Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> In this paper, we present the concept of diffusing models to perform image-to-image matching. Having two images to match, the main idea is to consider the objects boundaries in one image as semi-permeable membranes and to let the other image, considered as a deformable grid model, diffuse through these interfaces, by the action of effectors situated within the membranes. We illustrate this concept by an analogy with Maxwell's demons. We show that this concept relates to more traditional ones, based on attraction, with an intermediate step being optical flow techniques. We use the concept of diffusing models to derive three different non-rigid matching algorithms, one using all the intensity levels in the static image, one using only contour points, and a last one operating on already segmented images. Finally, we present results with synthesized deformations and real medical images, with applications to heart motion tracking and three-dimensional inter-patients matching. <s> BIB001 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> A computational framework has evolved in which individual anatomies are modeled as warped versions of a canonical representation of the anatomy. To realize this framework, the method of elastic matching was invented for determining the spatial mapping between a three-dimensional image pair in which one image volume is modeled as an elastic continuum that is deformed to match the appearance of the second volume. This chapter describes the basic concepts underlying the original method and their probabilistic generalization within a Bayesian framework. For brain warping, a number of effective similarity metrics exist, whereas there is comparatively little known about the kinds of prior models that are specifically suited to the problem (and its applications) or how their influence on the solution, relative to the likelihood, should be determined. The resolution of these issues directly impacts the viability of any matching procedure, Bayesian or otherwise, but is best addressed within a probabilistic setting. To reduce the likelihood of false matches that arise when the local variations in anatomy are very large in magnitude, a standard approach is to solve the problem at different spatial scales. <s> BIB002 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> In this paper we classify inhomogeneous non-linear registration algorithms into those of variable data influence, of variable deformability and of variable model type. As examples we introduce three modifications of the viscous fluid registration algorithm: passing a filter over the computed force field, adding boundary conditions onto the velocity field, and re-writing the viscous fluid PDE to accommodate a spatially-varying viscosity field. We demonstrate their application on artificial test data, on pre-/post-operative MR head slices and on MR neck volumes. <s> BIB003 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> A biomechanical model of the brain is presented, using a finite-element formulation. Emphasis is given to the modeling of the soft-tissue deformations induced by the growth of tumors and its application to the registration of anatomical atlases, with images from patients presenting such pathologies. First, an estimate of the anatomy prior to the tumor growth is obtained through a simulated biomechanical contraction of the tumor region. Then a normal-to-normal atlas registration to this estimated pre-tumor anatomy is applied. Finally, the deformation from the tumor-growth model is applied to the resultant registered atlas, producing an atlas that has been deformed to fully register to the patient images. The process of tumor growth is simulated in a nonlinear optimization framework, which is driven by anatomical features such as boundaries of brain structures. The deformation of the surrounding tissue is estimated using a nonlinear elastic model of soft tissue under the boundary conditions imposed by the skull, ventricles, and the falx and tentorium. A preliminary two-dimensional (2-D) implementation is presented in this paper, and tested on both simulated and patient data. One of the long-term goals of this work is to use anatomical brain atlases to estimate the locations of important brain structures in the brain and to use these estimates in pre-surgical and radiosurgical planning systems. <s> BIB004 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> This paper describes two new atlas-based methods of 2D single modality non-rigid registration using the combined power of physical and statistical shape models. The transformations are constrained to be consistent with the physical properties of deformable elastic solids in the first method and those of viscous fluids in the second, to maintain smoothness and continuity. A Bayesian formulation, based on each physical model, an intensity similarity measure, and statistical shape information embedded in corresponding boundary points, is employed to derive more accurate and robust approaches to non-rigid registration. A dense set of forces arises from the intensity similarity measure to accommodate complex anatomical details. A sparse set of forces constrains consistency with statistical shape models derived from a training set. A number of experiments were performed on both synthetic and real medical images of the brain and heart to evaluate the approaches. It is shown that statistical boundary shape information significantly augments and improves physical model-based non-rigid registration and the two methods we present each have advantages under different conditions. <s> BIB005 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Abstract Rationale and Objectives Live guidance during needle breast procedures is not currently possible with high-field-strength (1.5-T), superconducting magnetic resonance (MR) imaging. The physician can calculate only the approximate location and extent of a tumor in the compressed patient breast before inserting the needle, and the tissue specimen removed at biopsy may not actually belong to the lesion of interest. The authors developed a virtual reality system for guiding breast biopsy with MR imaging, which uses a deformable finite element model of the breast. Materials and Methods The geometry of the model is constructed from MR data, and its mechanical properties are modeled by using a nonlinear material model. This method allows the breast to be imaged with or without mild compression before the procedure. The breast is then compressed, and the finite element model is used to predict the position of the tumor during the procedure. Three breasts of patients with cancer were imaged with and without compression. Deformable models of these breasts were built, virtually compressed, and used to predict tumor positions in the real compressed breasts. The models were also used to register MR data sets of the same patient breast imaged with different amounts of compression. Results The model is shown to predict reasonably well the displacement by plate compression of breast lesions 5 mm or larger. Conclusion A deformable model of the breast based on finite elements with nonlinear material properties can help in modeling and predicting breast deformation. The entire procedure lasts less than half an hour, making it clinically practical. <s> BIB006 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Breast tissue deformation modeling has recently gained considerable interest in various medical applications. A biomechanical model of the breast is presented using a finite element (FE) formulation. Emphasis is given to the modeling of breast tissue deformation which takes place in breast imaging procedures. The first step in implementing the FE modeling (FEM) procedure is mesh generation. For objects with irregular and complex geometries such as the breast, this step is one of the most difficult and tedious tasks. For FE mesh generation, two automated methods are presented which process MRI breast images to create a patient-specific mesh. The main components of the breast are adipose, fibroglandular and skin tissues. For modeling the adipose and fibroglandular tissues, we used eight noded hexahedral elements with hyperelastic properties, while for the skin, we chose four noded hyperelastic membrane elements. For model validation, an MR image of an agarose phantom was acquired and corresponding FE meshes were created. Based on assigned elasticity parameters, a numerical experiment was performed using the FE meshes, and good results were obtained. The model was also applied to a breast image registration problem of a volunteer's breast. Although qualitatively reasonable, further work is required to validate the results quantitatively. <s> BIB007 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> X-ray mammograms and MR volumes provide complementary information for early breast cancer diagnosis. The breast is deformed during mammography, therefore the images can not be compared directly. A registration algorithm is investigated to fuse the images automatically. A finite element simulation was applied to a MR image of an underformed breast and compared to a compressed breast using different tissue models and boundary conditions. Based on the results a set of patient data was registered. To archive the requested accuracy distinguishing between the different tissue types of the breast was not necessary. A linear elastic model was sufficient. It was possible to simulate the deformation with an average deviation of approximately of the size of a voxel in the MRI data and retrieve the position of a lesion with an error of 3.8 mm in the patient data. <s> BIB008 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> An approach for estimating the deformation of the prostate caused by transrectal ultrasound (TRUS) probe insertion is presented. This work is particularly useful during brachytherapy procedures, in which planning for radioactive seed insertion is performed on preoperative scans, and significant deformation of the prostate can occur during the procedure. The approach makes use of a patient specific biomechanical model to run simulations for TRUS probe insertion, extract the main modes of the deformation of the prostate, and use this information to establish a deformable registration between 2 orthogonal cross-sectional ultrasound images and the preoperative prostate. In the work presented here, the approach is tested on an anatomy-realistic biomechanical phantom for the prostate and results are reported for 5 test simulations. More than 73% of maximum deformation of the prostate was recovered, with the estimation error mostly attributed to the relatively small number of biomechanical simulations used for training. <s> BIB009 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> The quantitative estimation of regional cardiac deformation from three-dimensional (3-D) image sequences has important clinical implications for the assessment of viability in the heart wall. We present here a generic methodology for estimating soft tissue deformation which integrates image-derived information with biomechanical models, and apply it to the problem of cardiac deformation estimation. The method is image modality independent. The images are segmented interactively and then initial correspondence is established using a shape-tracking approach. A dense motion field is then estimated using a transversely isotropic, linear-elastic model, which accounts for the muscle fiber directions in the left ventricle. The dense motion field is in turn used to calculate the deformation of the heart wall in terms of strain in cardiac specific directions. The strains obtained using this approach in open-chest dogs before and after coronary occlusion, exhibit a high correlation with strains produced in the same animals using implanted markers. Further, they show good agreement with previously published results in the literature. This proposed method provides quantitative regional 3-D estimates of heart deformation. <s> BIB010 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> In this paper, we show how the concept of statistical deformation models (SDMs) can be used for the construction of average models of the anatomy and their variability. SDMs are built by performing a statistical analysis of the deformations required to map anatomical features in one subject into the corresponding features in another subject. The concept of SDMs is similar to statistical shape models (SSMs) which capture statistical information about shapes across a population, but offers several advantages over SSMs. First, SDMs can be constructed directly from images such as three-dimensional (3-D) magnetic resonance (MR) or computer tomography volumes without the need for segmentation which is usually a prerequisite for the construction of SSMs. Instead, a nonrigid registration algorithm based on free-form deformations and normalized mutual information is used to compute the deformations required to establish dense correspondences between the reference subject and the subjects in the population class under investigation. Second, SDMs allow the construction of an atlas of the average anatomy as well as its variability across a population of subjects. Finally, SDMs take the 3-D nature of the underlying anatomy into account by analysing dense 3-D deformation fields rather than only information about the surface shape of anatomical structures. We show results for the construction of anatomical models of the brain from the MR images of 25 different subjects. The correspondences obtained by the nonrigid registration are evaluated using anatomical landmark locations and show an average error of 1.40 mm at these anatomical landmark positions. We also demonstrate that SDMs can be constructed so as to minimize the bias toward the chosen reference subject. <s> BIB011 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> We propose a voxel-based nonrigid registration algorithm for temporal subtraction of two-dimensional thorax X-ray computed radiography images of the same subject. The deformation field is represented by a B-spline with a limited number of degrees of freedom, that allows global rib alignment to minimize subtraction artifacts within the lung field without obliterating interval changes of clinically relevant soft-tissue abnormalities. The spline parameters are constrained by a statistical deformation model that is learned from a training set of manually aligned image pairs using principal component analysis. Optimization proceeds along the transformation components rather then along the individual spline coefficients, using pattern intensity of the subtraction image within the automatically segmented lung field region as the criterion to be minimized and applying a simulated annealing strategy for global optimization in the presence of multiple local optima. The impact of different transformation models with varying number of deformation modes is evaluated on a training set of 26 images using a leave-one-out strategy and compared to the manual registration result in terms of criterion value and deformation error. Registration quality is assessed on a second set of validation images by a human expert rating each subtraction image on screen. In 85% of the cases, the registration is subjectively rated to be adequate for clinical use. <s> BIB012 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> In this paper we propose a novel approach to define task-driven regularization constraints in deformable image registration using learned deformation priors. Our method consists of representing deformation through a set of control points and an interpolation strategy. Then, using a training set of images and the corresponding deformations we seek for a weakly connected graph on the control points where edges define the prior knowledge on the deformation. This graph is obtained using a clustering technique which models the co-dependencies between the displacements of the control points. The resulting classification is used to encode regularization constraints through connections between cluster centers and cluster elements. Additionally, the global structure of the deformation is encoded through a fully connected graph on the cluster centers. Then, registration of a new pair of images consists of displacing the set of control points where on top of conventional image correspondence costs, we introduce costs that are based on the relative deformation of two control points with respect to the learned deformation. The resulting paradigm is implemented using a discrete Markov Random Field which is optimized using efficient linear programming. Promising experimental results on synthetic and real data demonstrate the potential of our approach. <s> BIB013 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Presents a novel method for validation of nonrigid medical image registration. This method is based on the simulation of physically plausible, biomechanical tissue deformations using finite-element methods. Applying a range of displacements to finite-element models of different patient anatomies generates model solutions which simulate gold standard deformations. From these solutions, deformed images are generated with a range of deformations typical of those likely to occur in vivo. The registration accuracy with respect to the finite-element simulations is quantified by co-registering the deformed images with the original images and comparing the recovered voxel displacements with the biomechanically simulated ones. The functionality of the validation method is demonstrated for a previously described nonrigid image registration technique based on free-form deformations using B-splines and normalized mutual information as a voxel similarity measure, with an application to contrast-enhanced magnetic resonance mammography image pairs. The exemplar nonrigid registration technique is shown to be of subvoxel accuracy on average for this particular application. The validation method presented here is an important step toward more generic simulations of biomechanically plausible tissue deformations and quantification of tissue motion recovery using nonrigid image registration. It will provide a basis for improving and comparing different nonrigid registration techniques for a diversity of medical applications, such as intrasubject tissue deformation or motion correction in the brain, liver or heart. <s> BIB014 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> We propose a method for brain atlas deformation in the presence of large space-occupying tumors, based on an a priori model of lesion growth that assumes radial expansion of the lesion from its starting point. Our approach involves three steps. First, an affine registration brings the atlas and the patient into global correspondence. Then, the seeding of a synthetic tumor into the brain atlas provides a template for the lesion. The last step is the deformation of the seeded atlas, combining a method derived from optical flow principles and a model of lesion growth. Results show that a good registration is performed and that the method can be applied to automatic segmentation of structures and substructures in brains with gross deformation, with important medical applications in neurosurgery, radiosurgery, and radiotherapy. <s> BIB015 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Abstract Brain atlases are valuable tools which assist neurosurgeons during the planning of an intervention. Since a printed atlas book has several disadvantages—among them the difficulty to map the information onto a patient’s individual anatomy—we have developed a digital version of the well-established stereotaxic brain atlas of Talairach and Tournoux. Our atlas system is mainly dedicated to assist neurosurgical planning, and its benefits are: (i) a three-dimensional (3D) representation of most brain structures contained in the Talairach atlas; (ii) a nonrigid matching capability which warps the standard atlas anatomy to an individual brain magnetic resonance imaging (MRI) dataset in a few minutes and which is able to take deformations due to tumors into account; (iii) the integration of several sources of neuroanatomical knowledge; (iv) an interface to a navigation system which allows utilization of atlas information intraoperatively. In this paper we outline the algorithm we have developed to achieve 3D surface models of the brain structures. Moreover, we describe the nonrigid matching method which consists of two tasks: firstly, point correspondences between the atlas and the patient are established in an automatic fashion, and secondly these displacement vectors are interpolated using a radial basis function approach to form a continuous transformation function. To generate appropriate target structures for the first of these tasks, we implemented a quick segmentation tool which is capable to segment the cortex and ventricles in less than 5 min. An evaluation shows that our nonrigid approach is more precise than the conventional piecewise linear matching, though it should be further improved for the region around the deep grey nuclei. Summarizing, we developed a Win32 program which permits the convenient and fast application of standardized anatomy to individual brains which potentially contain tumors. <s> BIB016 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> In inter-subject registration, one often lacks a good model of the transformation variability to choose the optimal regularization. Some works attempt to model the variability in a statistical way, but the re-introduction in a registration algorithm is not easy. In this paper, we interpret the elastic energy as the distance of the Green-St Venant strain tensor to the identity, which reflects the deviation of the