Volume-preserving nonrigid registration of MR breast images using free-form deformation with an incompressibility constraint

In this paper, we extend a previously reported intensity-based nonrigid registration algorithm by using a novel regularization term to constrain the deformation. Global motion is modeled by a rigid transformation while local motion is described by a free-form deformation based on B-splines. An information theoretic measure, normalized mutual information, is used as an intensity-based image similarity measure. Registration is performed by searching for the deformation that minimizes a cost function consisting of a weighted combination of the image similarity measure and a regularization term. The novel regularization term is a local volume-preservation (incompressibility) constraint, which is motivated by the assumption that soft tissue is incompressible for small deformations and short time periods. The incompressibility constraint is implemented by penalizing deviations of the Jacobian determinant of the deformation from unity. We apply the nonrigid registration algorithm with and without the incompressibility constraint to precontrast and post-contrast magnetic resonance (MR) breast images from 17 patients. Without using a constraint, the volume of contrast-enhancing lesions decreases by 1%-78% (mean 26%). Image improvement (motion artifact reduction) obtained using the new constraint is compared with that obtained using a smoothness constraint based on the bending energy of the coordinate grid by blinded visual assessment of maximum intensity projections of subtraction images. For both constraints, volume preservation improves, and motion artifact correction worsens, as the weight of the constraint penalty term increases. For a given volume change of the contrast-enhancing lesions (2% of the original volume), the incompressibility constraint reduces motion artifacts better than or equal to the smoothness constraint in 13 out of 17 cases (better in 9, equal in 4, worse in 4). The preliminary results suggest that incorporation of the incompressibility regularization term improves intensity-based free-form nonrigid registration of contrast-enhanced MR breast images by greatly reducing the problem of shrinkage of contrast-enhancing structures while simultaneously allowing motion artifacts to be substantially reduced.     

An automatic nonrigid registration for stained histological sections.

Automatic computer-based analyses of histological sections which are differently stained require that they are related to each other. Most registration methods are only able to perform rigid-body motion and are sensitive to noise and artifacts. Histological images, however, are accompanied by several artifacts and different contrasts, which require a nonrigid registration. In this paper, we present a hierarchical nonrigid registration algorithm able to align images, which contain minor image artifacts. The algorithm requires no a priori knowledge of the true image. The hierarchical design of the algorithm enhances robustness and accuracy, and saves computational costs. The proposed algorithm is decomposed into a fast, coarse, rigid registration step and a slower, but finer, nonrigid step. For the coarse registration, we use image pyramids, while for the second step, we combine a point-based registration with an elastic thin-plate spline interpolation. Accuracy tests, performed for 20 histological images obtained from human arteries, have shown that the error measure is acceptable, and that the image noise does not cause a problem. The associated convergence rate of the mean pixel displacement error during the rigid and nonrigid registrations is satisfying. The algorithm can be applied to various multicontrast elastic registration problems in medical imaging and may be extended to three dimensions.     

A new validation method for X-ray mammogram registration algorithms using a projection model of breast X-ray compression

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 nonrigid 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.     

Analysis of 3-D myocardial motion in tagged MR images using nonrigid image registration

Tagged magnetic resonance imaging (MRI) is unique in its ability to noninvasively image the motion and deformation of the heart in vivo, but one of the fundamental reasons limiting its use in the clinical environment is the absence of automated tools to derive clinically useful information from tagged MR images. In this paper, we present a novel and fully automated technique based on nonrigid image registration using multilevel free-form deformations (MFFDs) for the analysis of myocardial motion using tagged MRI. The novel aspect of our technique is its integrated nature for tag localization and deformation field reconstruction using image registration and voxel based similarity measures. To extract the motion field within the myocardium during systole we register a sequence of images taken during systole to a set of reference images taken at end-diastole, maximizing the normalized mutual information between the images. We use both short-axis and long-axis images of the heart to estimate the full four-dimensional motion field within the myocardium. We also present validation results from data acquired from twelve volunteers.     

