Consistency of Parametric Registration in Serial MRI Studies of Brain Tumor Progression Andreas Mang1 , Julia A. Schnabel2,3 , William R. Crum2,4 , Marc Modat2 , Oscar Camara-Rey2,5 , Christoph Palm2,6 , Gisele Brasil Caseiras7 , H. Rolf J¨ager7 , S´ebastien Ourselin2 , Thorsten M. Buzug1 , David J. Hawkes2 1
Institute of Medical Engineering, University of L¨ubeck, Germany Centre for Medical Image Computing, University College London, United Kingdom 3 Institute of Biomedical Engineering, Dept. Engineering Science, University of Oxford, UK 4 Centre for NeuroImaging Sciences, Institute of Psychiatry, King’s College London, UK 5 Center for Computational Imaging and Simulation Technologies in Biomedicine, Universitat Pompeu Fabra Spain 6 Institute of Neuroscience and Biophysics 3, Medicine Research Centre J¨ulich, Germany 7 Institute of Neuroradiology, University College London, United Kingdom 2
E-mail: {mang,buzug}@imt.uni-luebeck.de,
[email protected] Abstract. Object: The consistency of parametric registration in multi-temporal magnetic resonance (MR) imaging studies was evaluated. Materials and Methods: Serial MRI scans of adult patients with a brain tumor (glioma) were aligned by parametric registration. The performance of low-order spatial alignment (6/9/12 degrees of freedom) of different 3D serial MR-weighted images is evaluated. A registration protocol for the alignment of all images to one reference coordinate system at baseline is presented. Registration results were evaluated for both, multimodal intra-timepoint and mono-modal multi-temporal registration. The latter case might present a challenge to automatic intensity based registration algorithms due to ill-defined correspondences. The performance of our algorithm was assessed by testing the inverse registration consistency. Four different similarity measures were evaluated to assess consistency. Results: Careful visual inspection suggests that images are well aligned, but their consistency may be imperfect. Sub-voxel inconsistency within the brain was found for all similarity measures used for parametric multi-temporal registration. T1-weighted images were most reliable for establishing spatial correspondence between different timepoints. Conclusions: The parametric registration algorithm is feasible for use in this application. The sub-voxel resolution mean displacement error of registration transformations demonstrates that the algorithm converges to an almost identical solution for forward and reverse registration. key words: Inverse registration consistency, parametric serial MR image registration, tumor disease progression.
1. Introduction Glioma is a common brain tumor with heterogeneous presentation and poor prognosis. In clinical practice multi-modal magnetic resonance imaging (MRI) is commonly used to
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non-invasively collect information about location, size, spread, and functional state of the tumor and its surroundings (Shah et al. 2006)(Galanis et al. 2006). It provides a useful snapshot of the current state of the tumor. This information is vital for the assessment of disease progression, surgical planning and monitoring treatment response. A potentially more powerful approach for learning about disease progression is to study changes observed in multi-temporal imaging studies. To enable the analysis of such changes, correspondence between features on scans acquired at different timepoints has to be established. Intensitybased image registration algorithms represent an automated means to solve this very correspondence problem. The present work is devoted to the analysis of low-order parametric multi-temporal registration. Registered to a baseline scan (which is usually chosen to be the first in the temporal sequence), images can be further processed by means of high-order parametric and non-parametric registration approaches (Mang et al. 2007) to provide quantitative measures of change. The registration itself, however, represents a challenging problem because of gross changes in volume due to tumor growth or therapeutic intervention as well as associated large changes in texture within and in the vicinity of the tumor. Additionally, serial images usually suffer from image acquisition related factors, such as signal non-uniformity, imaging noise, scanner calibration problems, or modality specific imaging artifacts. Ground truth correspondence to judge the performance of a registration algorithm is seldom available and moreover very difficult to establish in real clinical data even for evaluation purposes. In the present work analysis of low-order parametric registration of serial MRI scans on the basis of registration consistency is presented. Inconsistency in the transformation estimates arises from the fundamental problem that matching criteria