local deformation from a rigid transformation. By changing the Euclidean metric for a more suitable Riemannian one, we define a consistent statistical framework to quantify the amount of deformation. In particular, the mean and the covariance matrix of the strain tensor can be consistently and efficiently computed from a population of non-linear transformations. These statistics are then used as parameters in a Mahalanobis distance to measure the statistical deviation from the observed variability, giving a new regularization criterion that we called the statistical Riemannian elasticity. This new criterion is able to handle anisotropic deformations and is inverse-consistent. Preliminary results show that it can be quite easily implemented in a non-rigid registration algorithms. <s> BIB017 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Deforming a digital atlas towards a patient image allows the simultaneous segmentation of several structures. Such an intersubject registration is difficult as the deformations to recover are highly inhomogeneous. A priori information about the local amount of deformation to expect is precious, since it allows to optimally balance the quality of the matching versus the regularity of the deformation. However, intersubject variability makes it hard to heuristically estimate the degree of deformation. Indeed, the sizes and shapes of various structures differ greatly and their relative positions vary in a rather complex manner. In this article, we perform a statistical study of the deformations yielded by the registration of an image database with an anatomical atlas, and we propose methods to re-inject this information into the registration. We show that this provides more accurate segmentations of brain structures. <s> BIB018 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> We propose a new model to simulate the three-dimensional (3-D) growth of glioblastomas multiforma (GBMs), the most aggressive glial tumors. The GBM speed of growth depends on the invaded tissue: faster in white than in gray matter, it is stopped by the dura or the ventricles. These different structures are introduced into the model using an atlas matching technique. The atlas includes both the segmentations of anatomical structures and diffusion information in white matter fibers. We use the finite element method (FEM) to simulate the invasion of the GBM in the brain parenchyma and its mechanical interaction with the invaded structures (mass effect). Depending on the considered tissue, the former effect is modeled with a reaction-diffusion or a Gompertz equation, while the latter is based on a linear elastic brain constitutive equation. In addition, we propose a new coupling equation taking into account the mechanical influence of the tumor cells on the invaded tissues. The tumor growth simulation is assessed by comparing the in-silico GBM growth with the real growth observed on two magnetic resonance images (MRIs) of a patient acquired with 6 mo difference. Results show the feasibility of this new conceptual approach and justifies its further evaluation. <s> BIB019 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Rationale and Objectives Determination of distorted brain anatomy surrounding a tumor causing a mass effect is much more difficult than interpretation of normal brain scans, particularly because this distortion is not easily predictable a tumor may be located in any place and vary substantially in size, shape, and radiological appearance. The objective of our work is to provide a qualitative means for rapid estimation of brain anatomy distorted by tumor. Materials and Methods Toward achieving this objective, we use an electronic and deformable brain atlas of gross anatomy along with a fast atlas-to-data warping technique. The deformed atlas determines the distorted anatomy surrounding a tumor and can be used for structure labeling (naming). The warping algorithm uses the Talairach transformation followed by three-dimensional nonlinear tumor deformation based on a geometric assumption that the tumor, delineated on radiological images, compresses its surrounding tissues radially. Results The approach is implemented and a dedicated application is developed. It processes the data automatically in five steps: (1) load data, (2) set the Talairach landmarks and perform the Talairach transformation, (3) segment the tumor, (4) warp the scan nonlinearly in three dimensions, and (5) explore the scan. The approach is very fast, and a magnetic resonance imaging scan is processed in 10–15 seconds on a standard personal computer. It is fully automatic and gives the user control over the entire process. Conclusion Despite its limitations in modeling and validation, this practical solution provides a rapid and potentially useful qualitative assessment of anatomy deformed by a mass effect tumor. <s> BIB020 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> In this article, we propose a new registration method, based on a statistical analysis of deformation fields. At first, a set of MRI brain images was registered using a viscous fluid algorithm. The obtained deformation fields are then used to calculate a Principal Component Analysis (PCA) based decomposition. Since PCA models the deformations as a linear combination of statistically uncorrelated principal components, new deformations can be created by changing the coefficients in the linear combination. We then use the PCA representation of the deformation fields to non-rigidly align new sets of images. We use a gradient descent method to adjust the coefficients of the principal components, such that the resulting deformation maximizes the mutual information between the deformed image and an atlas image. The results of our method are promising. Viscous fluid registrations of new images can be recovered with an accuracy of about half a voxel. Better results can be obtained by using a more extensive database of learning images (we only used 84). Also, the optimization method used here can be improved, especially to shorten computation time. <s> BIB021 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Abstract This paper proposes a 3D statistical model aiming at effectively capturing statistics of high-dimensional deformation fields and then uses this prior knowledge to constrain 3D image warping. The conventional statistical shape model methods, such as the active shape model (ASM), have been very successful in modeling shape variability. However, their accuracy and effectiveness typically drop dramatically in high-dimensionality problems involving relatively small training datasets, which is customary in 3D and 4D medical imaging applications. The proposed statistical model of deformation (SMD) uses wavelet-based decompositions coupled with PCA in each wavelet band, in order to more accurately estimate the pdf of high-dimensional deformation fields, when a relatively small number of training samples are available. SMD is further used as statistical prior to regularize the deformation field in an SMD-constrained deformable registration framework. As a result, more robust registration results are obtained relative to using generic smoothness constraints on deformation fields, such as Laplacian-based regularization. In experiments, we first illustrate the performance of SMD in representing the variability of deformation fields and then evaluate the performance of the SMD-constrained registration, via comparing a hierarchical volumetric image registration algorithm, HAMMER, with its SMD-constrained version, referred to as SMD+HAMMER. This SMD-constrained deformable registration framework can potentially incorporate various registration algorithms to improve robustness and stability via statistical shape constraints. <s> BIB022 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Atlas registration is a recognized paradigm for the automatic segmentation of normal MR brain images. Unfortunately, atlas-based segmentation has been of limited use in presence of large space-occupying lesions. In fact, brain deformations induced by such lesions are added to normal anatomical variability and they may dramatically shift and deform anatomically or functionally important brain structures. In this work, we chose to focus on the problem of inter-subject registration of MR images with large tumors, inducing a significant shift of surrounding anatomical structures. First, a brief survey of the existing methods that have been proposed to deal with this problem is presented. This introduces the discussion about the requirements and desirable properties that we consider necessary to be fulfilled by a registration method in this context: To have a dense and smooth deformation field and a model of lesion growth, to model different deformability for some structures, to introduce more prior knowledge, and to use voxel-based features with a similarity measure robust to intensity differences. In a second part of this work, we propose a new approach that overcomes some of the main limitations of the existing techniques while complying with most of the desired requirements above. Our algorithm combines the mathematical framework for computing a variational flow proposed by Hermosillo et al. [G. Hermosillo, C. Chefd'Hotel, O. Faugeras, A variational approach to multi-modal image matching, Tech. Rep., INRIA (February 2001).] with the radial lesion growth pattern presented by Bach et al. [M. Bach Cuadra, C. Pollo, A. Bardera, O. Cuisenaire, J.-G. Villemure, J.-Ph. Thiran, Atlas-based segmentation of pathological MR brain images using a model of lesion growth, IEEE Trans. Med. Imag. 23 (10) (2004) 1301-1314.]