PET-CT image registration in the chest using free-form deformations

We have implemented and validated an algorithm for three-dimensional positron emission tomography transmission-to-computed tomography registration in the chest, using mutual information as a similarity criterion. Inherent differences in the two imaging protocols produce significant nonrigid motion between the two acquisitions. A rigid body deformation combined with localized cubic B-splines is used to capture this motion. The deformation is defined on a regular grid and is parameterized by potentially several thousand coefficients. Together with a spline-based continuous representation of images and Parzen histogram estimates, our deformation model allows closed-form expressions for the criterion and its gradient. A limited-memory quasi-Newton optimization algorithm is used in a hierarchical multiresolution framework to automatically align the images. To characterize the performance of the method, 27 scans from patients involved in routine lung cancer staging were used in a validation study. The registrations were assessed visually by two expert observers in specific anatomic locations using a split window validation technique. The visually reported errors are in the 0- to 6-mm range and the average computation time is 100 min on a moderate-performance workstation.     

A nonrigid registration framework using spatially encoded mutual information and free-form deformations

Mutual information (MI) registration including spatial information has been shown to perform better than the traditional MI measures for certain nonrigid registration tasks. In this work, we first provide new insight to problems of the MI-based registration and propose to use the spatially encoded mutual information (SEMI) to tackle these problems. To encode spatial information, we propose a hierarchical weighting scheme to differentiate the contribution of sample points to a set of entropy measures, which are associated to spatial variable values. By using free-form deformations (FFDs) as the transformation model, we can first define the spatial variable using the set of FFD control points, and then propose a local ascent optimization scheme for nonrigid SEMI registration. The proposed SEMI registration can improve the registration accuracy in the nonrigid cases where the traditional MI is challenged due to intensity distortion, contrast enhancement, or different imaging modalities. It also has a similar computation complexity to the registration using traditional MI measures, improving up to two orders of magnitude of computation time compared to the traditional schemes. We validate our algorithms using phantom brain MRI, simulated dynamic contrast enhanced mangetic resonance imaging (MRI) of the liver, and in vivo cardiac MRI. The results show that the SEMI registration significantly outperforms the traditional MI registration.     

Filtering in the diffeomorphism group and the registration of point sets

The registration of a pair of point sets as well as the estimation of their pointwise correspondences is a challenging and important task in computer vision. In this paper, we present a method to estimate the diffeomorphic deformation, together with the pointwise correspondences, between a pair of point sets. Many of the registration problems are iteratively solved by estimating the correspondence, locally optimizing certain cost functionals over the rigid or similarity or affine transformation group, then estimating the correspondence again, and so on. This type of approach, however, is well-known to be susceptible to suboptimal local solutions. In this paper, we first adopt the perspective of treating the registration as a posterior estimation optimization problem and solve it accordingly via a particle-filtering framework. Second, within such a framework, the diffeomorphic registration is performed to correct the nonlinear deformation of the points. In doing so, we provide a solution less susceptible to local minima. We provide the experimental results, which include challenging medical data sets where the two point sets differ by 180 (°) rotation as well as local deformations, to highlight the algorithm's capability of robustly finding the more globally optimal solution for the registration task.     

Diffeomorphic metric mapping of high angular resolution diffusion imaging based on Riemannian structure of orientation distribution functions

In this paper, we propose a novel large deformation diffeomorphic registration algorithm to align high angular resolution diffusion images (HARDI) characterized by orientation distribution functions (ODFs). Our proposed algorithm seeks an optimal diffeomorphism of large deformation between two ODF fields in a spatial volume domain and at the same time, locally reorients an ODF in a manner such that it remains consistent with the surrounding anatomical structure. To this end, we first review the Riemannian manifold of ODFs. We then define the reorientation of an ODF when an affine transformation is applied and subsequently, define the diffeomorphic group action to be applied on the ODF based on this reorientation. We incorporate the Riemannian metric of ODFs for quantifying the similarity of two HARDI images into a variational problem defined under the large deformation diffeomorphic metric mapping framework. We finally derive the gradient of the cost function in both Riemannian spaces of diffeomorphisms and the ODFs, and present its numerical implementation. Both synthetic and real brain HARDI data are used to illustrate the performance of our registration algorithm.     

