A comparison of a similarity-based and a feature-based 2-D-3-D registration method for neurointerventional use.

Two-dimensional (2-D)-to-three-dimensional (3-D) registration can improve visualization which may aid minimally invasive neurointerventions. Using clinical and phantom studies, two state-of-the-art approaches to rigid registration are compared quantitatively: an intensity-based algorithm using the gradient difference similarity measure; and an iterative closest point (ICP)-based algorithm. The gradient difference approach was found to be more accurate, with an average registration accuracy of 1.7 mm for clinical data, compared to the ICP-based algorithm with an average accuracy of 2.8 mm. In phantom studies, the ICP-based algorithm proved more reliable, but with more complicated clinical data, the gradient difference algorithm was more robust. Average computation time for the ICP-based algorithm was 20 s per registration, compared with 14 min and 50 s for the gradient difference algorithm.     

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/).     

Intensity-based 2-D-3-D registration of cerebral angiograms

We propose a new method for aligning three-dimensional (3-D) magnetic resonance angiography (MRA) with 2-D X-ray digital subtraction angiograms (DSA). Our method is developed from our algorithm to register computed tomography volumes to X-ray images based on intensity matching of digitally reconstructed radiographs (DRRs). To make the DSA and DRR more similar, we transform the MRA images to images of the vasculature and set to zero the contralateral side of the MRA to that imaged with DSA. We initialize the search for a match on a user defined circular region of interest. We have tested six similarity measures using both unsegmented MRA and three segmentation variants of the MRA. Registrations were carried out on images of a physical neuro-vascular phantom and images obtained during four neuro-vascular interventions. The most accurate and robust registrations were obtained using the pattern intensity, gradient difference, and gradient correlation similarity measures, when used in conjunction with the most sophisticated MRA segmentations. Using these measures, 95% of the phantom start positions and 82% of the clinical start positions were successfully registered. The lowest root mean square reprojection errors were 1.3 mm (standard deviation 0.6) for the phantom and 1.5 mm (standard deviation 0.9) for the clinical data sets. Finally, we present a novel method for the comparison of similarity measure performance using a technique borrowed from receiver operator characteristic analysis.     

Voxel similarity measures for 3-D serial MR brain image registration

The authors have evaluated eight different similarity measures used for rigid body registration of serial magnetic resonance (MR) brain scans. To assess their accuracy the authors used 33 clinical three-dimensional (3-D) serial MR images, with deformable extradural tissue excluded by manual segmentation and simulated 3-D MR images with added intensity distortion. For each measure the authors determined the consistency of registration transformations for both sets of segmented and unsegmented data. They have shown that of the eight measures tested, the ones based on joint entropy produced the best consistency. In particular, these measures seemed to be least sensitive to the presence of extradural tissue. For these data the difference in accuracy of these joint entropy measures, with or without brain segmentation, was within the threshold of visually detectable change in the difference images     

Multiple-object 2-D-3-D registration for noninvasive pose identification of fracture fragments

This paper presents a multiple-object 2-D-3-D registration technique for noninvasively identifying the poses of fracture fragments in the space of a preoperative treatment plan. The plan is made by manipulating and aligning computer models of individual fracture fragments that are segmented from a diagnostic computed tomography. The registration technique iteratively updates the treatment plan and matches its digitally reconstructed radiographs to a small number of intraoperative fluoroscopic images. The proposed approach combines an image similarity metric that integrates edge information with mutual information, and a global-local optimization scheme, to deal with challenges associated with the registration of multiple small fragments and limited imaging orientations in the operating room. The method is easy to use as minimum user interaction is required. Experiments on simulated fractures and two distal radius fracture phantoms demonstrate clinically acceptable target registration errors with capture range as large as 10 mm.     

Postoperative calculation of acetabular cup position using 2-D-3-D registration.

A method to accurately measure the position and orientation of an acetabular cup implant from postoperative X-rays has been designed and validated. The method uses 2-D-3-D registration to align both the prosthesis and the preoperative computed tomography (CT) volume to the X-ray image. This allows the position of the implant to be calculated with respect to a CT-based surgical plan. Experiments have been carried out using ten sets of patient data. A conventional plain-film measurement technique was also investigated. A gold standard implant position and orientation was calculated using postoperative CT. Results show our method to be significantly more accurate than the plain-film method for calculating cup anteversion. Cup orientation and position could be measured to within a mean absolute error of 1.4 mm or degrees.     

