step will be preserved. To overcome this limitation, a number of researchers have proposed to use the correspondences that were estimated during the first step to constrain the estimation of the correspondences during the following step. The spatial influence of these constraints varies from point-wise to global. a) Additional Information Used as Soft Constraint: The Hellier and Barillot proposed to couple dense and landmark-based approaches for nonrigid brain registration in BIB006 . In a first step, sulci were extracted and modeled as active ribbons. Then, a matching point algorithm was used to establish geometric correspondences. These correspondences were subsequently used in a robust function as constraints with local spatial support. Hartkens et al. combined normalized mutual information with geometric cues to tackle brain registration in  . Two kinds of geometric cues were employed, landmarks and surfaces. The correspondences for the landmarks were fixed while the surface correspondences were estimated in an ICP fashion. The ratio between the iconic and geometric terms was calculated automatically based on their derivatives. Papademetris et al. BIB002 used sulcal constraints to constrain iconic registration. A robust point matching method was used to establish correspondences between the sulcal landmarks while accounting for outliers. The matching criterion comprised an intensity similarity term and a term ensuring that the estimated deformation field adhered to the point correspondences. Rohr et al. BIB008 used the local correlation coefficient as intensity similarity criterion along with the adherence to point correspondences to register electrophoresis images. Avants et al. BIB009 added a landmark inexact matching term in the LDDMM framework in order to compare human and chimpanzee cortices. Landmarks were provided manually to establish either anatomical or functional correspondences between the two species. Azar et al. proposed a user-guided registration method BIB010 . The proposed algorithm iterated between estimating the transformation that maps one image to another and the estimation of two dense deformation fields. The landmark-based deformation field was initialized by using the user provided landmark correspondences and TPS interpolation. In subsequent iterations it was estimated by taking into account the landmark correspondences and the transformation of the previous iteration. The intensity-based deformation field was estimated by minimizing an intensity based similarity criterion while taking into account the transformation of the previous iteration. The transformation was given as an adaptive combination of the intensityand landmark-based deformation fields. Landmark information was weighted more in their vicinity of landmarks. This method was able to incorporate any intensity-based algorithm though it could not guarantee convergence. Wörz and Rohr proposed a spline-based registration framework that uses both intensity and landmark information BIB014 . The authors proposed to estimate a dense deformation field by using a set of corresponding landmarks and their localization uncertainties. The solution of the registration problem was a compromise between matching the image data, being regular and being close to the landmark-based deformation field. Biesdorf et al. presented a similar approach in BIB019 . The difference was that a local measure of mutual information was used as an intensity criterion. Lu et al. BIB022 incorporated landmark information in the diffeomorphic Demons registration algorithm BIB016 . The authors proposed to include the sum of squared landmark Euclidean distances in the matching criterion along with point-wise mutual information BIB023 . b) Additional Information Used as Hard Constraint: While most methods establish geometric correspondences and then encourage the intensity driven deformation field to comply with them without guaranteeing their preservation, Joshi et al. BIB015 imposed geometric correspondences as hard constraints. First correspondences were established between the cortical gray/white matter and gray/CSF surfaces using sulcal constraints. The correspondences were then propagated to the whole cortical volume with the use of an harmonic map. Following that, the dense deformation field was refined by considering image intensity information under the hard constraint that the deformation is zero for the previously registered surfaces. 3) Coupled Approaches: In the previous approaches, the information flows in one direction. By formulating the problems in a decoupled way, iconic registration may profit from geometric methods either by being initialized closer to the solution or by being driven by an extra force of adherence to correspondences. However, geometric registration does not benefit from iconic registration because its solution is independently obtained. In this class of methods, the two problems are unified and solved by minimizing a single objective function simultaneously. As a consequence, the solution of each problem takes advantage of the information coming from the other problem, and the final solution of the registration is consistent with both types of information. Cachier et al. BIB003 proposed such a universal energy function for the problem of deformable registration. The coupling of the two problems was performed through the introduction of an auxiliary smooth deformation field. The authors proposed to extract sulci modeled as point distributions and use them in the coupled formulation to accomplish brain registration. The problem was solved by iterating between three steps: 1) solving for the deformation that minimizes the iconic criterion, 2) solving the geometric problem by establishing correspondences between the closest points of the geometrical structures, 3) and finally opting for a smooth deformation that respects both iconic and geometric constraints. Joshi et al. BIB020 proposed an approach to couple surface-and intensity-based registration. An approach to tackle surface registration is to map both surfaces to a sphere and perform registration there. Joshi et al. proposed to additionally map the interior brain volumes to the interior of the spheres through harmonic maps. Then, correspondences can be established by involving the complete sphere domain, or both the surface and iconic information at the same time. Sotiras et al. BIB024 presented a coupled approach that aims to simultaneously estimate the correspondences between two landmark sets, and a dense displacement field parametrized by cubic -splines that maps one image space to another. The problem was formulated as a first-order Markov Random Field described by a two-layer undirected graph. The graph nodes represent the latent variables (displacement parameters and landmark correspondences), while the edges represent the relationships between the variables. The first layer of the graph modeled the iconic registration problem, while the second layer modeled the geometric correspondence problem. Inter-layer edges imposed the consistency between the two problems by approximating a coupling constraint. Some of the limitations of this work were addressed in subsequent attempts. Honnorat et al.  used the exact distance to couple the geometric and iconic information for the problem of guide-wire tracking. The inner product was developed to allow its modeling by pairwise relations. Kurkure et al. BIB027 used learned higher-order potential for the layer of the graph that models the geometric problem. As a consequence, the requirement for a global linear registration was reduced. Siless et al.  proposed a coupled approach based on the diffeomorphic Demons algorithm BIB016 . The authors proposed to define the update field as the addition of an intensity-based update field and a geometric-based update field. The intensitybased update field was calculated as in BIB016 . The geometricbased update field was estimated by minimizing the squared Euclidean distance between each point and its closest one. In a subsequent work, Siless et al. extended log-domain diffeomorphic demons BIB017 to take into account geometric information represented in the space of currents BIB028 . Cifor et al. BIB029 also extended BIB017 to take into account geometric information.