Visual Assessment of the Accuracy of Retrospective Registration of MR and CT Images of the Brain

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1 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 17, NO. 4, AUGUST Visual Assessment of the Accuracy of Retrospective Registration of MR and CT Images of the Brain J. Michael Fitzpatrick,* Member, IEEE, Derek L. G. Hill, Member, IEEE, Yu Shyr, Jay West, Colin Studholme, and Calvin R. Maurer, Jr., Member, IEEE Abstract 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 Manuscript received April 30, 1997; revised July 9, This work was supported in part by the UK Engineering and Physical Sciences Research Council and Philips Medical Systems (EasyVision/EasyGuide Advanced Development). The work of J. M. Fitzpatrick and J. West was supported in part by the National Science Foundation under Grant BES The Associate Editor responsible for coordinating the review of this paper and recommending its publication was M. Viergever. Asterisk indicates corresponding author. *J. M. Fitzpatrick is with the Departments of Computer Science, Neurological Surgery, and Radiology, Vanderbilt University, Nashville, TN USA ( jmf@vuse.vanderbilt.edu). D. L. G. Hill is with the Division of Radiological Sciences and Medical Engineering, Guy s, King s College, and St. Thomas Hospitals School of Medicine, King s College, London SE1 9RT U.K. Y. Shyr is with the Department of Biostatistics, Vanderbilt University, Nashville, TN USA. J. West is with the Department of Computer Science, Vanderbilt University, Nashville, TN USA. C. Studholme was with the Division of Radiological Sciences and Medical Engineering, Guy s, King s College, and St. Thomas Hospitals School of Medicine, King s College London SE1 9RT U.K. He is now with the Departments of Diagnostic Radiology and Electrical Engineering, Yale University, New Haven, CT USA. C. R. Maurer, Jr. was with the Departments of Computer Science and Neurological Surgery, Vanderbilt University, Nashville, TN USA. He is now with the Departments of Neurosurgery and Biomedical Engineering, University of Rochester, Rochester, NY USA. Publisher Item Identifier S (98) 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 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. Index Terms Accuracy, computed tomography (CT), image registration, magnetic resonance (MR), retrospective registration, visual assessment. I. INTRODUCTION THE widespread use of both computed tomography (CT) and magnetic resonance (MR) imaging of the head for diagnosis and surgical planning indicates that physicians and surgeons gain important complementary information on bony and soft tissue anatomy from these two tomographic modalities. In current practice image volumes of each modality may be ordered for a given patient, each comprising a set of slices, typically contiguous, spanning some region of interest. Each slice of each image will then be transferred to film and examined side-by-side in the traditional light box, or they may, in rare cases, be examined on a computer screen, where window and level adjustments can be made interactively. Unfortunately, because of differences in the positioning and orientation of the head, field of view (FOV), and resolution, the correspondence between three-dimensional (3-D) points in different images can be difficult to determine. During the examination of the images the information from the various image modalities is combined in the physician s mind to produce a mapping of points from one image space to another. This 3-D mapping relies on experience that allows the physician to recognize homologous anatomical features in CT and MR. This combined image information is then used in making a diagnosis or in planning for surgical intervention. Uncertainty in the mental mapping from one image to another may lead to uncertainty in the diagnosis or planning. In the last decade, much work has been done to reduce the uncertainty in mapping from one brain image to another /98$ IEEE

2 572 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 17, NO. 4, AUGUST 1998 through the development of 3-D registration algorithms. Many automatic and semiautomatic methods of image registration have been developed and tested [1] [16]. Several comprehensive reviews of these methods are available [17] [19]. In this paper, we use the term retrospective registration algorithm to refer to methods that perform the registration without any markers or frames being attached to the patient prior to imaging. The use of a registration algorithm means that the question of uncertainty in mapping one point to another is answered by measuring its registration accuracy. Recently, some of us undertook a study to measure registration error relative to a gold standard [20]. In that study, in which 16 methods were applied by investigators at 12 sites to a standard set of images, we found that, while retrospective techniques have the potential to produce satisfactory results, frequently registering images with an accuracy of better than 2 mm, they sometimes fail, leading to errors of 6 mm or more. In order to guard against such large errors in clinical practice, 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 assess the registration results visually and to reject images that have been registered with insufficient accuracy. The reliability of visual assessment for detecting registration errors is a matter of some controversy. Recently, Holton et al. [21] provided a systematic study of the accuracy of visual assessment using receiver-operating-characteristic (ROC) analysis. These results are promising and suggest that further study is warranted. In that work two experiments were performed. In the first experiment pairs of images, one of low resolution and a second of high resolution, were simulated from a single MR image volume for each of several patients. This experiment has the advantage that the actual registration errors are known to an arbitrarily high level of accuracy but has the disadvantage that both images are simulated from the same original, which is quite different from the clinical situation. 