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.     

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.     

Standardized evaluation methodology for 2-D-3-D registration

In the past few years, a number of two-dimensional (2-D) to three-dimensional (3-D) (2-D-3-D) registration algorithms have been introduced. However, these methods have been developed and evaluated for specific applications, and have not been directly compared. Understanding and evaluating their performance is therefore an open and important issue. To address this challenge we introduce a standardized evaluation methodology, which can be used for all types of 2-D-3-D registration methods and for different applications and anatomies. Our evaluation methodology uses the calibrated geometry of a 3-D rotational X-ray (3DRX) imaging system (Philips Medical Systems, Best, The Netherlands) in combination with image-based 3-D-3-D registration for attaining a highly accurate gold standard for 2-D X-ray to 3-D MR/CT/3DRX registration. Furthermore, we propose standardized starting positions and failure criteria to allow future researchers to directly compare their methods. As an illustration, the proposed methodology has been used to evaluate the performance of two 2-D-3-D registration techniques, viz. a gradient-based and an intensity-based method, for images of the spine. The data and gold standard transformations are available on the internet (http://www.isi.uu.nl/Research/Databases/).     

Fast point-based 3-D alignment of live cells.

Typical time intervals between acquisitions of three-dimensional (3-D) images of the same cell in live cell imaging are in the orders of minutes. In the meantime, the live cell can move in a water basin on the stage. This movement can hamper the studies of intranuclear processes. We propose a fast point-based image registration method for the suppression of the movement of a cell as a whole in the image data. First, centroids of certain intracellular objects are computed for each image in a time-lapse series. Then, a matching between the centroids, which have the maximal number of pairs, is sought between consecutive point sets by a 3-D extension of a two-dimensional fast point pattern matching method, which is invariant to rotation, translation, local distortion, and extra/missing points. The proposed 3-D extension assumes rotations only around the z axis to retain the complexity of the original method. The final step involves computing the optimal fully 3-D transformation between images from corresponding points in the least-squares manner. The robustness of the method was evaluated on generated data. The results of the simulations show that the method is very precise and its correctness can be estimated. This article also presents two practical application examples, namely the registration of images of HP1 domains and the registration of images of telomeres. More than 97% of time-consecutive images were successfully registered. The results show that the method is very well suited to live cell imaging.     

Gradient-based 2-D/3-D rigid registration of fluoroscopic X-ray to CT

We present a gradient-based method for rigid registration of a patient preoperative computed tomography (CT) to its intraoperative situation with a few fluoroscopic X-ray images obtained with a tracked C-arm. The method is noninvasive, anatomy-based, requires simple user interaction, and includes validation. It is generic and easily customizable for a variety of routine clinical uses in orthopaedic surgery. Gradient-based registration consists of three steps: 1) initial pose estimation; 2) coarse geometry-based registration on bone contours, and; 3) fine gradient projection registration (GPR) on edge pixels. It optimizes speed, accuracy, and robustness. Its novelty resides in using volume gradients to eliminate outliers and foreign objects in the fluoroscopic X-ray images, in speeding up computation, and in achieving higher accuracy. It overcomes the drawbacks of intensity-based methods, which are slow and have a limited convergence range, and of geometry-based methods, which depend on the image segmentation quality. Our simulated, in vitro, and cadaver experiments on a human pelvis CT, dry vertebra, dry femur, fresh lamb hip, and human pelvis under realistic conditions show a mean 0.5-1.7 mm (0.5-2.6 mm maximum) target registration accuracy.     