A protocol for evaluation of similarity measures for rigid registration

The accuracy and robustness of a registration method depend on a number of factors, such as imaging modality, image content and image degrading effects, the class of spatial transformation used for registration, similarity measure, optimization, and numerous implementation details. The complex interdependence of these factors makes the assessment of the influence of a particular factor on registration difficult, although it is often desirable to have some estimate of such influences prior to registration. The similarity measure used to create the cost function is one of the factors that most influences the quality of registration. Traditionally, limited information on the behavior of a similarity measure is obtained either by studying the quality of the final registration or by drawing plots of similarity measure values obtained by translating or rotating one image relative to the "gold standard." In this paper, we present a protocol for a more thorough, optimization-independent, and systematic statistical evaluation of similarity measures. This protocol estimates a similarity measure's capture range, the number, location and extent of local optima, and the accuracy and distinctiveness of the global optimum. To show that the proposed evaluation protocol is viable, we have conducted several experiments with nine similarity measures and real computed tomography and magnetic resonance (MR) images of a spine phantom, MR brain images, and MR and positron emission tomography brain images, for which "gold standard" registrations were available. We have also studied the impact of histogram bin size on the behavior of nine similarity measures. The proposed evaluation protocol is useful for selecting the best similarity measure and corresponding optimization method for a particular application, as well as for studying the influence of sampling, interpolation, histogram bin size, partial image overlap, and image degradation, such as noise, intensity inhomogeneity, and geometrical distortions on the behavior of a similarity measure.     

Evaluating similarity measures for brain image registration

Evaluation of similarity measures for image registration is a challenging problem due to its complex interaction with the underlying optimization, regularization, image type and modality. We propose a single performance metric, named robustness, as part of a new evaluation method which quantifies the effectiveness of similarity measures for brain image registration while eliminating the effects of the other parts of the registration process. We show empirically that similarity measures with higher robustness are more effective in registering degraded images and are also more successful in performing intermodal image registration. Further, we introduce a new similarity measure, called normalized spatial mutual information, for 3D brain image registration whose robustness is shown to be much higher than the existing ones. Consequently, it tolerates greater image degradation and provides more consistent outcomes for intermodal brain image registration.     

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.     

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.     

Atlas-based indexing of brain sections via 2-D to 3-D image registration

A 2-D to 3-D nonlinear intensity-based registration method is proposed in which the alignment of histological brain sections with a volumetric brain atlas is performed. First, sparsely cut brain sections were linearly matched with an oblique slice automatically extracted from the atlas. Second, a planar-to-curved surface alignment was employed in order to match each section with its corresponding image overlaid on a curved-surface within the atlas. For the latter, a PDE-based registration technique was developed that is driven by a local normalized-mutual-information similarity measure. We demonstrate the method and evaluate its performance with simulated and real data experiments. An atlas-guided segmentation of mouse brains' hippocampal complex, retrieved from the Mouse Brain Library (MBL) database, is demonstrated with the proposed algorithm.     

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.     

Rapid elastic image registration for 3-D ultrasound

A Subvolume-based algorithm for elastic Ultrasound REgistration (SURE) was developed and evaluated. Designed primarily to improve spatial resolution in three-dimensional compound imaging, the algorithm registers individual image volumes nonlinearly before combination into compound volumes. SURE works in one or two stages, optionally using MIAMI Fuse software first to determine a global affine registration before iteratively dividing the volume into subvolumes and computing local rigid registrations in the second stage. Connectivity of the entire volume is ensured by global interpolation using thin-plate splines after each iteration. The performance of SURE was quantified in 20 synthetically deformed in vivo ultrasound volumes, and in two phantom scans, one of which was distorted at acquisition by placing an aberrating layer in the sound path. The aberrating layer was designed to induce beam aberrations reported for the female breast. Synthetic deformations of 1.5-2.5 mm were reduced by over 85% when SURE was applied to register the distorted image volumes with the original ones. Registration times were below 5 min on a 500-MHz CPU for an average data set size of 13 MB. In the aberrated phantom scans, SURE reduced the average deformation between the two volumes from 1.01 to 0.30 mm. This was a statistically significant (P = 0.01) improvement over rigid and affine registration transformations, which produced reductions to 0.59 and 0.50 mm, respectively.     

The 2-D-3-D crossover in modulation-doped GaAs-Ga1-xAlxAs quantum wells

We report on a method to analyze the 2-D-3-D crossover in n-type modulation-doped quantum wells. Finite well barrier, first and second subband population, many-body effects, and residual doping are included in our calculation. We found that the 2-D-3-D crossover remarkably depends not only upon the geometrical parameters, as for instance, the spacer layer width and quantum-well width, but also upon a residual p-type doping intentionally introduced. A diagram showing the 2-D-3-D dimensional crossover is presented     

Automatic generation of boundary conditions using demons nonrigid image registration for use in 3-D modality-independent elastography

Modality-independent elastography (MIE) is a method of elastography that reconstructs the elastic properties of tissue using images acquired under different loading conditions and a biomechanical model. Boundary conditions are a critical input to the algorithm and are often determined by time-consuming point correspondence methods requiring manual user input. This study presents a novel method of automatically generating boundary conditions by nonrigidly registering two image sets with a demons diffusion-based registration algorithm. The use of this method was successfully performed in silico using magnetic resonance and X-ray-computed tomography image data with known boundary conditions. These preliminary results produced boundary conditions with an accuracy of up to 80% compared to the known conditions. Demons-based boundary conditions were utilized within a 3-D MIE reconstruction to determine an elasticity contrast ratio between tumor and normal tissue. Two phantom experiments were then conducted to further test the accuracy of the demons boundary conditions and the MIE reconstruction arising from the use of these conditions. Preliminary results show a reasonable characterization of the material properties on this first attempt and a significant improvement in the automation level and viability of the method.     

