3-D/2-D registration of CT and MR to X-ray images

A crucial part of image-guided therapy is registration of preoperative and intraoperative images, by which the precise position and orientation of the patient's anatomy is determined in three dimensions. This paper presents a novel approach to register three-dimensional (3-D) computed tomography (CT) or magnetic resonance (MR) images to one or more two-dimensional (2-D) X-ray images. The registration is based solely on the information present in 2-D and 3-D images. It does not require fiducial markers, intraoperative X-ray image segmentation, or timely construction of digitally reconstructed radiographs. The originality of the approach is in using normals to bone surfaces, preoperatively defined in 3-D MR or CT data, and gradients of intraoperative X-ray images at locations defined by the X-ray source and 3-D surface points. The registration is concerned with finding the rigid transformation of a CT or MR volume, which provides the best match between surface normals and back projected gradients, considering their amplitudes and orientations. We have thoroughly validated our registration method by using MR, CT, and X-ray images of a cadaveric lumbar spine phantom for which "gold standard" registration was established by means of fiducial markers, and its accuracy assessed by target registration error. Volumes of interest, containing single vertebrae L1-L5, were registered to different pairs of X-ray images from different starting positions, chosen randomly and uniformly around the "gold standard" position. CT/X-ray (MR/ X-ray) registration, which is fast, was successful in more than 91% (82% except for L1) of trials if started from the "gold standard" translated or rotated for less than 6 mm or 17 degrees (3 mm or 8.6 degrees), respectively. Root-mean-square target registration errors were below 0.5 mm for the CT to X-ray registration and below 1.4 mm for MR to X-ray registration.     

Consistent landmark and intensity-based image registration

Two new consistent image registration algorithms are presented: one is based on matching corresponding landmarks and the other is based on matching both landmark and intensity information. The consistent landmark and intensity registration algorithm produces good correspondences between images near landmark locations by matching corresponding landmarks and away from landmark locations by matching the image intensities. In contrast to similar unidirectional algorithms, these new consistent algorithms jointly estimate the forward and reverse transformation between two images while minimizing the inverse consistency error-the error between the forward (reverse) transformation and the inverse of the the reverse (forward) transformation. This reduces the ambiguous correspondence between the forward and reverse transformations associated with large inverse consistency errors. In both algorithms a thin-plate spline (TPS) model is used to regularize the estimated transformations. Two-dimensional (2-D) examples are presented that show the inverse consistency error produced by the traditional unidirectional landmark TPS algorithm can be relatively large and that this error is minimized using the consistent landmark algorithm. Results using 2-D magnetic resonance imaging data are presented that demonstrate that using landmark and intensity information together produce better correspondence between medical images than using either landmarks or intensity information alone.     

Accelerating image registration with the Johnson-Lindenstrauss lemma: application to imaging 3-D neural ultrastructure with electron microscopy

We present a novel algorithm to accelerate feature based registration, and demonstrate the utility of the algorithm for the alignment of large transmission electron microscopy (TEM) images to create 3-D images of neural ultrastructure. In contrast to the most similar algorithms, which achieve small computation times by truncated search, our algorithm uses a novel randomized projection to accelerate feature comparison and to enable global search. Further, we demonstrate robust estimation of nonrigid transformations with a novel probabilistic correspondence framework, that enables large TEM images to be rapidly brought into alignment, removing characteristic distortions of the tissue fixation and imaging process. We analyze the impact of randomized projections upon correspondence detection, and upon transformation accuracy, and demonstrate that accuracy is maintained. We provide experimental results that demonstrate significant reduction in computation time and successful alignment of TEM images.     

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.     

Simultaneous nonrigid registration, segmentation, and tumor detection in MRI guided cervical cancer radiation therapy

External beam radiation therapy (EBRT) for the treatment of cancer enables accurate placement of radiation dose on the cancerous region. However, the deformation of soft tissue during the course of treatment, such as in cervical cancer, presents significant challenges for the delineation of the target volume and other structures of interest. Furthermore, the presence and regression of pathologies such as tumors may violate registration constraints and cause registration errors. In this paper, automatic segmentation, nonrigid registration and tumor detection in cervical magnetic resonance (MR) data are addressed simultaneously using a unified Bayesian framework. The proposed novel method can generate a tumor probability map while progressively identifying the boundary of an organ of interest based on the achieved nonrigid transformation. The method is able to handle the challenges of significant tumor regression and its effect on surrounding tissues. The new method was compared to various currently existing algorithms on a set of 36 MR data from six patients, each patient has six T2-weighted MR cervical images. The results show that the proposed approach achieves an accuracy comparable to manual segmentation and it significantly outperforms the existing registration algorithms. In addition, the tumor detection result generated by the proposed method has a high agreement with manual delineation by a qualified clinician.     

