A new method for averaging multidimensional images is presented, which is based on signed Euclidean distance maps computed for each of the pixel values. We refer to the algorithm as "shape-based averaging" (SBA) because of its similarity to Raya and Udupa's shape-based interpolation method. The new method does not introduce pixel intensities that were not present in the input data, which makes it suitable for averaging nonnumerical data such as label maps (segmentations). Using segmented human brain magnetic resonance images, SBA is compared to label voting for the purpose of averaging image segmentations in a multiclassifier fashion. SBA, on average, performed as well as label voting in terms of recognition rates of the averaged segmentations. SBA produced more regular and contiguous structures with less fragmentation than did label voting. SBA also was more robust for small numbers of atlases and for low atlas resolutions, in particular, when combined with shape-based interpolation. We conclude that SBA improves the contiguity and accuracy of averaged image segmentations.

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.

Generation of digitally reconstructed radiographs (DRRs) is computationally expensive and is typically the rate-limiting step in the execution time of intensity-based two-dimensional to three-dimensional (2D-3D) registration algorithms. We address this computational issue by extending the technique of light field rendering from the computer graphics community. The extension of light fields, which we call attenuation fields (AFs), allows most of the DRR computation to be performed in a preprocessing step; after this precomputation step, DRRs can be generated substantially faster than with conventional ray casting. We derive expressions for the physical sizes of the two planes of an AF necessary to generate DRRs for a given X-ray camera geometry and all possible object motion within a specified range. Because an AF is a ray-based data structure, it is substantially more memory efficient than a huge table of precomputed DRRs because it eliminates the redundancy of replicated rays. Nonetheless, an AF can require substantial memory, which we address by compressing it using vector quantization. We compare DRRs generated using AFs (AF-DRRs) to those generated using ray casting (RC-DRRs) for a typical C-arm geometry and computed tomography images of several anatomic regions. They are quantitatively very similar: the median peak signal-to-noise ratio of AF-DRRs versus RC-DRRs is greater than 43 dB in all cases. We perform intensity-based 2D-3D registration using AF-DRRs and RC-DRRs and evaluate registration accuracy using gold-standard clinical spine image data from four patients. The registration accuracy and robustness of the two methods is virtually identical whereas the execution speed using AF-DRRs is an order of magnitude faster.

It is well known in the pattern recognition community that the accuracy of classifications obtained by combining decisions made by independent classifiers can be substantially higher than the accuracy of the individual classifiers. We have previously shown this to be true for atlas-based segmentation of biomedical images. The conventional method for combining individual classifiers weights each classifier equally (vote or sum rule fusion). In this paper, we propose two methods that estimate the performances of the individual classifiers and combine the individual classifiers by weighting them according to their estimated performance. The two methods are multiclass extensions of an expectation-maximization (EM) algorithm for ground truth estimation of binary classification based on decisions of multiple experts (Warfield et al., 2004). The first method performs parameter estimation independently for each class with a subsequent integration step. The second method considers all classes simultaneously. We demonstrate the efficacy of these performance-based fusion methods by applying them to atlas-based segmentations of three-dimensional confocal microscopy images of bee brains. In atlas-based image segmentation, multiple classifiers arise naturally by applying different registration methods to the same atlas, or the same registration method to different atlases, or both. We perform a validation study designed to quantify the success of classifier combination methods in atlas-based segmentation. By applying random deformations, a given ground truth atlas is transformed into multiple segmentations that could result from imperfect registrations of an image to multiple atlas images. In a second evaluation study, multiple actual atlas-based segmentations are combined and their accuracies computed by comparing them to a manual segmentation. We demonstrate in both evaluation studies that segmentations produced by combining multiple individual registration-based segmentations are more accurate for the two classifier fusion methods we propose, which weight the individual classifiers according to their EM-based performance estimates, than for simple sum rule fusion, which weights each classifier equally.