. Results on patients with a meningioma are visually assessed and compared to those obtained with the most similar method from the state-of-the-art. <s> BIB023 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Abstract An approach to the deformable registration of three-dimensional brain tumor images to a normal brain atlas is presented. The approach involves the integration of three components: a biomechanical model of tumor mass-effect, a statistical approach to estimate the model’s parameters, and a deformable image registration method. Statistical properties of the sought deformation map from the atlas to the image of a tumor patient are first obtained through tumor mass-effect simulations on normal brain images. This map is decomposed into the sum of two components in orthogonal subspaces, one representing inter-individual differences in brain shape, and the other representing tumor-induced deformation. For a new tumor case, a partial observation of the sought deformation map is obtained via deformable image registration and is decomposed into the aforementioned spaces in order to estimate the mass-effect model parameters. Using this estimate, a simulation of tumor mass-effect is performed on the atlas image in order to generate an image that is similar to tumor patient’s image, thereby facilitating the atlas registration process. Results for a real tumor case and a number of simulated tumor cases indicate significant reduction in the registration error due to the presented approach as compared to the direct use of deformable image registration. <s> BIB024 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Magnetic resonance imaging (MRI) and magnetic resonance spectroscopic imaging (MRSI) have been shown to be very useful for identifying prostate cancers. For high sensitivity, the MRI/MRSI examination is often acquired with an endorectal probe that may cause a substantial deformation of the prostate and surrounding soft tissues. Such a probe is removed prior to radiation therapy treatment. To register diagnostic probe-in magnetic resonance (MR) images to therapeutic probe-out MR images for treatment planning, a new deformable image registration method is developed based on biomechanical modeling of soft tissues and estimation of uncertain tissue parameters using nonlinear optimization. Given two-dimensional (2-D) segmented probe-in and probe-out images, a finite element method (FEM) is used to estimate the deformation of the prostate and surrounding tissues due to displacements and forces resulting from the endorectal probe. Since FEM requires tissue stiffness properties and external force values as input, the method estimates uncertain parameters using nonlinear local optimization. The registration method is evaluated using images from five balloon and five rigid endorectal probe patient cases. It requires on average 37 s of computation time on a 1.6 GHz Pentium-M PC. Comparing the prostate outline in deformed probe-out images to corresponding probe-in images, the method obtains a mean Dice Similarity Coefficient (DSC) of 97.5% for the balloon probe cases and 98.1% for the rigid probe cases. The method improves significantly over previous methods (P < 0.05) with greater improvement for balloon probe cases with larger tissue deformations. <s> BIB025 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Statistical models of deformations (SMD) capture the variability of deformations of a group of sample images, and they are often used to constrain deformable registration, thereby improving their robustness and accuracy. Although low-dimensional statistical models, such as active shape and appearance models, have been successfully used in statistically-constrained deformable models, constraining of high-dimensional warping algorithms is a more challenging task, since conventional PCA-based statistics are limited to capture the full range of anatomical variability. This paper first proposes an SMD that is built upon the wavelet-PCA model and then uses it to constrain the deformable registration, wherein the template image is adaptively warped based on SMD during the registration procedure. Compared to the original template image, the adaptively deformed template image is more similar to the subject image, e.g., the deformation is relatively small and local, and it is less likely to be stuck in undesired local minima. In experiments, we show that the proposed statistically-constrained deformable registration is more robust and accurate than the conventional registration <s> BIB026 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> We present a framework for black-box and flexible simulation of soft tissue deformation for medical imaging and surgical planning applications. Our main motivation in the present work is to develop robust algorithms that allow batch processing for registration of brains with tumors to statistical atlases of normal brains and construction of brain tumor atlases. We describe a fully Eulerian formulation able to handle large deformations effortlessly, with a level-set-based approach for evolving fronts. We use a regular grid—fictitious domain method approach, in which we approximate coefficient discontinuities, distributed forces and boundary conditions. This approach circumvents the need for unstructured mesh generation, which is often a bottleneck in the modeling and simulation pipeline. Our framework employs penalty approaches to impose boundary conditions and uses a matrix-free implementation coupled with a multigrid-accelerated Krylov solver. The overall scheme results in a scalable method with minimal storage requirements and optimal algorithmic complexity. We illustrate the potential of our framework to simulate realistic brain tumor mass effects at reduced computational cost, for aiding the registration process towards the construction of brain tumor atlases. <s> BIB027 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Establishing spatial correspondence between features visible in X-ray mammograms obtained at different times has great potential to aid assessment and quantitation of change in the breast indicative of malignancy. The literature contains numerous non- rigid registration algorithms developed for this purpose, but existing approaches are flawed by the assumption of inappropriate 2-D transformation models and quantitative estimation of registration accuracy is limited. In this paper, we describe a novel validation method which simulates plausible mammographic compressions of the breast using a magnetic resonance imaging (MRI) derived finite element model. By projecting the resulting known 3-D displacements into 2-D and generating pseudo-mammograms from these same compressed magnetic resonance (MR) volumes, we can generate convincing images with known 2-D displacements with which to validate a registration algorithm. We illustrate this approach by computing the accuracy for two conventional nonrigid 2-D registration algorithms applied to mammographic test images generated from three patient MR datasets. We show that the accuracy of these algorithms is close to the best achievable using a 2-D one-to-one correspondence model but that new algorithms incorporating more representative transformation models are required to achieve sufficiently accurate registrations for this application. <s> BIB028 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Breast cancer detection, diagnosis and treatment increasingly involves images of the breast taken with different degrees of breast deformation. We introduce a new biomechanical modelling framework for predicting breast deformation and thus aiding the combination of information derived from the various images. In this paper, we focus on MR images of the breast under different loading conditions, and consider methods to map information between the images. ::: ::: We generate subject-specific finite element models of the breast by semi-automatically fitting geometrical models to segmented data from breast MR images, and characterizing the subject-specific mechanical properties of the breast tissues. We identified the unloaded reference configuration of the breast by acquiring MR images of the breast under neutral buoyancy (immersed in water). Such imaging is clearly not practical in the clinical setting, however this previously unavailable data provides us with important data with which to validate models of breast biomechanics, and provides a common configuration with which to refer and interpret all breast images. ::: ::: We demonstrate our modelling framework using a pilot study that was conducted to assess the mechanical performance of a subject-specific homogeneous biomechanical model in predicting deformations of the breast of a volunteer in a prone gravity-loaded configuration. The model captured the gross characteristics of the breast deformation with an RMS error of 4.2 mm in predicting the skin surface of the gravity-loaded shape, which included tissue displacements of over 20 mm. Internal tissue features identified from the MR images were tracked from the reference state to the prone gravity-loaded configuration with a mean error of 3.7 mm. We consider the modelling assumptions and discuss how the framework could be refined in order to further improve the tissue tracking accuracy. <s> BIB029 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Comparison of uncompressed volumetric breast data to compressed projection mammographic data poses a variety of challenges to accurately localize anatomy in both data sets. This work presents a method for simulating the mechanical compression of volumetric breast data. We use an approach based on a rectilinear-grid finite-element mesh and apply the method to known objects including volumetric breast data. Overall results show good agreement with theory and reasonable qualitative agreement with clinical results. Analysis times are sufficiently short to be used in the clinical setting for data comparison. The methods presented here provide a high quality method for simulating mechanical compression of breast data. <s> BIB030 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> PURPOSE ::: Endorectal coil (ERC) magnetic resonance imaging (MRI) provides superior visualization of the prostate compared with computed tomography at the expense of deformation. This study aimed to develop a multiorgan finite element deformable method, Morfeus, to accurately co-register these images for radiotherapy planning. ::: ::: ::: METHODS ::: Patients with prostate cancer underwent fiducial marker implantation and computed tomography simulation for radiotherapy planning. A series of axial MRI scans were acquired with and without an ERC. The prostate, bladder, rectum, and pubic bones were manually segmented and assigned linear elastic material properties. Morfeus mapped the surface of the bladder and rectum between two imaged states, calculating the deformation of the prostate through biomechanical properties. The accuracy of deformation was measured as fiducial marker error and residual surface deformation between the inferred and actual prostate. The deformation map was inverted to deform from 100 cm(3) to no coil. ::: ::: ::: RESULTS ::: The data from 19 patients were analyzed. Significant prostate deformation occurred with the ERC (mean intrapatient range, 0.88 +/- 0.25 cm). The mean vector error in fiducial marker position (n = 57) was 0.22 +/- 0.09 cm, and the mean vector residual surface deformation (n = 19) was 0.15 +/- 0.06 cm for deformation from no coil to 100-cm(3) ERC, with an image vector resolution of 0.22 cm. Accurately deformed MRI scans improved soft-tissue resolution of the anatomy for radiotherapy planning. ::: ::: ::: CONCLUSIONS ::: This method of multiorgan deformable registration enabled accurate co-registration of ERC-MRI scans with computed tomography treatment planning images. Superior structural detail was visible on ERC-MRI, which has potential for improving target delineation. <s> BIB031 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Two major factors preventing the routine clinical use of finite-element analysis for image registration are: 1) the substantial labor required to construct a