Registration of 3-D intraoperative MR images of the brain using a finite-element biomechanical model

We present a new algorithm for the nonrigid registration of three-dimensional magnetic resonance (MR) intraoperative image sequences showing brain shift. The algorithm tracks key surfaces of objects (cortical surface and the lateral ventricles) in the image sequence using a deformable surface matching algorithm. The volumetric deformation field of the objects is then inferred from the displacements at the boundary surfaces using a linear elastic biomechanical finite-element model. Two experiments on synthetic image sequences are presented, as well as an initial experiment on intraoperative MR images showing brain shift. The results of the registration algorithm show a good correlation of the internal brain structures after deformation, and a good capability of measuring surface as well as subsurface shift. We measured distances between landmarks in the deformed initial image and the corresponding landmarks in the target scan. Cortical surface shifts of up to 10 mm and subsurface shifts of up to 6 mm were recovered with an accuracy of 1 mm or less and 3 mm or less respectively.     

Nonrigid registration using free-form deformations: application tobreast MR images

In this paper we present a new approach for the nonrigid registration of contrast-enhanced breast MRI. A hierarchical transformation model of the motion of the breast has been developed. The global motion of the breast is modeled by an affine transformation while the local breast motion is described by a free-form deformation (FFD) based on B-splines. Normalized mutual information is used as a voxel-based similarity measure which is insensitive to intensity changes as a result of the contrast enhancement. Registration is achieved by minimizing a cost function, which represents a combination of the cost associated with the smoothness of the transformation and the cost associated with the image similarity. The algorithm has been applied to the fully automated registration of three-dimensional (3-D) breast MRI in volunteers and patients. In particular, we have compared the results of the proposed nonrigid registration algorithm to those obtained using rigid and affine registration techniques. The results clearly indicate that the nonrigid registration algorithm is much better able to recover the motion and deformation of the breast than rigid or affine registration algorithms.     

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.     

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.     

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.      

Robust nonrigid registration to capture brain shift from intraoperative MRI

We present a new algorithm to register 3-D preoperative magnetic resonance (MR) images to intraoperative MR images of the brain which have undergone brain shift. This algorithm relies on a robust estimation of the deformation from a sparse noisy set of measured displacements. We propose a new framework to compute the displacement field in an iterative process, allowing the solution to gradually move from an approximation formulation (minimizing the sum of a regularization term and a data error term) to an interpolation formulation (least square minimization of the data error term). An outlier rejection step is introduced in this gradual registration process using a weighted least trimmed squares approach, aiming at improving the robustness of the algorithm. We use a patient-specific model discretized with the finite element method in order to ensure a realistic mechanical behavior of the brain tissue. To meet the clinical time constraint, we parallelized the slowest step of the algorithm so that we can perform a full 3-D image registration in 35 s (including the image update time) on a heterogeneous cluster of 15 personal computers. The algorithm has been tested on six cases of brain tumor resection, presenting a brain shift of up to 14 mm. The results show a good ability to recover large displacements, and a limited decrease of accuracy near the tumor resection cavity.     

Registration and tracking to integrate X-ray and MR images in an XMR facility

We describe a registration and tracking technique to integrate cardiac X-ray images and cardiac magnetic resonance (MR) images acquired from a combined X-ray and MR interventional suite (XMR). Optical tracking is used to determine the transformation matrices relating MR image coordinates and X-ray image coordinates. Calibration of X-ray projection geometry and tracking of the X-ray C-arm and table enable three-dimensional (3-D) reconstruction of vessel centerlines and catheters from bi-plane X-ray views. We can, therefore, combine single X-ray projection images with registered projection MR images from a volume acquisition, and we can also display 3-D reconstructions of catheters within a 3-D or multi-slice MR volume. Registration errors were assessed using phantom experiments. Errors in the combined projection images (two-dimensional target registration error--TRE) were found to be 2.4 to 4.2 mm, and the errors in the integrated volume representation (3-D TRE) were found to be 4.6 to 5.1 mm. These errors are clinically acceptable for alignment of images of the great vessels and the chambers of the heart. Results are shown for two patients. The first involves overlay of a catheter used for invasive pressure measurements on an MR volume that provides anatomical context. The second involves overlay of invasive electrode catheters (including a basket catheter) on a tagged MR volume in order to relate electrophysiology to myocardial motion in a patient with an arrhythmia. Visual assessment of these results suggests the errors were of a similar magnitude to those obtained in the phantom measurements.     