in general are not capable of uniquely describing spatial correspondence between images, i.e. matching criteria in general are asymmetric. Good registration consistency can support the hypothesis that the correspondence problem is well-defined and soluble by a particular registration package even if it does not guarantee the absolute correctness of the transformations. Assessment of registration consistency for the evaluation of registration performance has been used in a variety of image registration applications to analyze longitudinal studies (cf. e.g. (Freeborough et al. 1996)(Holden et al. 2000)(Christensen & Johnson 2003)). Further, there exist methods that are designed to provide inverse-consistent transformations (inverse consistent image registration (ICIR), cf. e.g. (Christensen & Johnson 2001)(Leow et al. 2006=5)(Cachier & Rey 2000)). Here, consistency is enforced by explicitly computing the forward and reverse transformation. Moreover, there exist related symmetric approaches (Rogelj & Kovaˇciˇc 2006)(Avants et al. 2008), which are improving robustness of the algorithm without explicitly computing the reverse transformation. The majority of these approaches are designed to guarantee smooth, one to one, differentiable transformations, i.e. a diffeomorphism, in high order non-rigid registration. Such consistency, however, may not always be desirable in the context of pathology or intervention. Indeed, in the present application, textural changes within the tumor as well as large distortions due to the tumor mass effect (both of which are a direct consequence of tumor progression and therapeutic
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intervention), violate the basic assumptions of diffeomorphism. Consequently, analysis of consistency in non-rigid registration would only be meaningful within the healthy tissue. In this work we limit the analysis of registration performance to global low-order parametric registration which not explicitly resolve differences due to tumor progression. Even so, the considerable mechanical and textural effects of the tumor on the brain may negatively affect even such low-order methods (Studholme et al. 1999). An appropriate choice of the voxel-similarity measure, which drives the registration, can reduce the impact of confounding intensity changes. We compare four different similarity measures D computed over the whole brain in this work - no segmentation of areas affected by pathology is performed. We also investigate whether transformations incorporating global scaling and skew terms (so-called 9 dof and 12 dof transformations) are appropriate compared with rigid-body (6 dof) transformations. This is particularly important as 9 dof and 12 dof transformations are used to correct for temporal variation in the calibration of MR scanners; it is important to establish whether these methods will be confounded by pathological processes. The analysis is performed on three different types of morphological MR scans (T1 / T1contrast-enhanced / T2) commonly collected at each time-point with the aim of providing advice on which combinations of images result in the most stable registration performance. The rest of the paper is organized as follows: first, materials and methods are presented in section 2 including detailed descriptions of the imaging application and protocol and the specific registration techniques employed (section 2.1). Section 2.2 reviews registration consistency and in section 2.3 the four similarity measures D are discussed. Results are presented in section 3 and discussed in detail in section 4. Final conclusions are drawn in section 5. 2. Materials and Methods 2.1. Image Data Serial studies of different MR images were acquired at intervals of 6 months over a period of 2-5 years (J¨ager et al. 2005). Patients who initially had a low grade glioma (WHO grade II) were imaged, not undergoing any treatment until tumors transformed from low- to high-grade malignancy (WHO grade III and IV). The fusion of these images results in a unique feature space providing complimentary information measured by different types of scan protocols vital for tumor assessment. In this paper, six patients imaged at either three, four or five timepoints are included (cf. Fig. 1 for an example). The temporal consistency of registration was evaluated in T1 and T1-enhanced MR volumes (acquired volumetrically using a spoiled gradient echo (SPGR) sequence pre- and post-contrast; TR/TE/TI = 14.4/6.4/650 ms, 256 × 256 matrix, 24 cm × 24 cm FOV, contiguous sections, .2 mmol/kg meglumine gadoterate; voxel dimensions: [δx × δy × δz] = [.9375×.9375×1.5] mm), and the axial oblique T2 volumes (acquired using a fast spin echo (FSE) sequence, single echo, TR/TE = 600/102 ms, 256 × 224 matrix, 24 cm × 18 cm FOV; [δx × δy × δz] = [.4688×.4688×6.5] mm).
