An image registration scheme applied to verification ... - BIR Publications

T he British Journal of Radiology, 71 (1998), 413–426

© 1998 The British Institute of Radiology

An image registration scheme applied to verification of radiation therapy 1,2,3K W LESZCZYNSKI, PhD, FCCPM, 1,2S LOOSE, BSc and 1S BOYKO, BA, AC(T) 1Department of Medical Physics, Northeastern Ontario Regional Cancer Centre, 41 Ramsey Lake Road, Sudbury, P3E 5J1, 2Department of Physics, Laurentian University, Sudbury, and 3Department of Radiology, University of Ottawa, Ottawa, Canada Abstract. The introduction of modern conformal radiation therapy techniques requires high geometric precision in treatment delivery which must be verified. For that purpose we have developed an automated system based on registration of portal and simulation (or planning) image pairs. The image registration is performed on anatomical features which are automatically extracted from the portal image. The portal image is then registered with a planning or simulation radiographic image which represents the geometric prescription for the treatment, using an optimized version of the chamfer matching algorithm. Subsequently, the magnitude of the radiation field displacement during treatment is measured by registering the prescribed and treated field boundaries. Algorithms based on chamfer matching and polygon matching have been used for the field boundary registration. Performance of the entire scheme was evaluated on a series of 15 portal images of a pelvic phantom representing various known degrees of the radiation field displacement. The measurements of the radiation field displacements performed by the automated system proved very reliable and after correction for systematic bias agreed to within 1.5 mm or 1° with the displacements applied. Second test series involved comparisons between the automated registrations and those performed manually/visually by an experienced human observer, on 31 portal images acquired during treatments of 18 pelvic patients. These tests showed close agreement (in 80% of cases discrepancies were smaller than 1.5 mm or 1.5°) between the automated scheme and the human observer. It is concluded that the developed scheme would be suitable for online geometric verification of radiation therapy treatments.

Image registration, sometimes referred to as image matching, involves determining the geometrical correspondence between multiple images of the same object [1]. It involves finding the geometrical transformation from the coordinate system of one image to the coordinate system of another image, such that after the transformation reference features from one image are aligned with their correspondents in the other image. An important application of image registration in the field of therapeutic radiology is verification of geometric accuracy of radiation therapy treatments. The work presented here is focused on this latter application; however, the methods developed for this study are general enough to be suitable for other applications of image registration. The principal objective of radiation therapy is to cure a neoplastic disease by applying a sterilizing dose of radiation to the malignant lesion. In doing so, particular attention must be paid to sparing normal tissues surrounding the tumour as much as possible, to minimize morbidity of the treatment. This imposes stringent requirements for the Received 23 June 1997 and in revised form 27 November 1997, accepted 5 December 1997. T he British Journal of Radiology, April 1998

geometric accuracy and reproducibility with which the therapeutic radiation fields are placed over the diseased anatomical region in consecutive treatment fractions. It has been shown that geometric errors in the radiation field placement (field placement errors, or FPEs) may lead to local tumour recurrences as a result of inadvertent underdosage [2, 3]. On the other hand, improved geometric precision of the radiation field placement would allow us to reduce the size of the safety margin applied around the tumour volume while prescribing radiation fields. In this way the volume of irradiated normal tissues would also be reduced. Consequently, the tumour dose could be escalated to higher values which would increase the probability of local tumour control and patient cure [4]. Crucial to these potential improvements is the verification of the geometric accuracy of radiation field placement. Most directly, the position of the treatment beam with respect to a patient’s anatomy can be verified by acquiring portal radiographs with an image receptor placed on the exit side of the beam. Portal images can be acquired online during radiation therapy treatments, using one of the digital portal image detectors that have been developed over the 413