基于图像配准的纸币图像识别方法

提出了基于图像配准的多光谱纸币图像识别架构,通过对纸币图像的配准来实现相似纸币识别、纸币防伪特征检测。由于纸币图像同时具有显著的结构特性和不稳定的局部特性,采用分级的变换模型对纸币图像配准：对于全局的刚性形变采用基于Harris角点特征的仿射变换算法,对于纸币图像局部非刚性形变采用基于B-样条的FFD模型的非刚性配准算法。实验表明,本模型能很好的完成纸币图像的配准,并在相似纸币识别和红外防伪特征检测方面能达到较高的精确度。     

Validation of nonrigid image registration using finite-element methods: application to breast MR images

This paper 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.     

Adaptive Grid Generation Based Non-rigid Image Registration using Mutual Information for Breast MRI

In this paper a new approach for non-rigid image registration using mutual information is introduced. A fast parametric method for non-rigid registration is developed by adjusting divergence and curl of an intermediate vector field from which the deformation field is computed using finite-central difference method. Mutual information is newly employed as the similarity measure in the gradient-based cost minimization (or mutual information maximization) of the existing registration framework. The huge amount of data associated with MRI is handled by a fully automated multi-resolution scheme. The adaptive grid system naturally distributes more grids to deprived areas. The positive monitor function disallows grid folding and provides a mean to control the ratio of the areas between the original and transformed domain. The flexibility of the adaptive grid allocation could dramatically reduce processing time with quality preserved. Mutual information facilitates robust registration between different image modalities. Different types of joint histogram estimation are compared and integrated with the system. This scheme is applied on dynamic contrast-enhanced breast MRI, which requires the registration algorithm to be non-rigid, contrast-enhanced features preserving. Preliminary experiments show promising results and great potential for future extension.     

基于局部仿射配准的鲁棒非刚体配准算法

针对传统点集非刚体配准算法对复杂局部形变数据配准精度低,收敛速度慢等问题,该文提出一种基于局部仿射配准的鲁棒非刚体配准算法。该算法采用分层迭代的方式由粗到精地完成点集的非刚体配准。在每层迭代中,首先对子形状点集集合和子目标点集集合进行分块处理并更新分块后每一类子点集的形状控制点。然后利用控制点引导仿射迭代最近点(ICP)算法求解对应子点集间的局部仿射变换。接着利用上一步求解的局部仿射变换,更新子形状点集集合及其形状控制点集合。直到配准误差收敛时,循环结束并输出更新后的形状点集。实验结果表明,所提算法与传统点集非刚体算法相比具有更强的精确性和收敛性。     

A fast nonrigid image registration with constraints on the Jacobian using large scale constrained optimization

This paper presents a new nonrigid monomodality image registration algorithm based on B-splines. The deformation is described by a cubic B-spline field and found by minimizing the energy between a reference image and a deformed version of a floating image. To penalize noninvertible transformation, we propose two different constraints on the Jacobian of the transformation and its derivatives. The problem is modeled by an inequality constrained optimization problem which is efficiently solved by a combination of the multipliers method and the L-BFGS algorithm to handle the large number of variables and constraints of the registration of 3-D images. Numerical experiments are presented on magnetic resonance images using synthetic deformations and atlas based segmentation.     