Most image-guided surgery (IGS) systems track the positions of surgical instruments in the physical space occupied by the patient. This task is commonly performed using an optical tracking system that determines the positions of fiducial markers such as infrared-emitting diodes or retroreflective spheres that are attached to the instrument. Instrument tracking error is an important component of the overall IGS system error. This paper is concerned with the effect of fiducial marker configuration (number and spatial distribution) on tip position tracking error. Statistically expected tip position tracking error is calculated by applying results from the point-based registration error theory developed by Fitzpatrick et al. Tracking error depends not only on the error in localizing the fiducials, which is the error value generally provided by manufacturers of optical tracking systems, but also on the number and spatial distribution of the tracking fiducials and the position of the instrument tip relative to the fiducials. The theory is extended in two ways. First, a formula is derived for the special case in which the fiducials and the tip are collinear. Second, the theory is extended for the case in which there is a composition of transformations, as is the situation for tracking an instrument relative to a coordinate reference frame (i.e., a set of fiducials attached to the patient). The derivation reveals that the previous theory may be applied independently to the two transformations; the resulting independent components of tracking error add in quadrature to give the overall tracking error. The theoretical results are verified with numerical simulations and experimental measurements. The results in this paper may be useful for the design of optically tracked instruments for image-guided surgery; this is illustrated with several examples.

Registration of a preoperative CT (3D) image to one or more X-ray projection (2D) images, a special case of the pose estimation problem, has been attempted in a variety of ways with varying degrees of success. Recently, there has been a great deal of interest in intensity-based methods. One of the drawbacks to such methods is the need to create digitally reconstructed radiographs (DRRs) at each step of the optimization process. DRRs are typically generated by ray casting, an operation that requires O(n/sup 3/) time, where we assume that n is approximately the size (in voxels) of one side of the DRR as well as one side of the CT volume. We address this issue by extending light field rendering techniques from the computer graphics community to generate DRRs instead of conventional rendered images. Using light fields allows most of the computation to be performed in a preprocessing step; after this precomputation, very accurate DRRs can be generated in O(n/sup 2/) time. Another important issue for 2D-3D registration algorithms is validation. Previously reported 2D-3D registration algorithms were validated using synthetic data or phantoms but not clinical data. We present an intensity-based 2D-3D registration system that generates DRRs using light fields; we validate its performance using clinical data with a known gold standard transformation.

A sequential algorithm is presented for computing the exact Euclidean distance transform (DT) of a k-dimensional binary image in time linear in the total number of voxels N. The algorithm, which is based on dimensionality reduction and partial Voronoi diagram construction, can be used for computing the DT for a wide class of distance functions, including the L/sub p/ and chamfer metrics. At each dimension level, the DT is computed by constructing the intersection of the Voronoi diagram whose sites are the feature voxels with each row of the image. This construction is performed efficiently by using the DT in the next lower dimension. The correctness and linear time complexity are demonstrated analytically and verified experimentally. The algorithm may be of practical value since it is relatively simple and easy to implement and it is relatively fast (not only does it run in O(N) time but the time constant is small). A simple modification of the algorithm computes the weighted Euclidean DT, which is useful for images with anisotropic voxel dimensions. A parallel version of the algorithm runs in O(N/p) time with p processors.

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.

Recent studies have shown that the surface of the brain is deformed by up to 20 mm after the skull is opened during neurosurgery, which could lead to substantial error in commercial image-guided surgery systems. We quantitatively analyze the intraoperative brain deformation of 24 subjects to investigate whether simple rules can describe or predict the deformation. Interventional magnetic resonance images acquired at the start and end of the procedure are registered nonrigidly to obtain deformation values throughout the brain. Deformation patterns are investigated quantitatively with respect to the location and magnitude of deformation, and to the distribution and principal direction of the displacements. We also measure the volume change of the lateral ventricles by manual segmentation. Our study indicates that brain shift occurs predominantly in the hemisphere ipsi-lateral to the craniotomy, and that there is more brain deformation during resection procedures than during biopsy or functional procedures. However, the brain deformation patterns are extremely complex in this group of subjects. This paper quantitatively demonstrates that brain deformation occurs not only at the surface, but also in deeper brain structure, and that the principal direction of displacement does not always correspond with the direction of gravity. Therefore, simple computational algorithms that utilize limited intraoperative information (e.g., brain surface shift) will not always accurately predict brain deformation at the lesion.