K W L eszczynski, S L oose and S Boyko

past decade [5–8]. Currently, routine verification of patient–radiation beam set-ups is done primarily by visual analysis of online portal images. During this analysis the position of the radiation beam with respect to the patient’s anatomy, as shown in the portal image, is compared with the prescribed position as delineated in the corresponding treatment planning image. Most commonly the prescription image used as a reference in portal verification is produced during radiation therapy planning or simulation, using a diagnostic quality X-ray beam. The complexity of the task and the often stringent time limits render the visual analysis of portal images imprecise and mainly qualitative rather quantitative, as well as relatively inconsistent between different human observers [9]. This indicates that to improve the geometric accuracy of treatments using online electronic portal imaging, the comparative analysis of treatment planning and portal images has to be performed in a quantitative manner on a computer using techniques from the field of machine vision. Through registration of a portal image obtained during the treatment with the reference prescription radiograph, the prescribed and the actual radiation fields as well as the patient’s anatomical features are brought into a common reference frame. Any discrepancies between the prescribed and the actual radiation field positions can be quantified. In view of the time constraints, all the stages of the computerized portal verification scheme that are performed during a treatment, immediately following the acquisition of a portal image, should be fully automated, so that the human operator would play only a supervisory role. From a few previous attempts made by other investigators in the direction outlined above, the system proposed by Gilhuijs et al [10, 11] appears to be the most advanced and the closest to fulfill the objective of automated online treatment verification. The same authors also proposed a scheme for the measurement of radiation therapy field placement errors in three dimensions [12]. The method is based on matching bone ridges between planar radiograph pairs and volumetric computed tomography data. The stated advantage of this approach is that it is capable of measuring rotational errors occurring outside of the image plane. However, the magnitude of these so-called ‘‘out-of-plane’’ rotations is typically insignificant [13]. The three-dimensional (3D) verification requires considerably more data (portal image pairs instead of single images and CT volumes instead of single planar simulation radiographs), computation and human supervision/interaction than two-dimensional (2D) portal verification techniques in general. Therefore the measurement of field placement errors in 2D techniques can be considered not only adequate but also preferable 414

for online applications. In the following sections we will describe an alternative approach to automated 2D portal verification and present a quantitative assessment of its performance.

Materials and methods The building blocks and the information flow of the proposed computerized portal verification system are shown in Figure 1. We shall now describe in detail the constituent elements.

Input image data The optimization and testing of the techniques used in this study were carried out on a dataset of anteroposterior (AP) images of the pelvic region. Both real patient as well as anthropomorphic pelvic phantom images were employed. Simulation images were used as the reference that determines the intended size, shape and placement of the radiation field prescribed for treatment. Digital simulation images were obtained either by digitization of film radiographs (patient images) or by using a prototype digital imaging system capable of constructing a composite large field of view from multiple smaller fluoroscopic views (phantom images). The digital fluoroscopic images were corrected for the spatial distortion introduced by the image intensifier. The maximum residual error due to the distortion was of the order of 1 mm. Digital simulation images obtained either with film or with the fluoroscopic detector consisted of 512×480 eight-bit pixels. The pixel size for each simulation image was determined from the size of the shadow cast by a radioopaque reticule which is normally present during simulation to provide a reference scale for the images. Corresponding portal images were acquired during irradiations with a 23 MV X-ray beam on a linear accelerator (Mevatron KD-2) fitted with a BEAMVIEWPlus@ ( both Siemens Medical Systems–Oncology Care Systems Inc., Concord, CA) digital fluoroscopic portal imaging system. The portal image matrix also consisted of 512×480 eight-bit pixels. The pixel size for portal images was calibrated once and remained constant as the position of the image detector relative to the X-ray source was fixed.