finite-element model for an individual patient's anatomy and 2) the difficulty of determining an appropriate set of finite-element boundary conditions. This paper addresses these issues by presenting algorithms that automatically generate a high quality hexahedral finite-element mesh and automatically calculate boundary conditions for an imaged patient. Medial shape models called m-reps are used to facilitate these tasks and reduce the effort required to apply finite-element analysis to image registration. Encouraging results are presented for the registration of CT image pairs which exhibit deformation caused by pressure from an endorectal imaging probe and deformation due to swelling. <s> BIB032 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> A deformable registration method is proposed for registering a normal brain atlas with images of brain tumor patients. The registration is facilitated by first simulating the tumor mass effect in the normal atlas in order to create an atlas image that is as similar as possible to the patient's image. An optimization framework is used to optimize the location of tumor seed as well as other parameters of the tumor growth model, based on the pattern of deformation around the tumor region. In particular, the optimization is implemented in a multiresolution and hierarchical scheme, and it is accelerated by using a principal component analysis (PCA)-based model of tumor growth and mass effect, trained on a computationally more expensive biomechanical model. Validation on simulated and real images shows that the proposed registration framework, referred to as ORBIT (optimization of tumor parameters and registration of brain images with tumors), outperforms other available registration methods particularly for the regions close to the tumor, and it has the potential to assist in constructing statistical atlases from tumor-diseased brain images. <s> BIB033 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> We present a framework for modeling gliomas growth and their mechanical impact on the surrounding brain tissue (the so-called, mass-effect). We employ an Eulerian continuum approach that results in a strongly coupled system of nonlinear Partial Differential Equations (PDEs): a reaction-diffusion model for the tumor growth and a piecewise linearly elastic material for the background tissue. To estimate unknown model parameters and enable patient-specific simulations we formulate and solve a PDE-constrained optimization problem. Our two main goals are the following: (1) to improve the deformable registration from images of brain tumor patients to a common stereotactic space, thereby assisting in the construction of statistical anatomical atlases; and (2) to develop predictive capabilities for glioma growth, after the model parameters are estimated for a given patient. To our knowledge, this is the first attempt in the literature to introduce an adjoint-based, PDE-constrained optimization formulation in the context of image-driven modeling spatio-temporal tumor evolution. In this paper, we present the formulation, and the solution method and we conduct 1D numerical experiments for preliminary evaluation of the overall formulation/methodology. <s> BIB034 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Most surgical procedures in breast plastic surgery are either reconstructive procedures following oncologic interventions (tumorectomy, quadrantectomy, mastectomy ...) or aesthetic ones, both augmentation and reduction. With current techniques, the results of such procedures cannot be fully guaranteed. Usually, surgical planning is based on a photographic and anthropometric study of the breast only. Among others, one of the difficulties that the plastic surgeons have is the noticeable change of the breast shape with the position of the patient. Thus, it is more and more necessary to plan a presurgical methodology to help the plastic surgeon and guarantee the patient a successful result of the intervention. In order to establish a reliable simulation method that could predict a patient-specific outcome after breast surgery, this study started trying to correlate spatial features of the breast between lying and standing up positions. A biomechanical model of breast was proposed and implemented into a finite element context to predict deformations, and from these the breast shape in different positions. The resulting shapes were compared with multimodal images, whereas the breast surface displacements were compared with manually identified landmarks and 3D scanner images. From the results, it can be concluded that the model hereby presented reasonably approximates breast response to gravity forces, therefore providing accurate and useful information to the surgeon planning such surgical procedures. <s> BIB035 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> This paper reports on the development and preliminary testing of a three-dimensional implementation of an inverse problem technique for extracting soft-tissue elasticity information via non-rigid model-based image registration. The modality-independent elastography (MIE) algorithm adjusts the elastic properties of a biomechanical model to achieve maximal similarity between images acquired under different states of static loading. A series of simulation experiments with clinical image sets of human breasts were performed to test the ability of the method to identify and characterize a radiographically occult stiff lesion. Because boundary conditions are a critical input to the algorithm, a comparison of three methods for semi-automated surface point correspondence was conducted in the context of systematic and randomized noise processes. The results illustrate that 3D MIE was able to successfully reconstruct elasticity images using data obtained from both magnetic resonance and x-ray computed tomography systems. The lesion was localized correctly in all cases and its relative elasticity found to be reasonably close to the true values (3.5% with the use of spatial priors and 11.6% without). In addition, the inaccuracies of surface registration performed with thin-plate spline interpolation did not exceed empiric thresholds of unacceptable boundary condition error. <s> BIB036 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> A finite element model has been developed to investigate the effect of contact surfaces and hyperelastic material properties on the mechanical behavior of human lungs of one lung cancer patient. The three-dimensional model consists of four parts, namely the left lung, right lung, tumor in the left lung and chest wall. The interaction between the lungs and chest wall was modeled using frictionless surface-based contact. Hyperelastic material properties of the lungs are used in the model. The effect of the two parameters is investigated by tracking the tumor movement, and by comparing the analytical results to the patient bifurcation points: 45 points in each lung and 18 points around the tumor. The accuracy of the model is improved by including the contact surface and hyperelastic material properties. The average error and the standard deviation (SD) in modeling the displacement in the SI direction are reduced from 0.68 (SD = 0.34) cm in the elastic model to 0.09 (0.21) cm in the contact-hyperelastic model. Similarly, the average error (SD) of tumor location decreases from 0.71 (0.21) cm in the elastic material without contact to -0.03 (0.24) cm in the hyperelastic material with contact model. <s> BIB037 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> A brain image registration algorithm, referred to as RABBIT, is proposed to achieve fast and accurate image registration with the help of an intermediate template generated by a statistical deformation model. The statistical deformation model is built by principal component analysis (PCA) on a set of training samples of brain deformation fields that warp a selected template image to the individual brain samples. The statistical deformation model is capable of characterizing individual brain deformations by a small number of parameters, which is used to rapidly estimate the brain deformation between the template and a new individual brain image. The estimated deformation is then used to warp the template, thus generating an intermediate template close to the individual brain image. Finally, the shape difference between the intermediate template and the individual brain is estimated by an image registration algorithm, e.g., HAMMER. The overall registration between the template and the individual brain image can be achieved by directly combining the deformation fields that warp the template to the intermediate template, and the intermediate template to the individual brain image. The algorithm has been validated for spatial normalization of both simulated and real magnetic resonance imaging (MRI) brain images. Compared with HAMMER, the experimental results demonstrate that the proposed algorithm can achieve over five times speedup, with similar registration accuracy and statistical power in detecting brain atrophy. <s> BIB038 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Although a variety of diffeomorphic deformable registration methods exist in the literature, application of these methods in the presence of space-occupying lesions is not straightforward. The motivation of this work is spatial normalization of MR images from patients with brain tumors in a common stereotaxic space, aiming to pool data from different patients into a common space in order to perform group analyses. Additionally, transfer of structural and functional information from neuroanatomical brain atlases into the individual patient's space can be achieved via the inverse mapping, for the purpose of segmenting brains and facilitating surgical or radiotherapy treatment planning. A method that estimates the brain tissue loss and replacement by tumor is applied for achieving equivalent image content between an atlas and a patient's scan, based on a biomechanical model of tumor growth. Automated estimation of the parameters modeling brain tissue loss and displacement is performed via optimization of an objective function reflecting feature-based similarity and elastic stretching energy, which is optimized in parallel via APPSPACK (Asynchronous Parallel Pattern Search). The results of the method, applied to 21 brain tumor patients, indicate that the registration accuracy is relatively high in areas around the tumor, as well as in the healthy portion of the brain. Also, the calculated deformation in the vicinity of the tumor is shown to correlate highly with expert-defined visual scores indicating the tumor mass effect, thereby potentially leading to an objective approach to quantification of mass effect, which is commonly used in diagnosis. <s> BIB039 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> We propose a method for the analysis of cardiac images