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.

This paper presents a new method for image-guided surgery called image-enhanced endoscopy. Registered real and virtual endoscopic images (perspective volume renderings generated from the same view as the endoscope camera using a preoperative image) are displayed simultaneously; when combined with the ability to vary tissue transparency in the virtual images, this provides surgeons with the ability to see beyond visible surfaces and, thus, provides additional exposure during surgery. A mount with four photoreflective spheres is rigidly attached to the endoscope and its position and orientation is tracked using an optical position sensor. Generation of virtual images that are accurately registered to the real endoscopic images requires calibration of the tracked endoscope. The calibration process determines intrinsic parameters (that represent the projection of three-dimensional points onto the two-dimensional endoscope camera imaging plane) and extrinsic parameters (that represent the transformation from the coordinate system of the tracker mount attached to the endoscope to the coordinate system of the endoscope camera), and determines radial lens distortion. The calibration routine is fast, automatic, accurate and reliable, and is insensitive to rotational orientation of the endoscope. The routine automatically detects, localizes, and identifies dots in a video image snapshot of the calibration target grid and determines the calibration parameters from the sets of known physical coordinates and localized image coordinates of the target grid dots. Using nonlinear lens-distortion correction, which can be performed at real-time rates (30 frames per second), the mean projection error is less than 0.5 mm at distances up to 25 mm from the endoscope tip, and less than 1.0 mm up to 45 mm. Experimental measurements and point-based registration error theory show that the tracking error is about 0.5-0.7 mm at the tip of the endoscope and less than 0.9 mm for all points in the field of view of the endoscope camera at a distance of up to 65 mm from the tip. It is probable that much of the projection error is due to endoscope tracking error rather than calibration error. Two examples of clinical applications are presented to illustrate the usefulness of image-enhanced endoscopy. This method is a useful addition to conventional image-guidance systems, which generally show only the position of the tip (and sometimes the orientation) of a surgical instrument or probe on reformatted image slices.

The problem of providing surgical navigation using image overlays on the operative scene can be split into four main tasks--calibration of the optical system; registration of preoperative images to the patient; system and patient tracking, and display using a suitable visualization scheme. To achieve a convincing result in the magnified microscope view a very high alignment accuracy is required. We have simulated an entire image overlay system to establish the most significant sources of error and improved each of the stages involved. The microscope calibration process has been automated. We have introduced bone-implanted markers for registration and incorporated a locking acrylic dental stent (LADS) for patient tracking. The LADS can also provide a less-invasive registration device with mean target error of 0.7 mm in volunteer experiments. These improvements have significantly increased the alignment accuracy of our overlays. Phantom accuracy is 0.3-0.5 mm and clinical overlay errors were 0.5-1.0 mm on the bone fiducials and 0.5-4 mm on target structures. We have improved the graphical representation of the stereo overlays. The resulting system provides three-dimensional surgical navigation for microscope-assisted guided interventions (MAGI).

The primary objective of this study is to perform a blinded evaluation of two groups of retrospective image registration techniques, using as a gold standard a prospective marker-based registration method, and to compare the performance of one group with the other. These techniques have already been evaluated individually [27]. In this paper, however, we find that by grouping the techniques as volume based or surface based, we can make some interesting conclusions which were not visible in the earlier study. In order to ensure blindness, all retrospective registrations were performed by participants who had no knowledge of the gold-standard results until after their results had been submitted. Image volumes of three modalities: X-ray computed tomography (CT), magnetic resonance (MR), and positron emission tomography (PET) were obtained from patients undergoing neurosurgery at Vanderbilt University Medical Center on whom bone-implanted fiducial markers were mounted. These volumes had all traces of the markers removed and were provided via the Internet to project collaborators outside Vanderbilt, who then performed retrospective registrations on the volumes, calculating transformations from CT to MR and/or from PET to MR. These investigators communicated their transformations, again via the Internet, to Vanderbilt, where the accuracy of each registration was evaluated. In this evaluation, the accuracy is measured at multiple volumes of interest (VOI's). Our results indicate that the volume-based techniques in this study tended to give substantially more accurate and reliable results than the surface-based ones for the CT-to-MR registration tasks, and slightly more accurate results for the PET-to-MR tasks. Analysis of these results revealed that the rotational component of error was more pronounced for the surface-based group. It was also apparent that all of the registration techniques we examined have the potential to produce satisfactory results much of the time, but that visual inspection is necessary to guard against large errors.