Extraction of anatomical features and radiation field edges f rom images Fiducial anatomical features from the reference simulation images were manually entered into the computer by an experienced operator using a mouse and graphics software tools. There are two basic conditions that determine the choice of anatomical features. The first one is that the features T he British Journal of Radiology, April 1998

An image registration scheme for portal verification

Figure 1. The elementary building blocks and the flow of images and image-derived information in the computerized portal verification scheme.

must be relatively stable with respect to the intended treatment volume, and the second one is that the features should produce enough contrast in portal images so that they can be automatically detected. The edges produced by immobile large bones satisfy both of the above conditions and are selected as the reference anatomical features whenever possible. In particular, for the AP view of the pelvis the edges of the symphysis pubis, rim of the acetabulum, iliac crest and lumbar verterbra were chosen. The outlines of the prescribed radiation fields were also entered into the computer manually, via the mouse driven software tool. Entry of the reference anatomy and field data from simulation images is performed only once for an entire multifraction treatment course. It can be done well in advance of the first treatment, hence automation of this process was not considered and was outside the scope of the present work. Unlike the simulation images, anatomical features and radiation field edges have to be extracted from portal images during daily treatments which imposes stringent time constraints and calls for full automation of the process. In the paragraphs below the algorithms used for this purpose will be introduced. Automated extraction of radiation field edges f rom portal images Automated extraction of radiation field edges from portal images constitutes the first stage in their processing. The extracted field boundary can be used for fast verification of the field’s size and shape [14] and it also defines the region of interest for the search of anatomical features. Among previous investigators Gilhuijs and van Herk [10] adopted a two stage approach where the potential field edge pixels are first found by histogram thresholding of the original portal image. Subsequently, the field contour is refined using T he British Journal of Radiology, April 1998

edge strength and direction information obtained with the conventional Sobel gradient operator [15]. Since the Sobel operator tends to be overly sensitive to noise and its response to the somewhat slowly sloping (due to the radiographic penumbra) field edges is reduced, a different approach to the radiation field edge detection would generally be preferable. In the present work we have used the field edge extraction methods that were introduced in a previous paper [16]. Here we shall only briefly outline the three major components. The first one is used to extract the information on the field edge strength and direction from the original portal image. For this purpose we employed the derivative of gaussian (DoG) operator. This had been shown by Canny [17] to be nearly optimal for detection of step-like edges in images corrupted by noise. The response to the field edges increases relative to the response to anatomical edges and noise as the width parameter of the DoG operator, s, increases [16]. A wider DoG operator produces broader maxima in the response to the field edges which negatively affects field edge localization. We have selected the width parameter of the DoG operator to be equal to 3 pixel units (~1.5 mm at the isocentre) which provided a good compromise between these two opposing trends. The second element of the field edge extraction scheme is edge following. The location of the strongest response of the DoG operator, found over a number of horizontal and vertical scan lines, serves as the starting point of the field boundary. From the starting position, consecutive boundary points are found by following the highest response of the DoG operator. This next boundary point is selected from all neighbours of the current boundary point that lie along the current direction of the field edge. As a result, the boundary is found as a chain of connected pixels. To reduce the storage requirements and to facilitate further analysis and 415


manipulation of the boundary, at the third stage of field edge extraction the pixel chain is converted (segmented) into a polygon represented by an ordered set of polygon vertices.

were carried out only within the region enclosed by the previously found field edges. This reduced the amount of computation and eliminated the potential problem of interference between the field and anatomical edges. A different approach to the detection of anatomical features in portal images has been employed by Gilhuijs et al [11], who concentrated on detection of anatomical ridges rather than edges. They used two different ridge enhancing operators, namely a variation of the top-hat filter [18] and the Laplacian of the Gaussian [19]. Both of these operators were followed by thresholding to isolate the strongest ridge pixels. Additional processing was required to remove the interfering field edge pixels from the extracted collection of ridge pixels.