Markerless real-time 3-D target region tracking by motion backprojection from projection images

Accurate and fast localization of a predefined target region inside the patient is an important component of many image-guided therapy procedures. This problem is commonly solved by registration of intraoperative 2-D projection images to 3-D preoperative images. If the patient is not fixed during the intervention, the 2-D image acquisition is repeated several times during the procedure, and the registration problem can be cast instead as a 3-D tracking problem. To solve the 3-D problem, we propose in this paper to apply 2-D region tracking to first recover the components of the transformation that are in-plane to the projections. The 2-D motion estimates of all projections are backprojected into 3-D space, where they are then combined into a consistent estimate of the 3-D motion. We compare this method to intensity-based 2-D to 3-D registration and a combination of 2-D motion backprojection followed by a 2-D to 3-D registration stage. Using clinical data with a fiducial marker-based gold-standard transformation, we show that our method is capable of accurately tracking vertebral targets in 3-D from 2-D motion measured in X-ray projection images. Using a standard tracking algorithm (hyperplane tracking), tracking is achieved at video frame rates but fails relatively often (32% of all frames tracked with target registration error (TRE) better than 1.2 mm, 82% of all frames tracked with TRE better than 2.4 mm). With intensity-based 2-D to 2-D image registration using normalized mutual information (NMI) and pattern intensity (PI), accuracy and robustness are substantially improved. NMI tracked 82% of all frames in our data with TRE better than 1.2 mm and 96% of all frames with TRE better than 2.4 mm. This comes at the cost of a reduced frame rate, 1.7 s average processing time per frame and projection device. Results using PI were slightly more accurate, but required on average 5.4 s time per frame. These results are still substantially faster than 2-D to 3-D registration. We conclude that motion backprojection from 2-D motion tracking is an accurate and efficient method for tracking 3-D target motion, but tracking 2-D motion accurately and robustly remains a challenge.     

Registration of 3-D CT and 2-D Flat Images of Mouse via Affine Transformation

It is difficult to directly coregister the 3-D fluorescence molecular tomography (FMT) image of a small tumor in a mouse whose maximal diameter is only a few millimeters with a larger CT image of the entire animal that spans about 10 cm. This paper proposes a new method to register 2-D flat and 3-D CT image first to facilitate the registration between small 3-D FMT images and large 3-D CT images. A novel algorithm combining differential evolution and improved simplex method for the registration between the 2-D flat and 3-D CT images is introduced and validated with simulated images and real images of mice. The visualization of the alignment of the 3-D FMT and CT image through 2-D registration shows promising results.      

Semantic image retrieval in magnetic resonance brain volumes

Practitioners in the area of neurology often need to retrieve multimodal magnetic resonance (MR) images of the brain to study disease progression and to correlate observations across multiple subjects. In this paper, a novel technique for retrieving 2-D MR images (slices) in 3-D brain volumes is proposed. Given a 2-D MR query slice, the technique identifies the 3-D volume among multiple subjects in the database, associates the query slice with a specific region of the brain, and retrieves the matching slice within this region in the identified volumes. The proposed technique is capable of retrieving an image in multimodal and noisy scenarios. In this study, support vector machines (SVM) are used for identifying 3-D MR volume and for performing semantic classification of the human brain into various semantic regions. In order to achieve reliable image retrieval performance in the presence of misalignments, an image registration-based retrieval framework is developed. The proposed retrieval technique is tested on various modalities. The test results reveal superior robustness performance with respect to accuracy, speed, and multimodality.     

A comprehensive cardiac motion estimation framework using both untagged and 3-D tagged MR images based on nonrigid registration

In this paper, we present a novel technique based on nonrigid image registration for myocardial motion estimation using both untagged and 3-D tagged MR images. The novel aspect of our technique is its simultaneous usage of complementary information from both untagged and 3-D tagged MR images. To estimate the motion within the myocardium, we register a sequence of tagged and untagged MR images during the cardiac cycle to a set of reference tagged and untagged MR images at end-diastole. The similarity measure is spatially weighted to maximize the utility of information from both images. In addition, the proposed approach integrates a valve plane tracker and adaptive incompressibility into the framework. We have evaluated the proposed approach on 12 subjects. Our results show a clear improvement in terms of accuracy compared to approaches that use either 3-D tagged or untagged MR image information alone. The relative error compared to manually tracked landmarks is less than 15% throughout the cardiac cycle. Finally, we demonstrate the automatic analysis of cardiac function from the myocardial deformation fields.     