In recent years, advances in computer technology and a significant increase in the accuracy of medical imaging have made it possible to develop systems that can assist the clinician in diagnosis, planning, and treatment. This paper deals with an area that is generally referred to as computer-assisted surgery, image-directed surgery, or image-guided surgery. We report the research, development, and clinical validation performed since January 1996 in the European Applications in Surgical Interventions (EASI) project, which is funded by the European Commission in their "4th Framework Telematics Applications for Health" program. The goal of this project is the improvement of the effectiveness and quality of image-guided neurosurgery of the brain and image-guided vascular surgery of abdominal aortic aneurysms, while at the same time reducing patient risks and overall cost. We have developed advanced prototype systems for preoperative surgical planning and intraoperative surgical navigation, and we have extensively clinically validated these systems. The prototype systems and the clinical validation results are described in this paper.

In a previous study we demonstrated that automatic retrospective registration algorithms can frequently register magnetic resonance (MR) and computed tomography (CT) images of the brain with an accuracy of better than 2 mm, but in that same study we found that such algorithms sometimes fail, leading to errors of 6 mm or more. Before these algorithms can be used routinely in the clinic, methods must be provided for distinguishing between registration solutions that are clinically satisfactory and those that are not. One approach is to rely on a human observer to inspect the registration results and reject images that have been registered with insufficient accuracy. In this paper, we present a methodology for evaluating the efficacy of the visual assessment of registration accuracy. Since the clinical requirements for level of registration accuracy are likely to be application dependent, we have evaluated the accuracy of the observer's estimate relative to six thresholds: 1-6 mm. The performance of the observers was evaluated relative to the registration solution obtained using external fiducial markers that are screwed into the patient's skull and that are visible in both MR and CT images. This fiducial marker system provides the gold standard for our study. Its accuracy is shown to be approximately 0.5 mm. Two experienced, blinded observers viewed five pairs of clinical MR and CT brain images, each of which had each been misregistered with respect to the gold standard solution. Fourteen misregistrations were assessed for each image pair with misregistration errors distributed between 0 and 10 mm with approximate uniformity. For each misregistered image pair each observer estimated the registration error (in millimeters) at each of five locations distributed around the head using each of three assessment methods. These estimated errors were compared with the errors as measured by the gold standard to determine agreement relative to each of the six thresholds, where agreement means that the two errors lie on the same side of the threshold. The effect of error in the gold standard itself is taken into account in the analysis of the assessment methods. The results were analyzed by means of the Kappa statistic, the agreement rate, and the area of receiver-operating-characteristic (ROC) curves. No assessment performed well at 1 mm, but all methods performed well at 2 mm and higher. For these five thresholds, two methods agreed with the standard at least 80% of the time and exhibited mean ROC areas greater than 0.84. One of these same methods exhibited Kappa statistics that indicated good agreement relative to chance (Kappa > 0.6) between the pooled observers and the standard for these same five thresholds. Further analysis demonstrates that the results depend strongly on the choice of the distribution of misregistration errors presented to the observers.