1 In the second experiment one MR and one single photon emission computed tomography image were used for each patient. This second experiment is much more realistic because the images come from a real clinical acquisition, but it has the disadvantage that the correct registration transformation is unknown. Wong et al. [22] also studied the ability of observers to assess registration accuracy. In their study, five observers inspected a single MR and positron emission tomography (PET) image pair that had been misregistered by translational and rotational displacements about all three axes separately. The gold standard for this study was an automatic registration algorithm that optimizes the mutual information of the joint probability distribution of the two images [12]. They assessed the proportion of observations for which the observers recorded a definite misregistration error and found that observers could always detect a translational misregistration of greater than 2 mm in the and directions, and greater than 3 mm in the direction. Similarly, the observers could always detect a rotation of greater than 4 and could detect a rotation error of 3 about any axis at least 80% of the time. There was good agreement between observers. The paper did not study any misregistrations that included combinations of rotations and translations. Providing a definitive evaluation of the effectiveness of visual assessment of registration accuracy as a clinical tool will require a much larger study than the one presented here. Our aim is to evaluate the methodology that could be used in such a large trial. We use a pilot study involving MR and CT images of the head to introduce a method for the collection and analysis of experimental data, and discuss the implications of our results on the design of larger studies. The major strength of our method is its basis on a highly accurate gold standard for clinical images that can provide estimates of misregistration error. The mean accuracy of this standard has been estimated in previous work to be better than 1 mm [23], [24] and in the present work to be better then 0.5 mm. Furthermore, estimates of the gold-standard s error can be accounted for in the analysis by means of an adjustment to its misregistration estimate. In addition, we misregister our images using transformations selected from the previous study of retrospective registration algorithms mentioned earlier so that our determinations are based on misregistrations that one might expect to find in clinical practice. We apply our evaluation method to three different methods of visual assessment, each of which is applied by two experienced observers to a CT and MR volume image from each of five patients. We employ several statistical tools for measuring and comparing the efficacies of visual assessment. II. MATERIALS AND METHODS A. The Gold Standard The gold standard in this project is a prospective registration system based on the implantation of fiducial markers into the skull of the patient. This system, which is called the ACUSTAR I Advanced Neurosurgical Navigation System, 2 is used to provide intraoperative guidance during neurosurgery [24]. Before the patient is imaged the surgeon implants four plastic posts into the outer table of the skull of the patient with one end remaining outside the skin. The specific locations of the posts are determined by individual clinical circumstances, but the posts are widely separated and are placed on both sides of the head. Image markers that contain contrast fluid and generate high intensity in both CT and MR scans are attached to the bases just prior to image acquisition. A detailed description of these markers can be found in [24]. 1 It may be possible to simulate images of different modalities accurately using very high-resolution data such as digitized cryosections by appropriately modeling the image formation process and by incorporating all common causes of artifact including motion. Validated simulations of this type are, however, not currently available. 2 The Acustar system we used was manufactured by Johnson & Johnson Professional, Inc., Randolph, MA. The Acustar trademark and associated intellectual property rights are now owned by Picker International, Highland Heights, OH.

3 FITZPATRICK et al.: ACCURACY OF RETROSPECTIVE REGISTRATION OF MR AND CT IMAGES 573 B. Image Acquisition We use X-ray CT and MR volume head images acquired preoperatively from five patients who subsequently underwent craniotomies for the resection of cerebral lesions. The CT images were acquired using a Siemens Somatom Plus scanner. Each image volume contains between 40 and 45 transverse slices with pixels. The voxel dimensions are approximately mm. Three-dimensional magnetization-prepared rapid gradient-echo (MP-RAGE) MR image volumes [25] were acquired using the head coil in a Siemens Magnetom SP T scanner. Each image volume contains 128 coronal slices with pixels. The voxel dimensions are approximately mm. The magnetization preparation consisted of an inversion pulse followed by a 400-ms delay which produced strong T1 weighting in the image. After the inversion time delay, 128 slice encoding lines were acquired sequentially at 10-ms intervals (TR: 10 ms; TE: 4 ms; flip angle: 10 ; and FLASH: type sequence). This was followed by a 400-ms recovery period after which the next inversion pulse was applied. Total imaging time was 8.9 min. The readout gradient was oriented in the cranio-caudal direction with a magnitude of 4.7 mt/m. C. MR Calibration The MR and CT scanners used in this study provide a direct or indirect measurement of the voxel sizes in all three dimensions. For the CT, there is additionally a skew angle corresponding to the gantry tilt. That angle was set to zero for all CT acquisitions. The image registration algorithms that we are considering here assume that the images are related by a rigid-body transformation. Such algorithms cannot correct for scaling differences between scans. Even if the calculated registration transformation is perfect, a scaling error of 2% can result in a registration error of up to 4 mm across a 200-mm FOV. It is our experience that CT scans are relatively accurate geometrically, with voxel dimensions within 1% and gantry tilt uncertainty within 0.5. The error in the nominal MR scanner voxel dimensions is typically greater than 1%, commonly 2% or 3%, and can occasionally