Accounting for signal loss due to dephasing in the correction of distortions in gradient-echo EPI via nonrigid registration

Gradient-echo (GE) echo planar imaging (EPI) is susceptible to both geometric distortions and signal loss. This paper presents a retrospective correction approach based on nonrigid image registration. A new physics-based intensity correction factor derived to compensate for intravoxel dephasing in GE EPI images is incorporated into a previously reported nonrigid registration algorithm. Intravoxel dephasing causes signal loss and thus intensity attenuation in the images. The new rephasing factor we introduce, which changes the intensity of a voxel in images during the registration, is used to improve the accuracy of the intensity-based nonrigid registration method and mitigate the intensity attenuation effect. Simulation-based experiments are first used to evaluate the method. A magnetic resonance (MR) simulator and a real field map are used to generate a realistic GE EPI image. The geometric distortion computed from the field map is used as the ground truth to which the estimated nonrigid deformation is compared. We then apply the algorithm to a set of real human brain images. The results show that, after registration, alignment between EPI and multi-shot, spin-echo images, which have relatively long acquisition times but negligible distortion, is improved and that signal loss caused by dephasing can be recovered.     

Automatic construction of multiple-object three-dimensional statistical shape models: application to cardiac modeling

A novel method is introduced for the generation of landmarks for three-dimensional (3-D) shapes and the construction of the corresponding 3-D statistical shape models. Automatic landmarking of a set of manual segmentations from a class of shapes is achieved by 1) construction of an atlas of the class, 2) automatic extraction of the landmarks from the atlas, and 3) subsequent propagation of these landmarks to each example shape via a volumetric nonrigid registration technique using multiresolution B-spline deformations. This approach presents some advantages over previously published methods: it can treat multiple-part structures and requires less restrictive assumptions on the structure's topology. In this paper, we address the problem of building a 3-D statistical shape model of the left and right ventricle of the heart from 3-D magnetic resonance images. The average accuracy in landmark propagation is shown to be below 2.2 mm. This application demonstrates the robustness and accuracy of the method in the presence of large shape variability and multiple objects.     

Automatic construction of 3-D statistical deformation models of the brain using nonrigid registration

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.     

Robust Gradient-Based 3-D/2-D Registration of CT and MR to X-Ray Images

One of the most important technical challenges in image-guided intervention is to obtain a precise transformation between the intrainterventional patient's anatomy and corresponding preinterventional 3-D image on which the intervention was planned. This goal can be achieved by acquiring intrainterventional 2-D images and matching them to the preinterventional 3-D image via 3-D/2-D image registration. A novel 3-D/2-D registration method is proposed in this paper. The method is based on robustly matching 3-D preinterventional image gradients and coarsely reconstructed 3-D gradients from the intrainterventional 2-D images. To improve the robustness of finding the correspondences between the two sets of gradients, hypothetical correspondences are searched for along normals to anatomical structures in 3-D images, while the final correspondences are established in an iterative process, combining the robust random sample consensus algorithm (RANSAC) and a special gradient matching criterion function. The proposed method was evaluated using the publicly available standardized evaluation methodology for 3-D/2-D registration, consisting of 3-D rotational X-ray, computed tomography, magnetic resonance (MR), and 2-D X-ray images of two spine segments, and standardized evaluation criteria. In this way, the proposed method could be objectively compared to the intensity, gradient, and reconstruction-based registration methods. The obtained results indicate that the proposed method performs favorably both in terms of registration accuracy and robustness. The method is especially superior when just a few X-ray images and when MR preinterventional images are used for registration, which are important advantages for many clinical applications.      