Guidance systems designed for neurosurgery, hip surgery, and spine surgery, and for approaches to other anatomy that is relatively rigid can use rigid-body transformations to accomplish image registration. These systems often rely on point-based registration to determine the transformation, and many such systems use attached fiducial markers to establish accurate fiducial points for the registration, the points being established by some fiducial localization process. Accuracy is important to these systems, as is knowledge of the level of that accuracy. An advantage of marker-based systems, particularly those in which the markers are bone-implanted, is that registration error depends only on the fiducial localization error (FLE) and is thus to a large extent independent of the particular object being registered. Thus, it should be possible to predict the clinical accuracy of marker-based systems on the basis of experimental measurements made with phantoms or previous patients. This paper presents two new expressions for estimating registration accuracy of such systems and points out a danger in using a traditional measure of registration accuracy. The new expressions represent fundamental theoretical results with regard to the relationship between localization error and registration error in rigid-body, point-based registration. Rigid-body, point-based registration is achieved by finding the rigid transformation that minimizes "fiducial registration error" (FRE), which is the root mean square distance between homologous fiducials after registration. Closed form solutions have been known since 1966. The expected value (FRE2) depends on the number N of fiducials and expected squared value of FLE, (FLE-2, but in 1979 it was shown that (FRE2) is approximately independent of the fiducial configuration C. The importance of this surprising result seems not yet to have been appreciated by the registration community: Poor registrations caused by poor fiducial configurations may appear to be good due to a small FRE value. A more critical and direct measure of registration error is the "target registration error" (TRE), which is the distance between homologous points other than the centroids of fiducials. Efforts to characterize its behavior have been made since 1989. Published numerical simulations have shown that (TRE2) is roughly proportional to (FLE2)/N and, unlike (FRE2), does depend in some way on C. Thus, FRE, which is often used as feedback to the surgeon using a point-based guidance system, is in fact an unreliable indicator of registration-accuracy. In this work we derive approximate expressions for (TRE2), and for the expected squared alignment error of an individual fiducial. We validate both approximations through numerical simulations. The former expression can be used to provide reliable feedback to the surgeon during surgery and to guide the placement of markers before surgery, or at least to warn the surgeon of potentially dangerous fiducial placements; the latter expression leads to a surprising conclusion: Expected registration accuracy (TRE) is worst near the fiducials that are most closely aligned! This revelation should be of particular concern to surgeons who may at present be relying on fiducial alignment as an indicator of the accuracy of their point-based guidance systems.

This paper presents a method designed to register preoperative computed tomography (CT) images to vertebral surface points acquired intraoperatively from ultrasound (US) images or via a tracked probe. It also presents a comparison of the registration accuracy achievable with surface points acquired from the entire posterior surface of the vertebra to the accuracy achievable with points acquired only from the spinous process and central laminar regions. Using a marker-based method as a reference, this work shows that submillimetric registration accuracy can be obtained even when a small portion of the posterior vertebral surface is used for registration. It also shows that when selected surface patches are used, CT slice thickness is not a critical parameter in the registration process. Furthermore, the paper includes qualitative results of registering vertebral surface points in US images to multiple CT slices. The method has been tested with US points and physical points on a plastic spine phantom and with simulated data on a patient CT scan.

All image-guided neurosurgical systems that we are aware of assume that the head and its contents behave as a rigid body. It is important to measure intraoperative brain deformation (brain shift) to provide some indication of the application accuracy of image-guided surgical systems, and also to provide data to develop and validate nonrigid registration algorithms to correct for such deformation. We are collecting data from patients undergoing neurosurgery in a high-field (1.5 T) interventional magnetic resonance (MR) scanner. High-contrast and high-resolution gradient-echo MR image volumes are collected immediately prior to surgery, during surgery, and at the end of surgery, with the patient intubated and lying on the operating table in the operative position. In this paper we report initial results from six patients: one freehand biopsy, one stereotactic functional procedure, and four resections. We investigate intraoperative brain deformation by examining threshold boundary overlays and difference images and by measuring ventricular volume. We also present preliminary results obtained using a nonrigid registration algorithm to quantify deformation. We found that some cases had much greater deformation than others, and also that, regardless of the procedure, there was very little deformation of the midline, the tentorium, the hemisphere contralateral to the procedure, and ipsilateral structures except those that are within 1 cm of the lesion or are gravitationally above the surgical site.