be 5% or more [20], [24], [26]. Therefore, we have made independent measurements of the MR voxel dimensions by scanning a calibration phantom as close in time as possible to the imaging of each patient, which for all but one case was within 36 h. We used the same pulse sequence, FOV, and slice orientation for the phantom acquisition as for the clinical image acquisitions. The calibration phantom is a 50-mm hollow cube suspended by 24-mm diameter hollow cylinders inside a 100-mm hollow cube. All dimensions were measured to an estimated accuracy of 0.05 mm using a micrometer. A computer model of the phantom was generated from the measured dimensions. For imaging, the phantom was filled with an aqueous solution of 0.5 mm gadopentetate dimeglumine (Magnevist, Berlex Laboratories, Wayne, NJ). The MR images of the phantom were registered to the computer model using a 9-degree of freedom registration algorithm that maximizes the mutual information of the joint probability distribution [27]. The scaling factors calculated were used to scale the patient images by modifying for each image volume each of the three nominal pixel dimensions (as opposed to generating a new image). This scale correction algorithm is described in greater detail in [28]. We refer to images modified in this way as scaled images. D. Airbrushing The patient images were postprocessed to remove the fiducial markers, a process that we call airbrushing. Airbrushing was achieved by manual outlining of regions containing the markers followed by an approximate reconstruction of the image background in each missing region In MR, where the background consists of unstructured noise, pixels at random positions between the edge of and the lateral image boundary were sampled and placed in In CT, as the outer region of the lower part of the image contains the head holder, an attempt at automated reconstruction of the region based on the intensities between and the image boundary would have resulted in obvious discontinuities in the image. In this case, the pixels within were simply set to an intensity value corresponding to the darkest background areas. The airbrushing process is illustrated in Fig. 1. Fig. 1(a) and (b) shows sample slices of original CT and MR image volumes, respectively. Abnormal window and level values have been set so that the head holder in CT and the background artifacts in MR may be seen. Fig. 1(c) and (d) shows the same slices after the region has been outlined and set to the darkest background value. This procedure is applied to every slice in the volume that contains any trace of one or more fiducial markers. Fig. 1(e) and (f) shows the final form of the slices. In MR, the background in the region has been reconstructed: it can be seen that the replaced area is indistinguishable from the rest of the background. In CT, no attempt at background reconstruction has been made, and Fig. 1(c) and (e) are therefore identical. There remains a discontinuity in intensity between the small values in and the slightly larger values in the surrounding head holder, but the intensity levels in the holder are small enough compared to those within the head that the discontinuity is invisible at normal window levels. E. Target Points Our evaluation of the accuracy of visual assessment is carried out at each of several specific anatomical regions. We have chosen five widely distributed regions and have designated a single point within each to be evaluated. It was found in our earlier study that registration error exhibits a smooth spatial variation. Thus, it is appropriate to characterize the error within a region by the error at the centroid of the region. The regions we have chosen are as follows: right cochlea, left cochlea, right globe, left globe, and the confluence of the sinuses (torcular). These points were chosen because they are widely spread and can be localized relatively accurately in all three dimensions. It is desirable to use points that can be localized well in all three dimensions so that observers are sensitive to misregistrations in arbitrary

4 574 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 17, NO. 4, AUGUST 1998 TABLE I TABLE OF FRE s FOR THE FIVE PATIENT IMAGES WITH AND WITHOUT SCALING Patient Unscaled Scaled Fig. 1. (a) (c) (e) (f) Removal of fiducial markers and stereotactic frame. (a) and (b) Sample original image slices from CT (a) and MR (b). The fiducial markers (two bright spots near the head) are clearly visible in both modalities, and the protective caps for the markers (square structure surrounding the markers) are visible in CT. The window and level have been set to show the background artifacts in MR and the head holder in CT. (c) and (d) The same image slices after the region R has been outlined and set to the darkest background level. All trace of the fiducial markers and marker caps has been removed. (e) and (f) The final form of the image slices. In MR, the region R has been reconstructed and is indistinguishable from the rest of the background. In CT, no reconstruction of the background has been attempted: (e) is, thus, identical to (c). There is a discontinuity between R and the surrounding head holder, but this is invisible at normal window levels. directions. Such points are also important for two of our assessment methods, which are based on point localization (see Section II-G). F. Registration and Misregistration Each CT volume is first registered via the gold standard to its corresponding MR volume. Then a series of misregistrations are applied to the registered CT volume to produce the set of CT volumes whose registration accuracy is to be assessed. (b) (d) 1) Registration: After the CT and MR image volumes have been acquired and the MR volumes have been corrected for scaling errors, the gold-standard transformation that registers the CT volume to the MR volume is determined using the Acustar markers [24]. First, the intensity-weighted centroid of each image marker is determined using the localization algorithm described in [29]. Then the rigid-body transformation that aligns the corresponding centroids in CT and MR in the least-squares (LS) sense is calculated using the closed-form solution reported in [30]. As a confirmation of the accuracy of the gold-standard