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.     

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.     

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.     

Clinical evaluation of respiratory motion compensation for anatomical roadmap guided cardiac electrophysiology procedures

X-ray fluoroscopically guided cardiac electrophysiological procedures are routinely carried out for diagnosis and treatment of cardiac arrhythmias. X-ray images have poor soft tissue contrast and, for this reason, overlay of static 3-D roadmaps derived from preprocedural volumetric data can be used to add anatomical information. However, the registration between the 3-D roadmap and the 2-D X-ray image can be compromised by patient respiratory motion. Three methods were designed and evaluated to correct for respiratory motion using features in the 2-D X-ray images. The first method is based on tracking either the diaphragm or the heart border using the image intensity in a region of interest. The second method detects the tracheal bifurcation using the generalized Hough transform and a 3-D model derived from 3-D preoperative volumetric data. The third method is based on tracking the coronary sinus (CS) catheter. This method uses blob detection to find all possible catheter electrodes in the X-ray image. A cost function is applied to select one CS catheter from all catheter-like objects. All three methods were applied to X-ray images from 18 patients undergoing radiofrequency ablation for the treatment of atrial fibrillation. The 2-D target registration errors (TRE) at the pulmonary veins were calculated to validate the methods. A TRE of 1.6 mm ± 0.8 mm was achieved for the diaphragm tracking; 1.7 mm ± 0.9 mm for heart border tracking, 1.9 mm ± 1.0 mm for trachea tracking, and 1.8 mm ± 0.9 mm for CS catheter tracking. We present a comprehensive comparison between the techniques in terms of robustness, as computed by tracking errors, and accuracy, as computed by TRE using two independent approaches.     

A robust 3-D IVUS transducer tracking using single-plane cineangiography

During an intravascular ultrasound (IVUS) intervention, a catheter with an ultrasound transducer is introduced in the body through a blood vessel, and then, pulled back to image a sequence of vessel cross sections. Unfortunately, there is no 3-D information about the position and orientation of these cross-section planes, which makes them less informative. To position the IVUS images in space, some researchers have proposed complex stereoscopic procedures relying on biplane angiography to get two X-ray image sequences of the IVUS transducer trajectory along the catheter. To simplify this procedure, we and others have elaborated algorithms to recover the transducer 3-D trajectory with only a single view X-ray image sequence. In this paper, we present an improved method that provides both automated 2-D and 3-D transducer tracking based on pullback speed as a priori information. The proposed algorithm is robust to erratic pullback speed and is more accurate than the previous single-plane 3-D tracking methods.     

Mumford–Shah Model for One-to-One Edge Matching

This paper presents a new algorithm based on the Mumford-Shah model for simultaneously detecting the edge features of two images and jointly estimating a consistent set of transformations to match them. Compared to the current asymmetric methods in the literature, this fully symmetric method allows one to determine one-to-one correspondences between the edge features of two images. The entire variational model is realized in a multiscale framework of the finite element approximation. The optimization process is guided by an estimation minimization-type algorithm and an adaptive generalized gradient flow to guarantee a fast and smooth relaxation. The algorithm is tested on T1 and T2 magnetic resonance image data to study the parameter setting. We also present promising results of four applications of the proposed algorithm: interobject monomodal registration, retinal image registration, matching digital photographs of neurosurgery with its volume data, and motion estimation for frame interpolation.     