Automated extraction of anatomical edges f rom portal images As it can be seen in Figure 2a, the anatomical features of interest in the AP pelvic images also form step-like edges in image brightness. Therefore, we also chose to use the DoG operator for the extraction of anatomical edges. This time, however, its width was optimized to the scale characteristics of the anatomical edges. The optimization was carried out by varying the width of the DoG and recording the strength of its response to the desired anatomical edges relative to other (anatomical and spurious noise) edges. An illustration of such optimization is shown in Figure 2b which contains profiles of the DoG response at different s (the width parameter) values. Overall, the relative response of the DoG edge detector to the anatomical features of interest was the highest at s#1.5 pixel units. If the DoG operator were to be used for edge detection in images of other anatomical sites its s would have to be re-optimized. As in the case of the field edges, continuous and easy to handle anatomical contours were obtained by applying boundary following and segmentation. The DoG operator and the boundary following

To be able to compare the position of the radiation field relative to the patient’s anatomy in the prescription and portal images, the anatomical features and the field boundaries extracted from both images must be registered. One has a choice of using either the anatomical or the field edges as the reference marks to establish the geometrical transformation between the two images. This choice is sometimes affected by the practicality of performing corrections of the field placement errors that were detected during portal verification. To

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Registration of simulation and portal images

Figure 2. (a) A sample profile of edges produced by the iliac crest in portal images of the pelvis. The responses to this edge by the derivative of gaussian and Sobel operators are also shown. ( b) Profiles of the response of the DoG operator to anatomical edges in the pelvic region for different values of the width parameter, s. 416

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perform these corrections efficiently, using the digitally controlled couch and/or collimator motions of a radiation treatment unit, the FPEs have to be expressed in the coordinate system of the treatment machine. Therefore some researchers [10] use the field boundaries for the purpose of portal image registration, as well as the reference to the machine coordinate system. This way they are able to determine the position of the patient with respect to the coordinate system of the radiation treatment unit, even if the position of the portal image detector with respect to the unit is not known independently. However, such an approach relies on the assumption of a perfect reproduction of the prescribed field in treatment. In general, this assumption is unwarranted, as the field size, shape and orientation are subject to set-up errors and equipment calibration inaccuracies. Furthermore, most of the commercially available portal imagers are nowadays rigidly attached to the gantry of the treatment unit and the coordinate system of the portal image can be directly related to the machine coordinate system to allow for an efficient FPE correction. Therefore, it is more appropriate to use the anatomical landmarks as the reference in registration of simulation and portal images. This approach was employed in the present work. Stringent time limitations for online radiotherapy treatment verification demand that a fully automated method is used for portal image registration. Therefore, methods based on matching of paired points [20], curves [21] or subregions [22] are not entirely suitable for the task, as they require human operator intervention to define at least the correspondence between features in the two images which are to be registered. On the other hand chamfer matching automatically establishes the correspondence between sets of linear features from the two images, and has been shown [23] to be a very effective and robust algorithm in registering images as diverse in quality and appearance as aerial photographs and cartographic maps. Chamfer matching has been employed by Gilhuijs and van Herk [10] and Fritsch et al [24] and was selected as the general method of automated registration of portal images for the present study. Detailed descriptions of the chamfer matching algorithm can be found elsewhere [25]. Here, we shall only briefly present its basic elements. From the two sets of linear features to be registered, one of them, selected to be the reference, is converted to a so-called ‘‘distance image’’. In the distance image the distances of each pixel to the nearest feature point are in encoded pixel grey scale values. The example of a set of anatomical features from a pelvic simulation radiograph and their corresponding distance image is shown in Figure 3. Borgefors [25] showed that the overall performance of chamfer matching is better when the T he British Journal of Radiology, April 1998

distance image closely approximates the Euclidean distances. However, since generation of a truly Euclidean distance image would be computationally very expensive, in practice, approximate distance images are obtained by iterative propagation of local ‘‘chamfer’’ distances. For computational effectiveness local distances between neighbouring pixels are expressed as small (3×3 or 5×5) kernels of integer numbers. Gilhuijs and van Herk [10] recommended using a distance transformation based on a 3×3 neighbourhood distance matrix. However, Borgefors [25] showed that such an eight-neighbour distance introduces artefacts to the approximation of the Euclidean distance that are 20 times greater than those associated with the so-called ‘‘5–7–11’’ 5×5 chamfer distance. These artefacts were also shown to affect negatively the performance of chamfer matching. Therefore, in the present study the distance image for chamfer matching was computed by propagating the ‘‘5–7–11’’ local neighbourhood distance kernel, defined as follows: 14