registration, the fiducial registration error (FRE) is calculated for each registration, where FRE is the root-mean-square (rms) distance between the centroids of corresponding markers in the MR volume and the registered CT volume. These values are listed in Table I for all five patients in this study for both the original and scaled MR images. The FRE values for the scaled MR images are considerably better than those for the original images and are also considerably better than the FRE values previously reported for spin-echo MR images that were corrected for scale distortion using a stereotactic frame as an object of known shape and size [20], [24], [26]. Smaller FRE values are known statistically to reflect more accurate registration systems [31], [32]. Registrations using MP-RAGE images in the current study are probably more accurate than registrations using spin-echo images in our previous studies because the MP-RAGE image resolution is higher (1.6- versus 3 5-mm slice thickness), because the MP-RAGE images have two phase encoding directions instead of one (theoretically no geometrical distortion due to static field inhomogeneity occurs along a phase encoding direction), and because the MP- RAGE images have a higher readout gradient magnitude (4.7- versus mT/m; geometrical distortion due to static field inhomogeneity is inversely proportional to readout gradient strength). Also, the use of a calibration phantom in this study to correct for MR scale distortion probably yields more accurate results than the use of a stereotactic frame as an object of known shape and size in previous studies. The latter approach potentially suffers from nonlinear distortion in the image periphery where the stereotactic frame -bars are located [33]. We estimate the accuracy of the gold-standard registrations in this study to be approximately.5 mm (see Section IV-B for more detail). 2) Misregistration: In the previous study of the accuracy of retrospective registration algorithms mentioned in the introduction approximately 80% of the errors fell in the range from zero to one centimeter. Guided by that distribution we confined our study to misregistrations of approximately one centimeter

5 FITZPATRICK et al.: ACCURACY OF RETROSPECTIVE REGISTRATION OF MR AND CT IMAGES 575 or less. We sampled this range with 14 misregistering transformations. We chose transformations on the basis of two criteria: 1) They should produce registration errors well distributed over the range from zero to one centimeter, and 2) they should be representative of misregistrations that might be observed in this range for typical image registration algorithms. Each such transformation will cause a registration error (possibly zero) at each of the five target points for each of the patient images to which it is applied. To satisfy these criteria, we took in turn each patient in the study ( to ) and chose a set of transformations for that patient. The transformations were chosen randomly, but with the stipulation that the maximum error caused by transformation ( ) on patient be distributed approximately uniformly over the range [0 10 mm]. To satisfy our first criterion, we chose the with a compromise of uniformity and randomness as follows: We shifted a 1-mm window to each of 14 positions, evenly spaced over the range [0 10 mm]. After each shift we selected one sample from the window utilizing a uniform sampling probability. A desired error can be achieved at a given point by any of an infinite number of misregistering transformations. The simplest, for example, would be simple translations, but such simple transformations are not representative of the errors made by typical image registration algorithms. To satisfy our second criterion we selected representative transformations by consulting the set of CT-to-MR registration transformations ( ) submitted as part of the project mentioned in the introduction in which 16 image registration methods were evaluated [20]. For each, a difference transform was derived, as a representation of how much differed from the corresponding gold standard for its registration task, i.e., For each each of the was applied to the gold-standard registration for patient, giving For each one was chosen, and altered, as follows. For each the error in millimeters of the corresponding at each target point in patient was calculated, and the maximum error over all targets was tabulated. The whose maximum error was closest to was chosen as the best. Its rotational and translational components were then scaled using an iterative method until its maximum error was in close agreement with For each patient in the study this scaled, applied to the gold standard for that patient, formed registration transform G. Visual Assessment The airbrushed images and misregistration transformations were generated at Vanderbilt University, Nashville, TN, and distributed via the Internet to The United Medical and Dental Schools of Guy s and St. Thomas Hospitals (UMDS), where the visual assessments of registration accuracy were made using the inspection software described later. Two studies were performed. The first study was a preliminary one involving four observers and one patient. Two of the observers, termed experts, had several years of experience in carrying out image registration by picking corresponding landmarks and checking the accuracy of the solutions produced by automatic algorithms. The remaining two observers, termed nonexperts, were newly recruited graduate students whose only experience comprised a few months in medical image processing. All observers were well motivated and had previous experience with the software. The purpose of the preliminary study was to test our assessment protocols and to determine whether there was a difference between experts and nonexperts. The second study involved only the two experts from the first study but included more patients and incorporated geometrical corrections for MR scaling errors based on phantom imaging. In each study, the observers were informed of the imaging protocols and were informed that according to the gold standard the registration errors ranged approximately uniformly from zero to an upper limit of around 1 cm. They were blinded to the actual misregistrations, which were presented in a random order. The observers results were returned to Vanderbilt University by . 