with the goal of reconstructing the motion of the ventricular walls. The main feature of our method is that the inversion parameter field is the active contraction of the myocardial fibers. This is accomplished with a biophysically-constrained, four-dimensional (space plus time) formulation that aims to complement information that can be gathered from the images by a priori knowledge of cardiac mechanics. Our main hypothesis is that by incorporating biophysical information, we can generate more informative priors and thus, more accurate predictions of the ventricular wall motion. In this paper, we outline the formulation, discuss the computational methodology for solving the inverse motion estimation, and present preliminary validation using synthetic and tagged MR images. The overall method uses patient-specific imaging and fiber information to reconstruct the motion. In these preliminary tests, we verify the implementation and conduct a parametric study to test the sensitivity of the model to material properties perturbations, model errors, and incomplete and noisy observations. <s> BIB040 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Development and optimization of methods for adequately accounting for respiratory motion in radiation therapy of thoracic tumors require detailed knowledge of respiratory dynamics and its impact on corresponding dose distributions. Thus, computer aided modeling and simulation of respiratory motion have become increasingly important. In this article a biophysical approach for modeling respiratory lung motion is described: Major aspects of the process of lung ventilation are formulated as a contact problem of elasticity theory which is solved by finite element methods; lung tissue is assumed to be isotropic, homogeneous, and linearly elastic. A main focus of the article is to assess the impact of biomechanical parameters (values of elastic constants) on the modeling process and to evaluate modeling accuracy. Patient-specific models are generated based on 4D CT data of 12 lung tumor patients. Simulated motion patterns of inner lung landmarks are compared with corresponding motion patterns observed in the 4D CT data. Mean absolute differences between model-based predicted landmark motion and corresponding breathing-induced landmark displacements as observed in the CT data sets are in the order of 3 mm (end expiration to end inspiration) and 2 mm (end expiration to midrespiration). Modeling accuracy decreases with increasing tumor size both locally (landmarks close to tumor) and globally (landmarks in other parts of the lung). The impact of the values of the elastic constants appears to be small. Outcomes show that the modeling approach is an adequate strategy in predicting lung dynamics due to lung ventilation. Nevertheless, the decreased prediction quality in cases of large tumors demands further study of the influence of lung tumors on global and local lung elasticity properties. <s> BIB041 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Image registration is typically formulated as an optimization problem with multiple tunable, manually set parameters. We present a principled framework for learning thousands of parameters of registration cost functions, such as a spatially-varying tradeoff between the image dissimilarity and regularization terms. Our approach belongs to the classic machine learning framework of model selection by optimization of cross-validation error. This second layer of optimization of cross-validation error over and above registration selects parameters in the registration cost function that result in good registration as measured by the performance of the specific application in a training data set. Much research effort has been devoted to developing generic registration algorithms, which are then specialized to particular imaging modalities, particular imaging targets and particular postregistration analyses. Our framework allows for a systematic adaptation of generic registration cost functions to specific applications by learning the “free” parameters in the cost functions. Here, we consider the application of localizing underlying cytoarchitecture and functional regions in the cerebral cortex by alignment of cortical folding. Most previous work assumes that perfectly registering the macro-anatomy also perfectly aligns the underlying cortical function even though macro-anatomy does not completely predict brain function. In contrast, we learn 1) optimal weights on different cortical folds or 2) optimal cortical folding template in the generic weighted sum of squared differences dissimilarity measure for the localization task. We demonstrate state-of-the-art localization results in both histological and functional magnetic resonance imaging data sets. <s> BIB042 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Reaction-diffusion based tumor growth models have been widely used in the literature for modeling the growth of brain gliomas. Lately, recent models have started integrating medical images in their formulation. Including different tissue types, geometry of the brain and the directions of white matter fiber tracts improved the spatial accuracy of reaction-diffusion models. The adaptation of the general model to the specific patient cases on the other hand has not been studied thoroughly yet. In this paper, we address this adaptation. We propose a parameter estimation method for reaction-diffusion tumor growth models using time series of medical images. This method estimates the patient specific parameters of the model using the images of the patient taken at successive time instances. The proposed method formulates the evolution of the tumor delineation visible in the images based on the reaction-diffusion dynamics; therefore, it remains consistent with the information available. We perform thorough analysis of the method using synthetic tumors and show important couplings between parameters of the reaction-diffusion model. We show that several parameters can be uniquely identified in the case of fixing one parameter, namely the proliferation rate of tumor cells. Moreover, regardless of the value the proliferation rate is fixed to, the speed of growth of the tumor can be estimated in terms of the model parameters with accuracy. We also show that using the model-based speed, we can simulate the evolution of the tumor for the specific patient case. Finally, we apply our method to two real cases and show promising preliminary results. <s> BIB043 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> During breast cancer diagnosis, the breasts undergo large deformations due to gravity or compression loads It is therefore non-trivial to recover the deformation and register medical images of the breast in different orientations (e.g prone versus supine) Free-form deformations and biomechanical finite element models have been used to non-rigidly register breast images from prone to supine, but with limited success In this paper, we demonstrate that the use of a finite element model to predict the deformation of the breast from prone to supine provides a significantly more accurate registration compared to free-form deformation methods We also show that the use of this biomechanical model prediction as a prior to free-form deformation provides a significantly more accurate match than does the use of either method independently. <s> BIB044 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> In this paper, we used a nonconservative Lagrangian mechanics approach to formulate a new statistical algorithm for fluid registration of 3-D brain images. This algorithm is named SAFIRA, acronym for statistically-assisted fluid image registration algorithm. A nonstatistical version of this algorithm was implemented, where the deformation was regularized by penalizing deviations from a zero rate of strain. In, the terms regularizing the deformation included the covariance of the deformation matrices Σ and the vector fields (q). Here, we used a Lagrangian framework to reformulate this algorithm, showing that the regularizing terms essentially allow nonconservative work to occur during the flow. Given 3-D brain images from a group of subjects, vector fields and their corresponding deformation matrices are computed in a first round of registrations using the nonstatistical implementation. Covariance matrices for both the deformation matrices and the vector fields are then obtained and incorporated (separately or jointly) in the nonconservative terms, creating four versions of SAFIRA. We evaluated and compared our algorithms' performance on 92 3-D brain scans from healthy monozygotic and dizygotic twins; 2-D validations are also shown for corpus callosum shapes delineated at midline in the same subjects. After preliminary tests to demonstrate each method, we compared their detection power using tensor-based morphometry (TBM), a technique to analyze local volumetric differences in brain structure. We compared the accuracy of each algorithm variant using various statistical metrics derived from the images and deformation fields. All these tests were also run with a traditional fluid method, which has been quite widely used in TBM studies. The versions incorporating vector-based empirical statistics on brain variation were consistently more accurate than their counterparts, when used for automated volumetric quantification in new brain images. This suggests the advantages of this approach for large-scale neuroimaging studies. <s> BIB045 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> This paper investigates the problem of atlas registration of brain images with gliomas. Multiparametric imaging modalities (T1, T1-CE, T2, and FLAIR) are first utilized for segmentations of different tissues, and to compute the posterior probability map (PBM) of membership to each tissue class, using supervised learning. Similar maps are generated in the initially normal atlas, by modeling the tumor growth, using reaction-diffusion equation. Deformable registration using a demons-like algorithm is used to register the patient images with the tumor bearing atlas. Joint estimation of the simulated tumor parameters (e.g., location, mass effect and degree of infiltration), and the spatial transformation is achieved by maximization of the log-likelihood of observation. An expectation-maximization algorithm is used in registration process to estimate the spatial transformation and other parameters related to tumor simulation are optimized through asynchronous parallel pattern search (APPSPACK). The proposed method has been evaluated on five simulated data sets created by statistically simulated deformations (SSD), and fifteen real multichannel glioma data sets. The performance has been evaluated both quantitatively and qualitatively, and the results have been compared to ORBIT, an alternative method solving a similar problem. The results show that our method outperforms