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The values of the elements of this kernel represent the distances from the central position to all the other pixels within the 5×5 square neighbourhood surrounding the central pixel. In this formulation the distance corresponding to one pixel width has a numerical value of 5. In chamfer matching the distance image is used to derive an overall measure of distance between two sets of linear features. This is done by overlaying the features to be matched over the reference distance image and finding the distances of each feature point to the nearest reference feature by simply reading the underlying pixel value of the distance image. The individual feature-to-feature distances can be combined into an overall distance indicator in a variety of ways. Borgefors [25] showed that the root-mean-square and the arithmetic mean distances are the most suitable measures of distance between two sets of features in terms of their robustness and consistency with the human perception of goodness of match. Throughout this study we have used both the arithmetic mean distance (AMD) and the root-mean-square distance (RMSD) measures, defined as follows: 1 ∑ d i N Pi µF 1 RMSD= ∑ d2 i N Pi µF AMD=

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Figure 3. Anatomical features outlined in the AP digital fluoroscopic image of the humanoid pelvic phantom (a) and the corresponding distance image (b). Distance from the nearest feature is encoded in pixel grey scale—the shorter the distance the brighter the pixel. The anatomical features from which the distance image was generated are superimposed as black lines.

where d is the distance of the ith point, P , in i i the feature-to-be-matched set, F, to the nearest reference feature, and N is the number of points in F that are utilized in the matching. The essence of the image registration by chamfer matching lies in determining the optimum geometric transformation between the portal and prescription image coordinate systems, such that the measure of distance between the two sets of features is minimized. Geometric transformations employed in the registration comprise global rotation and translation in two dimensions. Unlike Gilhuijs and van Herk [10] we exclude the relative magnification between the portal and the reference images from the transformation, as it can be derived from the pixel sizes that are known. Thus the registration process is reduced to minimization of the distance measure, AMD(t ,t ,a) or RMSD(t ,t ,a), with x y x y respect to the translation in X- and Y -, (t ,t ), and x y the rotation angle, a, between the portal and reference image coordinate systems. From the variety of optimization methods that do not require derivatives of the optimized function to have an analytical form, we selected Powell’s conjugate direction algorithm [26] for our application. It offers quadratic rate of convergence to a minimum and is practically always faster than alternative methods such as the simplex optimization [26] employed by Gilhuijs et al [10, 11].

Estimation of field placement errors After the anatomy based registration, the treatment field boundary can be transformed into a common reference frame, defined by the anatomical features, with the prescribed field boundary. 418

Then the final step in the computerized portal verification scheme becomes the estimation of translational and rotational errors in the position of the treatment field as well as detection of possible field size and shape mismatches. Chamfer matching has been used for the purpose of aligning the prescribed and treated field boundaries [10, 27]. The amount of translation and rotation that needs to be applied to the treatment field boundary to achieve the optimum chamfer match determines the field placement errors. It was shown by Borgefors [25] that the root-meansquare (RMS) measure of distance works best in chamfer matching of polygonal objects. Since radiation fields used in radiotherapy can be represented by polygons, the RMS distance optimization was used in this study while applying chamfer matching to the prescribed and treated field boundaries. In our recent work [28] we have shown that an alternative algorithm based on polygon matching offers certain advantages over the chamfer matching. The advantages are the clinically more desirable optimization of coverage of the prescribed treatment volume (rather than matching of just the boundary points), and also a potentially smaller computational burden. In brief, the polygon matching approach involves iterative optimization of the goodness-ofmatch measure called the compliance. The compliance is derived from the area of the intersection between the two polygons corresponding to the prescription and treatment fields, and achieves its maximum value of 1 when the two polygons perfectly match and overlap. The polygon intersection is found using an efficient algorithm specially developed for that purpose. The compliance is T he British Journal of Radiology, April 1998


optimized, using Powell’s algorithm, with respect to the translation and rotation in the plane that are applied to the polygon representing the treated field. Optimum translation and rotation define the adjustments in the position of the treated field, relative to the patient’s anatomy, which are necessary to bring the treated field into the best possible agreement with the prescription. Both chamfer (the RMSD variant) and polygon matching were used in the present study for registration of radiation fields.