1) Direct Method: We employed three distinct methods for visual assessment, which we will call the direct method, the single-point correspondence method, and the multiple-point correspondence method, respectively. In the direct method of assessment the observer views an MR image and a CT image in a common coordinate frame. The images in this study were viewed using software written in /Motif running on a Unix workstation. This software loads two image volumes plus a transformation that relates the images. The user can display the images individually as reformatted triplanar sections. One image is transformed on the fly using the loaded transformation. The user can select between color overlay, the overlay of a thresholded boundary from one image on the other, or the adjacent display of the two images with linked cursor. An example of the display is shown in Fig. 2. The user can manipulate the grey-level windows and the magnification of the images. A millimeter scale is marked on the display and is visible at all times. A cursor can be moved between the millimeter scale and features in the image to help quantify errors. As can be seen in this figure a cross-hair is placed by the software at the 3-D point in the MR image at which the assessment is to be made. This cross-hair is visible simultaneously in axial, sagittal and coronal sections. For each target point within each data set the observer is presented each of the 14 misregistered CT volumes in turn and, for each, answers the question What is the 3-D registration error (in millimeters) in the vicinity of the cross-hair? The observer s answer is tabulated and communicated to Vanderbilt for comparison with the estimated error based on the gold standard. 2) Single-Point Correspondence Method: In the singlepoint correspondence method the observer merely identifies, for each target point in the MR image, the corresponding 3-D point in CT. An example of the display used for this method is

6 576 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 17, NO. 4, AUGUST 1998 that brought them into optimal alignment in the LS sense, employing the same method as that described for the goldstandard system. By using the resulting registered position for each point in place of, and then proceeding as for the point method, we were able to effect a third visual assessment method based on the same point data. In what follows we refer to this method as the multiple-point method. Because the gold standard is imperfect, the true position in the CT image corresponding to the point in the MR image will differ from the gold-standard estimate and it will be some unknown distance from The true misregistration error, also unknown, is labeled in Fig. 4. Because the is not known for a selected point, neither nor are known. However it is possible to account for the effects of this error statistically as explained in Section IV-B. Fig. 2. A screen dump from the software used for the direct assessment of the registration accuracy in the vicinity of the right orbit. The upper left quadrant shows the acquired coronal plane, and the upper right and lower left quadrants are reformatted images in the sagittal and axial plane, respectively. The edge of the bone thresholded from the CT scan is shown overlaid on the MR image. This figure is reproduced in black and white, but in use, the overlay is in green. To assist the observer at quantifying the registration error, tick marks are displayed at 10-mm intervals, and a cursor of 5-mm diameter (not shown) can be moved around all three planes. shown in Fig. 3. Again a cross-hair indicates the target point in the MR scan. The observer indicates the corresponding CT point by means of a mouse click. In this method the coordinates of that point are communicated to Vanderbilt instead of an error assessment. In contrast to the direct method, which requires that each CT volume be subjected to each of the 14 transformations before it is viewed, the point requires no such transformations. The assessment of error is performed indirectly as illustrated in Fig. 4. In that figure the point represents the selected target point at which visual assessment is to be performed, and represents the point in CT that corresponds to according to the gold-standard transformation, which is indicated by. A misregistering transformation maps into, and represents the misregistration error according to the gold standard. The point is the point identified by the observer via the mouse click in CT as corresponding to in MR. It is that point whose coordinates are tabulated during the single-point correspondence method and communicated to Vanderbilt. That point is then compared with for each of the 14 misregistering transformations. The assessed error for this method is the distance between and In what follows we refer to this method as the single-point method. 3) Multiple-Point Correspondence Method: Because the observers in this study were asked to find corresponding CT positions for more than two points, it was possible to perform a registration based on these visually localized points. We used all five point pairs to determine the rigid-body transformation III. RESULTS In our preliminary study we recorded direct assessments of error on one pair of image volumes by the two expert observers and the two nonexperts at each of five anatomical locations for 14 misregistering transformations. These 280 assessments were paired with the corresponding gold-standard measurements and used to determine whether there was a difference between experts and nonexperts. In our second study we recorded direct assessments of error on five pairs of image volumes by the two expert observers at each of five anatomical locations for 14 misregistering transformations for a total of 700 direct assessments. We also recorded point localizations on the same five pairs of image volumes by the same two expert observers at the same anatomical locations for a total of 50 point localizations. Observer 1 required an average of approximately 30 s/point/transformation/patient, and observer 2, an average of 1 min/point/transformation/patient. Fig. 6 shows representative scatter plots