Genetic algorithms for a robust 3-D MR-CT registration

Presents an original usage of genetic algorithms as a robust search space sampler in an application to 3D medical image elastic registration. An overview of the standard steps of a registration algorithm is given. We focus on the genetic algorithm use, and particularly on the problem of extracting the optimal solution among the final genetic population. We provide an original encoding scheme relying on a structural approach of point matching and then point out the need for a local optimization process. We then illustrate the algorithm with a concrete registration example and assert the results with a direct multi-volume rendering tool. Finally, the algorithm is applied to the Vanderbilt medical image database to assert its robustness and in order to compare it with other techniques     

Voxel-based 2-D/3-D registration of fluoroscopy images and CT scansfor image-guided surgery

Registration of intraoperative fluoroscopy images with preoperative 3D CT images can he used for several purposes in image-guided surgery. On the one hand, it can be used to display the position of surgical instruments, which are being tracked by a localizer, in the preoperative CT scan. On the other hand, the registration result can be used to project preoperative planning information or important anatomical structures visible in the CT image on to the fluoroscopy image. For this registration task, a novel voxel-based method in combination with a new similarity measure (pattern intensity) has been developed. The basic concept of the method is explained at the example of 2D/3D registration of a vertebra in an X-ray fluoroscopy image with a 3D CT image. The registration method is described, and the results for a spine phantom are presented and discussed. Registration has been carried out repeatedly with different starting estimates to study the capture range. Information about registration accuracy has been obtained by comparing the registration results with a highly accurate “ground-truth” registration, which has been derived from fiducial markers attached to the phantom prior to imaging. In addition, registration results for different vertebrae have been compared. The results show that the rotation parameters and the shifts parallel to the projection plane can accurately be determined from a single projection. Because of the projection geometry, the accuracy of the height above the projection plane is significantly lower     

Improvement of depth position in 2-D/3-D registration of knee implants using single-plane fluoroscopy

Two-dimensional (2-D)/three-dimensional (3-D) registration techniques using single-plane fluoroscopy are highly important for analyzing 3-D kinematics in applications such as total knee arthroplasty (TKA) implants. The accuracy of single-plane fluoroscopy-based techniques in the determination of translation perpendicular to the image plane (depth position), however, is relatively poor because a change in the depth position causes only small changes in the 2-D silhouette. Accuracies achieved in depth position using conventional 2-D/3-D registration techniques are insufficient for clinical applications. Therefore, we propose a technique for improving the accuracy of depth position determination in order to develop a system for analyzing knee kinematics over the full six degrees of freedom (6 DOF) using single-plane fluoroscopy. In preliminary experiments, the behaviors of errors for each free variable were quantified as evaluation curves by examining changes in cost function with variations in the free variable. The evaluation curve for depth position was more jagged, and the curve peak less pointy, compared to the evaluation curves of the other five variables, and the curve was found to behave differently. Depth position is therefore optimized independently of the other variables, using an approximate evaluation curve of depth position prepared after initial registration. Accuracy of the proposed technique was evaluated by computer simulation and in vitro tests, with validation of absolute position and orientation performed for each knee component. In computer simulation tests, root-mean-square error (RMSE) in depth position was improved from 2.6 mm (conventional) to 0.9 mm (proposed), whereas for in vitro tests, RMSE improved from 3.2 mm to 1.4 mm. Accuracy of the estimation of the remaining two translational and three rotational variables was found to be almost the same as that obtained by conventional techniques. Results of in vivo tests are also described in which the possibility of full 6 DOF kinematic analysis of TKA implants is shown.     

2-D-3-D crossover in single asymmetric quantum wells: investigationof the electric field and temperature effects

The 2-D-3-D crossover in n-doped GaAs-Ga_0.63Al_0.37 As single asymmetric quantum wells is theoretically investigated. The coupled one-dimensional Schrodinger and Poisson equations are solved self-consistently, in the frame of the finite-difference method. The present study shows that the 2-D-3-D crossover depends upon the geometrical parameters, as for instance, the quantum well width and spacer layer width. It also depends on the temperature and the gate voltage applied on an asymmetric quantum-well-based device. The 2-D-3-D crossover diagrams involving the well width dependence of both the electric field and the temperature are presented and discussed     

A comparison of methods for mammogram registration

Mammogram registration is an important technique to optimize the display of cases on a digital viewing station, and to find corresponding regions in temporal pairs of mammograms for computer-aided diagnosis algorithms. Four methods for mammogram registration were tested and results were compared. The performance of all registration methods was measured by comparing the distance between annotations of abnormalities in the previous and current view before and after registration. Registration by mutual information outperformed alignment based on nipple location, alignment based on center of mass of breast tissue, and warping.