T esting of the portal image registration scheme A few different approaches to evaluation of portal image registration methods have been presented previously. Gilhuijs and van Herk [10] performed tests with registration of artificially generated field boundaries and anatomical registration of portal images which were transformed to simulate displacements of known magnitude. In a later study, Gilhuijs et al [11] evaluated the performance of the automated portal image registration in reference to that of a human observer by comparing variabilities in repeated registration attempts applied to a set of clinical portal images. In the present study we have attempted to evaluate the reliability and accuracy of the entire proposed portal registration scheme under conditions as close as possible to clinical reality. To this end we constructed and applied two kinds of tests. In the first test series results of the automated portal verification scheme were compared with known rotational and translational FPEs that were deliberately introduced to ‘‘treatments’’ of an anthropomorphic pelvic phantom (Radiology Support Devices, Inc., Long Beach, CA). In these tests a 20×20 cm2 AP radiation field was employed. During pre-treatment simulation a digital fluoroscopic radiograph was acquired on which the prescribed field and the appropriate anatomical landmarks were interactively entered, as it can be seen in Figure 3a. According to the standard practice, the entry point of the central ray of the radiation beam and the corners of the field boundary were marked on the surface of the phantom to serve as external reference marks for future treatment set-ups. Subsequently, the phantom was transferred to a radiation therapy linear accelerator where it was set up according to the surface marks using optical beam indicators. An electronic portal image was acquired for this treatment set-up. An additional 14 electronic portal images were acquired with the phantom and the radiation beam displaced from the original, optically aligned position to introduce FPEs of known degree. Translations in X- (right to left lateral ) and Y (cranio-caudad direction on the phantom) directions with magnitudes ranging from 0 to 20 mm T he British Journal of Radiology, April 1998

were applied to the phantom, and the radiation field was rotated (around the central axis) by up to 5°. The ‘‘exact’’ values for translations were measured using a ruler with a precision of approximately 1 mm. The angle of beam rotation was recorded from the machine read-out, with a precision of 0.1°. Portal images of the phantom were automatically analysed using the portal verification scheme as described above. Results of the automated analysis were compared against the exact values of the introduced FPEs. To evaluate further the performance of the automated techniques for anatomy and radiation field registration on a representative sample of clinical images, the second test series involved the analysis of 31 clinical portal images that were acquired during AP treatments to the pelvis for 18 different patients. Since in real patient treatments the ‘‘true’’ values of FPEs are normally not known, one cannot evaluate the accuracy and precision of the automated FPE measurements on clinical images as was possible in the anthropomorphic phantom experiments described above. Instead, we chose to evaluate the degree of agreement between anatomy and radiation field registrations performed by the automated methods and those performed manually based on visual perception. The registration parameters for the latter, in terms of x- and ytranslation and rotation angle, were derived from a computer assisted analysis performed by an experienced human observer. In this analysis, the anatomical landmarks were manually delineated on portal images and the anatomy, as well as field boundary alignment, was done interactively so that visually optimal matches were achieved. By comparing the results for the registration parameters, generated by the human observer and the automated scheme we were able to evaluate the reliability of the latter in application to a representative sample of clinical images as well as to assess the consistency between the visual and automated image registration. Since the automated methods for anatomy registration differ from those used for radiation field registration, the two types of registration in this case were evaluated separately.