of visual assessment versus the standard for observer 1(a) and (c) and observer 2(b) and (d) (all on the same patient). The direct assessment method was used for each plot. Each plot includes all five anatomical target points and all 14 misregistrations for a total of 70 points. (The meaning of the adjusted gold standard and the purpose of the dashed lines are explained in Section IV-B.) IV. TOOLS FOR STATISTICAL ANALYSIS We analyze our results by means of several statistical tools. Our goal with each statistic is to measure the quality of the visual assessment relative to our standard measure of misregistration error. We consider six different levels of misregistration as measured by the standard: 1 mm, 2 mm, 6 mm. We dichotomize the standard by treating these levels as a threshold and recording for each assessment instance whether or not the misregistration error is greater than An assessment instance is a single assessment of misregistration error by a particular observer using a particular assessment method of the error at a particular target point in a particular patient caused by a particular misregistering transformation. We also dichotomize the visual assessment by recording whether or not the visual assessment of misregistration is above some

7 FITZPATRICK et al.: ACCURACY OF RETROSPECTIVE REGISTRATION OF MR AND CT IMAGES 577 Fig. 3. A screen dump showing the software used for the assessment of registration error using the point correspondence method. Two versions of the same program are used, with the MR (left) and CT (right) loaded, respectively. Both versions of the software show coronal (top left), sagittal (top right) and axial (bottom left) views reformatted around a previously identified 3-D point of interest (in this case, the right cochlea). Since the MR was acquired coronally and the CT axially, the CT has been reformatted using a 90 rotation to make the orientation of corresponding quadrants similar. The observer was asked to mark the same point in the CT scan as is indicated by the cross-hair in the MR scan, and had to mentally compensate for any difference in slice orientation between modalities. The three cross-hairs in the three image planes identify the selected point in three dimensions. TABLE II CONTINGENCY TABLE FOR VISUAL ASSESSMENT OF MISREGISTRATION ERROR VERSUS A STANDARD. THE SYMBOL > INDICATES A FINDING THAT THE ERROR IS ABOVE THE THRESHOLD, WHICH IS A POSITIVE FINDING; INDICATES THAT THE ERROR IS NOT ABOVE THE THRESHOLD, WHICH ISA NEGATIVE FINDING Fig. 4. Depiction of registration errors at a target point TS selected in MR. The dashed lines represent the gold standard transformation G (based on the Acustar fiducial markers) and a misregistration M that is to be assessed. The point T represents the (unknown) point in CT that truly corresponds to TS :TM is the point to which TS is mapped by M: The points TG and TV represent the gold standard estimate of T and the visual estimate of T: The distances d; dg, and dv, represent the true misregistration error for TS, the gold standard estimate of d, and the visual estimate of d: threshold, not necessarily equal to The statistics can be most easily understood in terms of a contingency table as shown in Table II [34]: First, we select a visual assessment method and then, for that method, we identify a set of instances. might comprise, for example, one given patient, one given observer, and all target points, or all patients, both observers, and one given target point. We then partition into four subsets according to whether the misregistration error measured by the standard is above a given threshold and/or the visually assessed error is above a (possibly different) given threshold In the table the symbol indicates a finding that the misregistration is above a threshold, which is a positive finding, the symbol indicates a finding that the misregistration is at or below the threshold, which is a negative finding, is the number of true positives (TP), is the number of false positives (FP), is the number of false negatives (FN), and is the number of true negatives (TN). We will refer to this table and these quantities repeatedly in our analysis. A. Preliminary Study We begin by examining the results of our preliminary study on the direct method by two experts and two nonexperts. We first calculated the Kappa statistic where and are from Table II with Kappa is a descriptive statistic indicating the degree of beyondchance agreement between two ratings per subject based on the dichotomous response [35]. The value of ranges from zero, which means that there is only chance agreement between

8 578 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 17, NO. 4, AUGUST 1998 visual assessment and the standard, to one, which means that there is perfect agreement. Values below 0.40 are considered to represent poor agreement; values between 0.40 and 0.75 to represent fair to good agreement, and values greater than 0.75 to represent excellent agreement [36]. We found that all values were low, ranging from 0.12, which indicates only chance agreement, to a maximum of 0.46, and there were only slight differences between values for experts and nonexperts. Thus, on the basis of the results of the preliminary study were poor to fair with the nonexperts performing similarly to the experts. (All statistical analysis was performed using the SAS 6.12 statistical program, including the SAS IML macro. All tests of significance in this study are two-sided, and differences are considered statistically significant only for We next applied McNemar s test to check for the possibility of bias [37]. For this test we also set A value of then indicates a bias toward overestimation or underestimation of registration error by visual assessment. The value was greater than 0.5 for both experts and nonexperts for all thresholds except for the experts at 3 mm. We can reject the hypothesis of zero bias for the nonexperts for 2-, 3-, 4-, and 5-mm misregistration levels while we can reject the hypothesis for the experts at only the 1 mm level. Thus, on the basis of McNemar s test, the nonexperts were significantly biased much more often than the experts. B. Adjusting the Gold Standard While our gold standard is quite accurate, it is not perfect. As