Volume registration using needle paths and point landmarks for evaluation of interventional MRI treatments

We created a method for three-dimensional (3-D) registration of medical images (e.g., magnetic resonance imaging (MRI) or computed tomography) to images of physical tissue sections or to other medical images and evaluated its accuracy. Our method proved valuable for evaluation of animal model experiments on interventional-MRI guided thermal ablation and on a new localized drug delivery system. The method computes an optimum set of rigid body registration parameters by minimization of the Euclidean distances between automatically chosen correspondence points, along manually selected fiducial needle paths, and optional point landmarks, using the iterative closest point algorithm. For numerically simulated experiments, using two needle paths over a range of needle orientations, mean voxel displacement errors depended mostly on needle localization error when the angle between needles was at least 20 degrees. For parameters typical of our in vivo experiments, the mean voxel displacement error was < 0.35 mm. In addition, we determined that the distance objective function was a useful diagnostic for predicting registration quality. To evaluate the registration quality of physical specimens, we computed the misregistration for a needle not considered during the optimization procedure. We registered an ex vivo sheep brain MR volume with another MR volume and tissue section photographs, using various combinations of needle and point landmarks. Mean registration error was always < or = 0.54 mm for MR-to-MR registrations and < or = 0.52 mm for MR to tissue section registrations. We also applied the method to correlate MR volumes of radio-frequency induced thermal ablation lesions with actual tissue destruction. In this case, in vivo rabbit thigh volumes were registered to photographs of ex vivo tissue sections using two needle paths. Mean registration errors were between 0.7 and 1.36 mm over all rabbits, the largest error less than two MR voxel widths. We conclude that our method provides sufficient spatial correspondence to facilitate comparison of 3-D image data with data from gross pathology tissue sections and histology.     

3-D/2-D registration by integrating 2-D information in 3-D

In image-guided therapy, high-quality preoperative images serve for planning and simulation, and intraoperatively as "background", onto which models of surgical instruments or radiation beams are projected. The link between a preoperative image and intraoperative physical space of the patient is established by image-to-patient registration. In this paper, we present a novel 3-D/2-D registration method. First, a 3-D image is reconstructed from a few 2-D X-ray images and next, the preoperative 3-D image is brought into the best possible spatial correspondence with the reconstructed image by optimizing a similarity measure (SM). Because the quality of the reconstructed image is generally low, we introduce a novel SM, which is able to cope with low image quality as well as with different imaging modalities. The novel 3-D/2-D registration method has been evaluated and compared to the gradient-based method (GBM) using standardized evaluation methodology and publicly available 3-D computed tomography (CT), 3-D rotational X-ray (3DRX), and magnetic resonance (MR) and 2-D X-ray images of two spine phantoms, for which gold standard registrations were known. For each of the 3DRX, CT, or MR images and each set of X-ray images, 1600 registrations were performed from starting positions, defined as the mean target registration error (mTRE), randomly generated and uniformly distributed in the interval of 0-20 mm around the gold standard. The capture range was defined as the distance from gold standard for which the final TRE was less than 2 mm in at least 95% of all cases. In terms of success rate, as the function of initial misalignment and capture range the proposed method outperformed the GBM. TREs of the novel method and the GBM were approximately the same. For the registration of 3DRX and CT images to X-ray images as few as 2-3 X-ray views were sufficient to obtain approximately 0.4 mm TREs, 7-9 mm capture range, and 80%-90% of successful registrations. To obtain similar results for MR to X-ray registrations, an image, reconstructed from at least 11 X-ray images was required. Reconstructions from more than 11 images had no effect on the registration results.     

Robust and accurate registration of 2-D electrophoresis gels using point-matching.

Point-matching is a widely applied image registration method and many algorithms have been developed. Registration of 2-D electrophoresis gels is an important problem in biological research that presents many of the technical difficulties that beset point-matching: large numbers of points with variable densities, large nonrigid transformations between point sets, paucity of structural information and large numbers of unmatchable points (outliers) in either set. In seeking the most suitable algorithm for gel registration we have evaluated a number of approaches for accuracy and robustness in the face of these difficulties. Using synthetic images we test combinations of three algorithm components: correspondence assignment, distance metrics and image transformation. We show that a version of the iterated closest point (ICP) algorithm using a non-Euclidean distance metric and a robust estimation of transform parameters provides best performance, equalling SoftAssign in the presence of moderate image distortion, and providing superior robustness against large distortions and high outlier proportions. From this evaluation we develop a gel registration algorithm based on robust ICP and a novel distance metric combining Euclidean, shape context and image-related features. We demonstrate the accuracy of gel matching using synthetic distortions of real gels and show that robust estimation of transform parameters using M-estimators can enforce inverse consistency, ensuring that matching results are independent of the order of the images.     

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.