Experimental results An example portal image of the pelvic phantom showing a lateral FPE is shown in Figure 4a, and the anatomy based registration between this portal image and the simulation image of Figure 3, is shown in Figure 4b. The manually delineated anatomical features and the features automatically extracted from the portal image are shown as graphical overlay on the background of the fluoroscopic simulation image. After the subsequent registration of the prescribed field borders the translational and rotational FPEs were 419


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Figure 4. (a) An example of a portal image of the pelvic phantom exhibiting lateral displacement of the radiation field. ( b) The anatomical registration ( by chamfer matching) of the portal image with the corresponding simulation image (previously shown in Figure 3a). The manually delineated anatomical features (white lines) as well as the features automatically extracted from the portal image ( black lines) are shown as graphical overlay on the background of the simulation image. The prescribed and treated field borders are also shown as white and black lines, respectively. The field placement error primarily in the lateral direction, which occurred during the acquisition of the portal image, can be clearly seen. (c) The subsequent registration of the prescribed and treated field borders (white and black lines, respectively) by polygon matching, allowed for the correction for the detected FPEs and the optimum treatment field placement.

determined, and the correction for those leads to the optimum treatment field placement as shown in Figure 4c. To determine which of the two competing distance measures (AMD or RMSD) works better in chamfer matching of the anatomy, as well to compare the performance of the RMSD-chamfer and polygon matching of radiation field borders, three different variants of the portal image registration scheme were used. In the first one, denoted here as ‘‘RMSD/RMSD,’’ the RMSD measure based chamfer matching was used for the registration of both the anatomy and the field boundaries. In the second variant, referred to as ‘‘AMD/RMSD’’, the arithmetic mean distance measure was employed for chamfer matching of the

anatomy. For the field boundary registration, chamfer matching based on the RMSD optimization was used. The AMD measure was not used for chamfer matching of field boundaries, since in application to matching of polygonal objects its performance was already known to be inferior to that of the RMSD measure. The third portal image registration scheme, denoted as ‘‘AMD/PM’’ employed the polygon matching (PM) for the radiation field registration, while registration of the anatomy was done using the AMD based chamfer matching. All 15 portal images of the pelvic phantom were registered with the corresponding simulation image, using the automated schemes described above. In each case field placement errors were

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measured. The relationship between the applied translational and rotational FPEs and those measured with the three variants of the portal image registration scheme were analysed using statistical methods. Examples of this relationship, obtained using the ‘‘AMD/PM’’ scheme are plotted in Figure 5a. It can be seen that there is a strong linear correlation between the introduced set-up errors and the measurements derived from the image registration scheme. The differences between the ‘‘real’’ and the ‘‘AMD/PM’’ estimated FPEs are plotted in Figure 5b. The fact that the mean differences between the introduced and measured translational errors were significantly different from 0 indicates that there was a bias in the measurements. The bias most likely stems from the original phantom set-up on the treatment unit, based on optical alignment with surface marks, although assumed to be error-free, not being perfect. This is due to possible differences in the calibration of the optical indicators of the central axis and the cardinal directions (the reticule and lasers) between the simulator and the treatment unit and the finite accuracy of the set-up procedure. Therefore, we suggest that the standard as well as the maximum deviations of the differences between the pre-set and automatically measured FPEs from the average ( bias) values are a more meaningful indicator of the accuracy of the automated image registration scheme. Table 1 contains the correlation coefficients between the nominal and the

measured FPEs together with their confidence levels, as well as the means and the standard and maximum deviations of the differences between the measured and the nominal FPEs obtained for the three variants of the portal image registration scheme. Of the three competing variants of our portal image registration scheme the ‘‘AMD/RMSD’’ and the ‘‘AMD/PM’’ look very similar in the quoted measures of performance. In fact, the comparisons of their correlation coefficients using Fisher’s z-transformation, and the comparisons of their standard deviations (or rather variances) using the F-test show no significant differences ( p>0.2 in all cases). On the other hand, the ‘‘RMSD/RMSD’’ registration scheme was found to have performed the poorest as its correlation coefficients were significantly lower ( p