pointed out at the end of the Materials and Methods section, the imperfection causes the error depicted in Fig. 4. While which we refer to as the target registration error (TRE), cannot be known for a given pair of image volumes, expected values can be calculated. It has recently been shown that the root-mean-square (rms) value of TRE can be calculated if the rms of the fiducial localization error (FLE), which is the error in localizing a single fiducial, is known [31], [32]. rms[fle] can in turn be estimated from rms[fre] (see Section II-F.1). The formulas are given in the appendix to this paper. The rms[fre] for all patients in this study is 0.40 mm. Using this value to calculate the rms[tre] for each patient and each target position, we find that rms[tre] is 0.50 mm. Thus, for this study our standard provides a registration accuracy of approximately one-half millimeter. The direction of the displacement between and is determined entirely by the markers, while the direction of the displacement between and is determined by our selection of misregistering transformations from a previous study of retrospective registration methods. Thus, it is possible to calculate for each target in each patient s image a mean and standard deviation for a given by assuming that these two displacements are uncorrelated. The mathematical treatment is provided in the appendix. Fig. 5 depicts the relationships among and The curving solid line is a plot of versus the gold-standard estimate the straight line is shown for comparison. The dotted lines show Because rms[tre] varies with patient and Fig. 5. True misregistration error d as a function of the misregistration error dg calculated assuming that the gold standard is perfect. The 45 line represents dg, the curved solid line represents d, and the dotted lines represent d6d : The quantities d and d were calculated using (8) and (11) in the Appendix and using = 0:29 mm, which corresponds to rms[tre] = 0:50 mm, the rms value observed in this study. target, the plot will vary as well. The plot shown in Fig. 5 is based on rms[tre] mm, the rms value observed in this study. It can be seen from this plot that the gold standard is expected to underestimate the true misregistration error. This bias is small for values of above 0.5 mm, but for misregistrations that are very close to one of the thresholds, it can affect our evaluations of visual assessment. In about 5% of the target misregistrations in the study the difference is enough to move the standard estimate across one of the six thresholds. Because the bias is always in the same direction, every change adds to and subtracts from in the contingency table (Table II). Thus we base all our statistics in what follows on comparisons of visually assessed errors with instead of We call the adjusted gold standard. We ignore the effect of the variance of the standard until Section V. The effect of adjusting the gold standard is not large, but it can be seen by comparing Fig. 6(a) with Fig. 6(c) and Fig. 6(b) with Fig. 6(d). In these plots visual assessment by the direct method for a given observer is compared with the gold standard without and with adjustment. At the lower left of these plots it can be seen that six of the points have been shifted appreciably to the right by the adjustment. Elsewhere, the shift is too small to be seen in these plots. C. ROC Curves An ROC analysis can be performed for a given set of instances and for a given gold-standard threshold This analysis examines the relationship between the TP and FP rates (defined later) of visual assessment for a given standard threshold To perform the analysis it is necessary to generate multiple tables of the form of Table II for a given standard threshold. In generating these tables we fix the standard threshold (using the adjusted gold standard) and generate

9 FITZPATRICK et al.: ACCURACY OF RETROSPECTIVE REGISTRATION OF MR AND CT IMAGES 579 (a) (b) (c) (d) Fig. 6. Sample scatter plots of visual assessment versus the standard. All plots are for the direct assessment method. In the top row error assessments are plotted versus the (unadjusted) gold standard, dg : (a) is observer 1; (b) is observer 2. In the bottom row error assessments are plotted versus the adjusted gold standard, d : (c) is observer 1; (d) is observer 2. An appreciable shift to the right, d 0 dg can be seen between (a) and (c) and between (b) and (d) for five or six points in the range below dg =0:5mm. The vertical dashed lines show example thresholds for the standard. The horizontal dashed lines show example thresholds for visual assessment. one table for each of multiple values of visual assessment threshold one for each observed value of. The dashed lines in Fig. 6 illustrate the generation of one such table for each of two standard thresholds, mm and mm. In Fig. 6(c), the standard threshold has been set to 2 mm, as indicated by the vertical dashed line; the visual assessment threshold has been set to pass through a point whose visual assessment error mm, as indicated by the horizontal dashed line. Fig. 6(d) illustrates the situation for the table for which mm and mm. Once a pair of thresholds, and have been chosen, Table II is formed by setting and equal to the number of points in the upper right, upper left, lower right, and lower left quadrants, respectively, as delimited by the dashed lines (points on the line being credited to the lower category). The plot of the quantities or TP rate, versus or FP rate, from the set of tables generated for a given, fixed standard provides the ROC curve for that Fig. 7 shows examples of ROC curves. In this figure, direct assessment was used and the threshold is set to 2 mm. The set consists of 70 misregistered target points (five targets points in each of 14 misregistrations) for one patient. There are many measures for the quality of an ROC curve [38], but the most common is the area under the curve, which ranges from zero to one, with larger numbers generally indicating higher overall quality. We calculated ROC areas for each of the three visual assessment methods at six different thresholds For each method/threshold pair, ten areas were calculated, one for each of the two observers and five patients. The results are listed in Table III.