Most previously reported registration techniques that align three-dimensional image volumes by matching geometrical features such as points or surfaces use a single type of feature. We recently reported a hybrid registration technique that uses a weighted combination of multiple geometrical feature shapes. In this study we use the weighted geometrical feature (WGF) algorithm to register computed tomography (CT) images of the head to physical space using the skin surface only, the bone surface only, and various weighted combinations of these surfaces and one fiducial point (centroid of a bone-implanted marker). We use data acquired from 12 patients that underwent temporal lobe craniotomies for the resection of cerebral lesions. We evaluate and compare the accuracy of the registrations obtained using these various approaches by using as a reference gold standard the registration obtained using three bone-implanted markers. The results demonstrate that a combination of geometrical features can improve the accuracy of CT-to-physical space registration. Point-based registration requires a minimum of three noncolinear points. The position of a bone-implanted marker can be determined much more accurately than that of a skin-affixed marker or an anatomic landmark. A major disadvantage of using bone-implanted markers is that an invasive procedure is required to implant each marker. By combining surface information, the WGF algorithm allows registration to be performed using only one or two such markers. One important finding is that the use of a single very accurate point (a bone-implanted marker) allows very accurate surface-based registration to be achieved using very few surface points. Finally, the WGF algorithm, which not only allows the combination of multiple types of geometrical information but also handles point-based and surface-based registration as degenerate cases, could form the foundation of a "flexible" surgical navigation system that allows the surgeon to use what he considers the method most appropriate for an individual clinical situation.

In this paper, we describe an extrinsic-point-based, interactive image-guided neurosurgical system designed at Vanderbilt University, Nashville, TN, as part of a collaborative effort among the Departments of Neurological Surgery, Computer Science, and Biomedical Engineering. Multimodal image-to-image (II) and image-to-physical (IP) registration is accomplished using implantable markers. Physical space tracking is accomplished with optical triangulation. We investigate the theoretical accuracy of point-based registration using numerical simulations, the experimental accuracy of our system using data obtained with a phantom, and the clinical accuracy of our system using data acquired in a prospective clinical trial by six neurosurgeons at four medical centers from 158 patients undergoing craniotomies to resect cerebral lesions. We can determine the position of our markers with an error of approximately 0.4 mm in X-ray computed tomography (CT) and magnetic resonance (MR) images and 0.3 mm in physical space. The theoretical registration error using four such markers distributed around the head in a configuration that is clinically practical is approximately 0.5-0.6 mm. The mean CT-physical registration error for the phantom experiments is 0.5 mm and for the clinical data obtained with rigid head fixation during scanning is 0.7 mm. The mean CT-MR registration error for the clinical data obtained without rigid head fixation during scanning is 1.4 mm, which is the highest mean error that we observed. These theoretical and experimental findings indicate that this system is an accurate navigational aid that can provide real-time feedback to the surgeon about anatomical structures encountered in the surgical field.

The authors present a weighted geometrical feature (WGF) registration algorithm. Its efficacy is demonstrated by combining points and a surface. The technique is an extension of Besl and McKay's (1992) iterative closest point (ICP) algorithm. The authors use the WGF algorithm to register X-ray computed tomography (CT) and T2-weighted magnetic resonance (MR) volume head images acquired from eleven patients that underwent craniotomies in a neurosurgical clinical trial. Each patient had five external markers attached to transcutaneous posts screwed into the outer table of the skull. The authors define registration error as the distance between positions of corresponding markers that are not used for registration. The CT and MR images are registered using fiducial paints (marker positions) only, a surface only, and various weighted combinations of points and a surface. The CT surface is derived from contours corresponding to the inner surface of the skull. The MR surface is derived from contours corresponding to the cerebrospinal fluid (CSF)-dura interface. Registration using points and a surface is found to be significantly more accurate then registration using only points or a surface.

In 1966 the Communications and Electronics Division of the Philco-Ford Corporation developed a Computer-Aided-Design (C-A-D) Capability for multilayer printed interconnection wiring.1 At that time improvements were planned to enhance the efficiency and usefulness of the series of computer programs involved. Since then additions and changes have been incorporated which allow for the slope classifying of nets, provide data for the automatic generation of artwork, and adapt the series for use on revisions as well as original runs.