ORBIT, and the warped templates have better similarity to patient images. <s> BIB046 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> In breast conserving surgery clinicians may benefit from information from preoperative images (e.g. high quality dynamic contrast enhanced magnetic resonant image obtained in the prone position), by registering them to the supine patient on the operating table in the theatre. Due to large deformation involved between prone and supine, either non-rigid intensity-based mage registration methods or biomechanical model based methods alone have limited success. In this paper, we proposed a hybrid finite element method (FEM) based image registration method by combining patient-specific biomechanical models with nonrigid intensity-based image registration methods. FEM-based biomechanical models were used to estimate the major deformation of breasts while non-rigid intensity based image registration methods were used to recover the difference between experimental acquisitions and FE predictions due to the simplifications and approximations of biomechanical models. The proposed method shows a good performance for image registration, demonstrated by the experimental example of prone and supine MR breast image registration. <s> BIB047 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> In this paper, we propose a general framework for performance improvement of the current state-of-the-art registration algorithms in terms of both accuracy and computation time. The key concept involves rapid prediction of a deformation field for registration initialization, which is achieved by a statistical correlation model learned between image appearances and deformation fields. This allows us to immediately bring a template image as close as possible to a subject image that we need to register. The task of the registration algorithm is hence reduced to estimating small deformation between the subject image and the initially warped template image, i.e., the intermediate template (IT). Specifically, to obtain a good subject-specific initial deformation, support vector regression is utilized to determine the correlation between image appearances and their respective deformation fields. When registering a new subject onto the template, an initial deformation field is first predicted based on the subject's image appearance for generating an IT. With the IT, only the residual deformation needs to be estimated, presenting much less challenge to the existing registration algorithms. Our learning-based framework affords two important advantages: 1) by requiring only the estimation of the residual deformation between the IT and the subject image, the computation time can be greatly reduced; 2) by leveraging good deformation initialization, local minima giving suboptimal solution could be avoided. Our framework has been extensively evaluated using medical images from different sources, and the results indicate that, on top of accuracy improvement, significant registration speedup can be achieved, as compared with the case where no prediction of initial deformation is performed. <s> BIB048 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> In this paper, we propose an image registration algorithm named statistically-based FFD registration ::: (SFFD). This registration method is a modification of a well-known free-form deformations (FFD) ::: approach. Our framework dramatically reduces the number of parameters to optimise and only needs ::: to perform a single-resolution optimisation to account for coarse and fine local displacements, in contrast ::: to the multi-resolution strategy employed by the FFD-based registration. The proposed registration ::: uses statistical deformation models (SDMs) as a priori knowledge to guide the alignment of a new ::: subject to a common reference template. These SDMs account for the anatomical mean and variability ::: across a population of subjects. We also propose that available anatomical landmark information ::: can be encoded within the proposed SDM framework to enforce the alignment of certain anatomical ::: structures. We present results in terms of fiducial localisation error, which illustrate the ability of ::: the SDMs to encode landmark position information. We also show that our statistical registration ::: algorithm can provide registration results comparable to the standard FFD-based approach at a much ::: lower computational cost. <s> BIB049 </s> Deformable Medical Image Registration: A Survey <s> C. Knowledge-Based Geometric Transformations <s> Physically realistic simulations for large breast deformation are of great interest for many medical applications such as cancer diagnosis, image registration, surgical planning and image-guided surgery. To support fast, large deformation simulations of breasts in clinical settings, we proposed a patient-specific biomechanical modelling framework for breasts, based on an open-source graphics processing unit-based, explicit, dynamic, nonlinear finite element (FE) solver. A semi-automatic segmentation method for tissue classification, integrated with a fully automated FE mesh generation approach, was implemented for quick patient-specific FE model generation. To solve the difficulty in determining material parameters of soft tissues in vivo for FE simulations, a novel method for breast modelling, with a simultaneous material model parameter optimization for soft tissues in vivo, was also proposed. The optimized deformation prediction was obtained through iteratively updating material model parameters to maximize the image similarity between the FE-predicted MR image and the experimentally acquired MR image of a breast. The proposed method was validated and tested by simulating and analysing breast deformation experiments under plate compression. Its prediction accuracy was evaluated by calculating landmark displacement errors. The results showed that both the heterogeneity and the anisotropy of soft tissues were essential in predicting large breast deformations under plate compression. As a generalized method, the proposed process can be used for fast deformation analyses of soft tissues in medical image analyses and surgical simulations. <s> BIB050
In medical image analysis, there are registration scenarios that involve a specific well-defined task. More specifically, registration is either performed between any image and a specific target image or involves image acquisitions of specific anatomical organs. In these cases, it is possible to introduce knowledge about the deformations one tries to recover. Introducing knowledge regarding the deformation may be achieved in two ways. In the case that the target domain is fixed in registration because it exhibits desired properties (e.g., it is manually annotated), one can learn a high dimensional statistical model of deformations by performing pairwise registrations between the target image and the data that one has at their disposition. Subsequently, when a new image is to be registered to the target image, the learned model can be used to penalize configurations that diverge from it. The second method consists of exploiting our knowledge about the deformability of the tissues and constructing biomechanical/biophysical deformation models that mimic their properties. The main motivation behind creating more informed priors is to render the registration method more robust and stable. A registration method is characterized as robust, when its performance does not drastically degrade for small deviations of the input images from the nominal assumptions. In other words, the presence of a small fraction of artifacts or outliers results in small changes in the result. Robustness is, for example, important when encountering images of pathology (e.g., images characterized by the presence of tumors that can be regarded as outliers). A registration method is characterized as stable, when small changes in the input data result in small changes in the result. The stability of the method is, for example, important in longitudinal studies when temporal smoothness, or stable results, can be associated to normality and differences are attributed to temporal anatomical changes. On the other hand, the quality of the solution is conditioned on the quality of the learned model. Learning a high dimensional model is a challenging task that is further impeded by the limited number of training samples. 1) Statistically-Constrained Geometric Transformations: Statistical deformation models (SDMs) capture statistical information about deformation fields across a population of subjects. These methods are able to reduce the number of degrees of freedom, and consequently the computational demands of the problem, while achieving robust performance. Nonetheless, the use of SDMs implies important assumptions. First, one should be able to train the high dimensional statistical model from an often limited number of subjects. Second, it is assumed that the set of images used during the learning step is representative of the population that will be analyzed. Hence, a statistically-constrained registration framework is limited by previously-observed deformations. Subsequent refinement by conventional registration has been proposed to cope with this limitation. Statistical models of variability have been applied successfully to many problems in medical image analysis. One of the most prominent examples concerns statistical models of shape variability applied to segmentation  . Cootes et al.  studied shape variability by performing principal component analysis (PCA) on point correspondences. Wang and Staib BIB005 combined a statistical shape model over boundary points and a physics-based regularization term in a Bayesian approach to solve the atlas-based registration problem. PCA has also been applied in the case of dense deformation fields to derive priors that can be used to constrain registration. Gee and Bajcsy BIB002 described a recursive way to update the model given new observations while accounting for the limited number of samples. Wouters et al. BIB021 used PCA to model the deformation and registration was performed by adjusting the coefficients of the principal components while maximizing mutual information (MI). Tang et al. BIB038 also used PCA to learn an SDM to accelerate image alignment. Once the model was learned, the authors created a set of intermediate target images by sampling along each dimension of the estimated multidimensional Gaussian distribution. The registration of a new image was performed by projecting it to the intermediate target image that is closest in intensity similarity, and by refining the result with a conventional registration method. In a similar approach, Kim et al. BIB048 used support vector regression models to predict the intermediate target image. The regression models had learned the correlations between deformations and image appearances. Rueckert