Motion compensated fan-beam reconstruction for nonrigid transformation

We develop an approximate fan-beam algorithm to reconstruct an object with time-dependent nonrigid transformation such as the heart. The method is in the form of derivative backprojection filtering with compensation of affine transformations on a local basis. Computer simulations showed the proposed method significantly reduces image artifact due to nonrigid motion. Therefore, with very little motion artifact, the proposed method allowed us to reconstruct images from projections over about one motion cycle, resulting in reduced image noise level down to 40% of the current level.      

Nonrigid 2D/3D registration of coronary artery models with live fluoroscopy for guidance of cardiac interventions

A 2D/3D nonrigid registration method is proposed that brings a 3D centerline model of the coronary arteries into correspondence with bi-plane fluoroscopic angiograms. The registered model is overlaid on top of interventional angiograms to provide surgical assistance during image-guided chronic total occlusion procedures, thereby reducing the uncertainty inherent in 2D interventional images. The proposed methodology is divided into two parts: global structural alignment and local nonrigid registration. In both cases, vessel centerlines are automatically extracted from the 2D fluoroscopic images, and serve as the basis for the alignment and registration algorithms. In the first part, an energy minimization method is used to estimate a global affine transformation that aligns the centerline with the angiograms. The performance of nine general purpose optimizers has been assessed for this problem, and detailed results are presented. In the second part, a fully nonrigid registration method is proposed and used to compensate for any local shape discrepancy. This method is based on a variational framework, and uses a simultaneous matching and reconstruction process to compute a nonrigid registration. With a typical run time of less than 3 s, the algorithms are fast enough for interactive applications. Experiments on five different subjects are presented and show promising results.     

Nonrigid image registration in shared-memory multiprocessor environments with application to brains, breasts, and bees

One major problem with nonrigid image registration techniques is their high computational cost. Because of this, these methods have found limited application to clinical situations where fast execution is required, e.g., intraoperative imaging. This paper presents a parallel implementation of a nonrigid image registration algorithm. It takes advantage of shared-memory multiprocessor computer architectures using multithreaded programming by partitioning of data and partitioning of tasks, depending on the computational subproblem. For three different biomedical applications (intraoperative brain deformation, contrast-enhanced MR mammography, intersubject brain registration), the scaling behavior of the algorithm is quantitatively analyzed. The method is demonstrated to perform the computation of intra-operative brain deformation in less than a minute using 64 CPUs on a 128-CPU shared-memory supercomputer (SGI Origin 3800). It is shown that its serial component is no more than 2% of the total computation time, allowing a speedup of at least a factor of 50. In most cases, the theoretical limit of the speedup is substantially higher (up to 132-fold in the application examples presented in this paper). The parallel implementation of our algorithm is, therefore, capable of solving nonrigid registration problems with short execution time requirements and may be considered an important step in the application of such techniques to clinically important problems such as the computation of brain deformation during cranial image-guided surgery.     

Noise estimation in infrared image sequences: a tool for the quantitative evaluation of the effectiveness of registration algorithms

Dynamic infrared imaging has been proposed in literature as an adjunctive technique to mammography in breast cancer diagnosis. It is based on the acquisition of hundreds of consecutive thermal images with a frame rate ranging from 50 to 200 frames/s, followed by the harmonic analysis of temperature time series at each image pixel. However, the temperature fluctuation due to blood perfusion, which is the signal of interest, is small compared to the signal fluctuation due to subject movements. Hence, before extracting the time series describing temperature fluctuations, it is fundamental to realign the thermal images to attenuate motion artifacts. In this paper, we describe a method for the quantitative evaluation of any kind of feature-based registration algorithm on thermal image sequences, provided that an estimation of local velocities of reference points on the skin is available. As an example of evaluation of a registration algorithm, we report the evaluation of the SNR improvement obtained by applying a nonrigid piecewise linear algorithm.     