A model-based, semi-global segmentation approach for automatic 3-D point landmark localization in neuroimages

The existing differential approaches for localization of 3-D anatomic point landmarks in 3-D images are sensitive to noise and usually extract numerous spurious landmarks. The parametric model-based approaches are not practically usable for localization of landmarks that can not be modeled by simple parametric forms. Some dedicated methods using anatomic knowledge to identify particular landmarks are not general enough to cope with other landmarks. In this paper, we propose a model-based, semi-global segmentation approach to automatically localize 3-D point landmarks in neuroimages. To localize a landmark, the semi-global segmentation (meaning the segmentation of a part of the studied structure in a certain neighborhood of the landmark) is first achieved by an active surface model, and then the landmark is localized by analyzing the segmented part only. The joint use of global model-to-image registration, semi-global structure registration, active surface-based segmentation, and point-anchored surface registration makes our method robust to noise and shape variation. To evaluate the method, we apply it to the localization of ventricular landmarks including curvature extrema, centerline intersections, and terminal points. Experiments with 48 clinical and 18 simulated magnetic resonance (MR) volumetric images show that the proposed approach is able to localize these landmarks with an average accuracy of 1 mm (i.e., at the level of image resolution). We also illustrate the use of the proposed approach to cortical landmark identification and discuss its potential applications ranging from computer-aided radiology and surgery to atlas registration with scans.      

Mumford-Shah model for one-to-one edge matching.

This paper presents a new algorithm based on the Mumford-Shah model for simultaneously detecting the edge features of two images and jointly estimating a consistent set of transformations to match them. Compared to the current asymmetric methods in the literature, this fully symmetric method allows one to determine one-to-one correspondences between the edge features of two images. The entire variational model is realized in a multiscale framework of the finite element approximation. The optimization process is guided by an estimation minimization-type algorithm and an adaptive generalized gradient flow to guarantee a fast and smooth relaxation. The algorithm is tested on T1 and T2 magnetic resonance image data to study the parameter setting. We also present promising results of four applications of the proposed algorithm: interobject monomodal registration, retinal image registration, matching digital photographs of neurosurgery with its volume data, and motion estimation for frame interpolation.     

Reconstruction of 3-D geometry using 2-D profiles and a geometric prior model

A method has been developed to reconstruct three-dimensional (3-D) surfaces from two-dimensional (2-D) projection data. It is used to produce individualized boundary element models, consisting of thorax and lung surfaces, for electro- and magnetocardiographic inverse problems. Two orthogonal projections are utilized. A geometrical prior model, built using segmented magnetic resonance images, is deformed according to profiles segmented from projection images. In the authors' method, virtual X-ray images of the prior model are first constructed by simulating real X-ray imaging. The 2-D profiles of the model are segmented from the projections and elastically matched with the profiles segmented from patient data. The displacement vectors produced by the elastic 2-D matching are back projected onto the 3-D surface of the prior model. Finally, the model is deformed, using the back-projected vectors. Two different deformation methods are proposed. The accuracy of the method is validated by a simulation. The average reconstruction error of a thorax and lungs was 1.22 voxels, corresponding to about 5 mm     

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.     

Biomechanical modeling of the human head for physically based, nonrigid image registration

The accuracy of image-guided neurosurgery generally suffers from brain deformations due to intraoperative changes. These deformations cause significant changes of the anatomical geometry (organ shape and spatial interorgan relations), thus making intraoperative navigation based on preoperative images error prone. In order to improve the navigation accuracy, we developed a biomechanical model of the human head based on the finite element method, which can be employed for the correction of preoperative images to cope with the deformations occurring during surgical interventions. At the current stage of development, the two-dimensional (2-D) implementation of the model comprises two different materials, though the theory holds for the three-dimensional (3-D) case and is capable of dealing with an arbitrary number of different materials. For the correction of a preoperative image, a set of homologous landmarks must be specified which determine correspondences. These correspondences can be easily integrated into the model and are maintained throughout the computation of the deformation of the preoperative image. The necessary material parameter values have been determined through a comprehensive literature study. Our approach has been tested for the case of synthetic images and yields physically plausible deformation results. Additionally, we carried out registration experiments with a preoperative MR image of the human head and a corresponding postoperative image simulating an intraoperative image. We found that our approach yields good prediction results, even in the case when correspondences are given in a relatively small area of the image only.