et al. BIB011 performed statistical analysis on the displacement of the control points of the FFD grid that deforms the image. Loeckx et al. BIB012 used a similar model to tackle lung radiograph registration. The statistical model was augmented by incorporating translation and scaling, to account for the fact that the training set was created by manual alignment of image pairs without prior global spatial normalization. Pszczolkowski et al. demonstrated that the model in BIB011 can encode landmark position information BIB049 . Glocker et al. BIB013 also proposed a model that captures variations in the displacements of the control points of the FFD grid. In the first place, a clustering step was performed to reveal the co-dependencies between node displacements. Then, Gaussian mixture models were used to represent the probability density function (PDF) of the relative displacement of two cluster centers and thus capture information about the global nature of the desired deformations. Similarly, PDFs were learned over the relative displacements of the cluster and its cluster members capturing the local information of the desired deformations. The learned priors were introduced as soft constraints in a discrete Markov Random Field registration framework through the consideration of appropriate pairwise interactions. Xue et al. BIB022 tackled the problem of training a high dimensional SDM from a limited number of samples by employing wavelet-based decompositions and estimating the PDF of each band by applying PCA to each one. Two SDMs were trained, one captured variations about the deformation fields while the second encoded information about the Jacobian determinant of the deformation fields. The registration result was constrained by the these models as well as a nested Markov random field (MRF) regularization scheme. In a subsequent work, Xue and Shen BIB026 proposed the use of conventional registration to refine the result of the statistically-constrained method. Pennec et al. BIB017 presented a statistical framework for nonlinear registration that takes into account the means and the covariances of the deformation tensors by computing their Mahalanobis distance. Brun et al. BIB045 further developed this framework by computing statistical priors on both the deformation tensors and the displacement vector fields in a nonconservative Lagrangian fluid registration algorithm. In both approaches, statistical priors were used to guide registration, instead of constraining it to follow the learned distribution. Lester et al. BIB003 presented a modified version of the viscous fluid registration algorithm that incorporated tissue information by letting the viscosity vary according to the tissue. In a similar context, Commowick et al. BIB018 proposed to introduce prior knowledge regarding the stiffness of the deformability of different structures by weighting an elastic-type regularization term by a space-varying scalar or tensor field. The computation of the scalar map of deformability was based on the mean of the absolute value of the logarithm of the determinant of the Jacobian while the stiffness tensor map was based on the mean of the absolute value of the logarithm of the deformation tensor. Yeo et al. BIB042 presented a conceptually complementary approach. Instead of learning the set of admissible deformations, the weights for a weighted SSD similarity criterion were inferred by optimizing the cross-validation error of a specific task. One could argue that estimating these weights is implicitly equivalent to estimating a stiffness map. 2) Geometric Transformations Inspired by Biomechanical/ Biophysical Models: Biomechanical/Biophysical models are also inspired by physical properties. Their difference with respect to the models presented in Section II-A is that they relate closely to anatomy and physiology. Usually, finite element methods (FEMs) are employed to model the biomechanical/biophysical properties of the tissues under consideration. The main motivation behind using the methods of this category is the surmise that more informed priors regarding the biomechanical properties of the tissues will allow the reliable estimation of complex deformation fields with the use of few degrees of freedom. What is more, the limited search space results in improved efficiency when compared to the standard approaches. Moreover, one assumes that by creating models of deforming organs that are consistent to their physical properties, the plausibility of the estimated deformation will improve and registration will be able to better cope with challenges due to the presence of outliers or large deformations. These models are more suitable for intra-individual registration since the biophysical model is no longer valid in inter-individual settings. Nonetheless, one may advocate in favor of their use in inter-individual settings on the basis that, depending on the application, it may be meaningful to let an anatomical structure behave realistically. On the downside, when opting for models that aim to faithfully represent anatomical structures, one needs to accurately define the material properties as well as the necessary geometry and boundary conditions. This is a challenging procedure that is emphasized by our limited understanding of the material properties. As a consequence, the choice of the parameter values is approximately determined, while at the same time is general and not case-specific. The definition of the geometry requires an accurate segmentation of anatomical structures as well as appropriately meshing the image domain. Suitable boundary conditions can be specified by providing displacement constraints for the segmented organ surfaces. Uncertainty in the specification of these parameters may lead to undesirable bias. a) Tumor Growth Models: Registration between normal atlas and pathological brain images in the presence of tumors is a problem that may profit from the existence of brain-tumor interaction models BIB019 - BIB043 . One approach to tackle such cases is to correct for the topological difference between the pair of images by accounting for the tumor and its effects in neighboring structures in the normal subject. Kyriacou et al. BIB004 used a simple uniform expansion model for the tumor. The authors simulated a tumor-free anatomy that was subsequently used in a normal-to-normal atlas registration. The tumor influence was taken into account in order to produce the final deformation field. Cuadra et al. used a radial expansion model of the lesion in two cases BIB015 , BIB023 . In the first case BIB015 , the authors combined the model of lesion growth with the Demons registration algorithm BIB001 . In the second case BIB023 , they used a variational method based on mutual information  . Ganser et al. also employed a simple radial growth model in order to perform registration between the Talairach atlas and a subject BIB016 . The matching process was driven by establishing point correspondences between segmented structures and the atlas. An RBF deformation model was used to estimate the dense deformation field. Nowinski and Belov BIB020 refined the result of a Talairach landmark registration by assuming a radial mass-effect tumor model. Richer models have also been considered. Clatz et al. BIB019 refined the result of an affine registration between a normal atlas and a patient's image by using a coupled model that predicts the anisotropic evolution of the tumor as well as its mass-effect. Methods that combine sophisticated brain-tumor interaction with deformable registration have been proposed in BIB024 - BIB046 . Mohamed et al. BIB024 trained a statistical model of the tumor-induced deformation based on a great number of tumor model simulations. This model was used to estimate the mass-effect in the atlas domain before applying deformable registration. Zacharaki et al. BIB033 , BIB039 also trained a statistical model based on simulations of the tumor effect BIB027 . The parameters of the learned model were inferred through optimization that considered both deformation field information and image similarity. Gooya et al. BIB046 addressed the registration between a normal subject and a subject with Glioblastoma multiforme brain tumors. The tumor was modeled by BIB034 . An expectation-maximization setting was used to jointly estimate the parameters of the model and the warping. b) Biomechanical Models of the Breast: Another field for application of biomechanical models is breast imaging. Biomechanical modeling is important in tackling large deformations which are typical in breast imaging applications such as imageguided interventions BIB006 , cancer diagnosis BIB008 and surgical planning BIB035 . The ability of FEMs to realistically simulate breast deformations has led to their use for the validation of registration methods BIB014 - BIB028 . There are two main causes of breast deformation, gravity and plate compression. When patients are imaged under different positions (typically prone-supine), the breast is deformed greatly under the influence of gravity. FEMs have been used either to register the images BIB035 , BIB029 or to provide a more appropriate initialization for standard intensity-based nonrigid registration methods BIB044 - BIB047 . The breast is typically compressed in mammography under the pressure of two plates in order to flatten and spread the tissue. As a consequence, alignment between 2D mammograms and images from other, (typically 3D), modalities is a challenging problem. FEMs have been used to tackle this problem BIB006 , BIB007 - BIB030 . While these methods aim to align different images, they do not opt to optimize an image-similarity criterion. Instead, alignment is determined by the modeling assumptions and boundary conditions. Image driven approaches have been proposed toward estimating subject-specific tissue properties BIB036 - BIB050 . c) Biomechanical Models of the Prostate: Biomechanical models have also been used to model the prostate and its surrounding organs with applications in preoperative-intraoperative image registration problems  and treatment planning BIB031 . Mohamed et al. BIB009 and Hu et al. used a biomechanical model of the prostate to simulate training data to learn a statistical model that was subsequently used to constrain the registration. Alterovitz et al. BIB025 presented a 2D biomechanical model whose material properties and external forces were optimized by maximizing the overlap between the segmented prostate in both images. Crouch et al. BIB032 used medial shape models to facilitate meshing and boundary condition calculation. d) Miscellaneous: Biomechanical models span a great range of applications. Detailing them all here is both out of scope and impossible. Nonetheless, let us note that they have been applied in the estimation of: cardiac movement BIB010 - BIB040 , brain shift during surgical operations  and lung movement BIB041 , BIB037 .