10 580 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 17, NO. 4, AUGUST 1998 TABLE IV INTEROBSERVER KAPPA STATISTICS FOR EACH OF THE THREE VISUAL ASSESSMENT METHODS AND EACH OF THE SIX THRESHOLDS BASED ON DATA FROM ALL FIVE PATIENTS, ALL FIVE TARGET POINTS, AND ALL 14 MISREGISTRATIONS. THE NUMBERS IN PARENTHESES ARE THE 95% CONFIDENCE INTERVALS TABLE V KAPPA STATISTICS FOR VISUAL ASSESSMENT VERSUS THE ADJUSTED GOLD STANDARD FOR EACH OF THE THREE VISUAL ASSESSMENT METHODS AND EACH OF THE SIX THRESHOLDS BASED ON DATA FROM BOTH OBSERVERS, ALL FIVE PATIENTS, ALL FIVE TARGET POINTS, AND ALL 14 MISREGISTRATIONS. THE NUMBERS IN PARENTHESES ARE THE 95% CONFIDENCE INTERVALS Fig. 7. ROC curve for the direct assessment method using an adjusted gold standard threshold of 2 mm. The set of instances includes all five target points for one patient. The solid line represents the results for both observers pooled together and the dotted and dashed lines represent the observers 1 and 2, respectively. TABLE III ROC AREAS FOR EACH OF THE THREE VISUAL ASSESSMENT METHODS AND FOR EACH OF THE SIX THRESHOLDS. EACH ROC CURVE IS BASED ON ALL FIVE TARGET POINTS AND ALL 14 MISREGISTRATIONS. FOR EACH METHOD/THRESHOLD PAIR, TEN AREAS WERE CALCULATED, ONE FOR EACH OF THE TWO OBSERVERS AND FIVE PATIENTS. EACH ENTRY IN THIS TABLE IS THE MEAN OF THESE TEN AREAS, PLUS THE RANGE [MINIMUM, MAXIMUM] IN BRACKETS TABLE VI AGREEMENT RATES FOR THE THREE VISUAL ASSESSMENT METHODS RELATIVE TO THE ADJUSTED GOLD STANDARD AT EACH OF THE SIX THRESHOLDS BASED ON DATA FROM BOTH OBSERVERS, ALL FIVE PATIENTS, ALL FIVE TARGET POINTS, AND ALL 14 MISREGISTRATIONS. AGREEMENT MEANS THAT BOTH VISUAL ASSESSMENT AND THE STANDARD AGREE ON WHETHER THE MISREGISTRATION IS ABOVE THE THRESHOLD D. Kappa Statistics and Agreement Rates for the Main Study Our primary tools for measuring the quality of of visual assessment in this study are the agreement rate,, which is the fraction of instances for which two raters agree on whether or not the misregistration value exceeds a common threshold, and the Kappa statistic, which measures the degree to which the agreement between raters is beyond chance. We first calculated Kappa values for one observer relative to the other when both used the same assessment method. For each method, included 14 misregistrations, five patients, and five target points for a total of 350 instances per method. For each method we constructed six tables of the form of Table II with mm, mm, mm, but with Visual Assessment representing the assessment of observer 1 and Standard being replaced by the assessment of observer 2. Thus there were 18 tables with one agreement rate calculated from each table. These inter-observer Kappa values are shown in Table IV. Next we calculated Kappa values for each assessment method relative to the adjusted gold standard by pooling the data from the two observers. Thus, in this case, there were a total of 700 instances per method per threshold. Again, we constructed six tables for each method, but this time the tables are as labeled in Table II. These Kappa values and their 95% confidence intervals are shown in Table V. Finally, using these same tables, we calculated the agreement rates between each method and the adjusted gold standard at each threshold. The agreement rates are given in Table VI. To determine whether differences in agreement rates between methods were significant, we used the generalized estimating equation (GEE) statistical procedure for longitudinal data analysis with multiple observable vectors for the same subject [39], [40]. This procedure is a repeated-measures analysis for correlated dichotomous outcomes and a set of predictors, i.e., a multiple logistic regression in which the outcomes are correlated. In this analysis an outcome is agreement or disagreement. There are three predictors : the assessment method, the observer who is applying the method, and the location of the target point at which the method is applied. The measures are repeated in the sense that more than one outcome is observed on a given patient. Because of this repetition the outcomes must be treated as correlated. Since there are 700 instances of assessment for each of three

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