Model evaluation and calibration for prospective respiratory motion correction in coronary MR angiography based on 3-D image registration

Image processing was used as a fundamental tool to derive motion information from magnetic resonance (MR) images, which was fed back into prospective respiratory motion correction during subsequent data acquisition to improve image quality in coronary MR angiography (CMRA) scans. This reduces motion artifacts in the images and, in addition, enables the usage of a broader gating window than commonly used today to increase the scan efficiency. The aim of the study reported in this paper was to find a suitable motion model to be used for respiratory motion correction in cardiac imaging and to develop a calibration procedure to adapt the motion model to the individual patient. At first, the performance of three motion models [one-dimensional translation in feet-head (FH) direction, three-dimensional (3-D) translation, and 3-D affine transformation] was tested in a small volunteer study. An elastic image registration algorithm was applied to 3-D MR images of the coronary vessels obtained at different respiratory levels. A strong intersubject variability was observed. The 3-D translation and affine transformation model were found to be superior over the conventional FH translation model used today. Furthermore, a new approach is presented, which utilizes a fast model-based image registration to extract motion information from time series of low-resolution 3-D MR images, which reflects the respiratory motion of the heart. The registration is based on a selectable global 3-D motion model (translation, rigid, or affine transformation). All 3-D MR images were registered with respect to end expiration. The resulting time series of model parameters were analyzed in combination with additionally acquired motion information from a diaphragmatic MR pencil-beam navigator to calibrate the respiratory motion model. To demonstrate the potential of a calibrated motion model for prospective motion correction in coronary imaging, the approach was tested in CMRA examinations in five volunteers.     

A study of the motion and deformation of the heart due to respiration

This paper describes a quantitative assessment of respiratory motion of the heart and the construction of a model of respiratory motion. Three-dimensional magnetic resonance scans were acquired on eight normal volunteers and ten patients. The volunteers were imaged at multiple positions in the breathing cycle between full exhalation and full inhalation while holding their breath. The exhalation volume was segmented and used as a template to which the other volumes were registered using an intensity-based rigid registration algorithm followed by nonrigid registration. The patients were imaged at inhale and exhale only. The registration results were validated by visual assessment and consistency measurements indicating subvoxel registration accuracy. For all subjects, we assessed the nonrigid motion of the heart at the right coronary artery, right atrium, and left ventricle. We show that the rigid-body motion of the heart is primarily in the craniocaudal direction with smaller displacements in the right-left and anterior-posterior directions; this is in agreement with previous studies. Deformation was greatest for the free wall of the right atrium and the left ventricle; typical deformations were 3-4 mm with deformations of up to 7 mm observed in some subjects. Using the registration results, landmarks on the template surface were mapped to their correct positions through the breathing cycle. Principal component analysis produced a statistical model of the motion and deformation of the heart. We discuss how this model could be used to assist motion correction.     

A "twisting and bending" model-based nonrigid image registration technique for 3-D ultrasound carotid images

Atherosclerosis at the carotid bifurcation resulting in cerebral emboli is a major cause of ischemic stroke. Most strokes associated with carotid atherosclerosis can be prevented by lifestyle/dietary changes and pharmacological treatments if identified early by monitoring carotid plaque changes. Registration of 3-D ultrasound (US) images of carotid plaque obtained at different time points is essential for sensitive monitoring of plaque changes in volume and surface morphology. This registration technique should be nonrigid, since different head positions during image acquisition sessions cause relative bending and torsion in the neck, producing nonlinear deformations between the images. We modeled the movement of the neck using a “twisting and bending” model with only six parameters for nonrigid registration. We evaluated the algorithm using 3-D US carotid images acquired at two different head positions to simulate images acquired at different times. We calculated the mean registration error (MRE) between the segmented vessel surfaces in the target image and the registered image using a distance-based error metric after applying our “twisting and bending” model-based nonrigid registration algorithm. We achieved an average registration error of $0.80 pm 0.26$ mm using our nonrigid registration technique, which was a significant improvement in registration accuracy over rigid registration, even with reduced degrees-of-freedom compared to the other nonrigid registration algorithms.