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Figure 1: Time series of T1-weigthed MR images of two patients after parametric 12 dof registration. Tumor growth and associated distortions of tissue distal to the primary tumor site are especially visible in the patient shown in the upper row. Large changes in textural information and morphology within the tumor itself are particularly prominent for the patient in the second row. 2.2. Registration Consistency Before defining registration consistency let us consider the problem of parametric image registration between two images T , target image, and S , source image. It can be formulated as a minimization problem ϕ (1) D T, S ◦ ϕ (x s ) → min subject to ϕ ∈ Φ where D is the similarity measure and Φ is a linear, finite-dimensional, parameterizable search space Φ = span ψ1 , . . . , ψ j , . . . , ψm for the desired spatial transformation ϕ : ΩS → ΩT , xS 7→ xT that maps image S to image T . Here, xT ∈ ΩT and xS ∈ ΩS are the voxel co-ordinates in the respective image domain Ωi = [0, 1]d ⊂ Rd , i = T, S . Given a set of parameters α j and a set of basis functions ψ j , ϕ can then be expanded as X ϕ (α) (x) = α j ψ j (x) . (2) j
The choice of the particular subspace, can be thought of as a regularization of the problem to overcome ill-posedness (cf. (Modersitzki 2004) for further details). In this paper we limit the subspace to global transformation models (6/9/12 dof). Inverse registration consistency (Freeborough et al. 1996)(Holden et al. 2000)(Christensen & Johnson 2003) is one measure of the precision of a registration algorithm. In theory, the composition of the forward transformation ϕS ,T and its reverse ϕT,S should be the identity I, i.e. ϕS ,T ◦ ϕT,S = I. With an imperfect registration, however, we obtain an error ∆ϕ = I − ϕS ,T ◦ ϕT,S , 0. Different schemes can be used to compute the consistency error (cf. e.g. (Holden et al. 2000) for a detailed description). We analyze registration consistency on the basis of
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a 2-transformation scheme (inverse consistency) (cf. Fig. 2(a) for an illustration). For this, each image S is independently mapped to the target image T (forward transformation ϕS ,T ) and vice versa (reverse transformation ϕT,S ).
(a)
(b)
Figure 2: Registration consistency. In (a) the 2-transformation scheme is illustrated. (b) shows a brain mask computed using BET (Smith 2002). The error arising from ∆ϕ can then be computed as a mean displacement error 1 X hδiS = kϕS ,T ◦ϕT,S (xT ) − xT k2 Nroi x ∈Ω T
(3)
roi
with respect to S . The mean error hδiS is computed for each voxel xT ∈ Ωroi in a defined region of interest (ROI) Ωroi ⊂ ΩT in the target image T . Here, Nroi = |{xT ∈ Ωroi }| is the cardinality of the set of voxels xT ∈ Ωroi and k · k2 is the standard Euclidean norm. Since it has been argued that the root mean squared error s X 1 rms δS = kϕS ,T ◦ϕT,S (xT ) − xT k22 (4) Nroi x ∈Ω T
roi
is less biased than hδiS (Lemieux et al. 1998), this error is used to compute the results presented in section 3. Consistency is analyzed for the composition of the forward and reverse registration of each type of MR image to its corresponding image at baseline (monomodal multi-temporal registration) with respect to four different similarity measures D (cf. section 2.3). In the presence of a global transformation ϕ, the registration error will increase with the distance from the origin. Therefore we limit the evaluation to a brain region of interest (ROI) Ωroi ⊂ ΩT to account only for errors observed within anatomy of interest. Brain masks were generated using the freely available Brain Extraction Tool (BET) (Smith 2002) (cf. Fig. 2(b)). The root mean squared error δrms , the standard deviation σ, and the maximum (max) error over all voxels xA ∈ Ωroi are calculated wrt. different transformation models ϕ and similarity measures D. 2.3. Similarity Measures The similarity measure D used to compute the cost function is one of the most important factors influencing the quality of the registration results. For the multi-modal intra-timepoint registration, normalized mutual information (NMI) is used. This is motivated by the fact that
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measures based on the assumption of a probabilistic intensity relationship seem to perform best in multi-modal registration problems (Studholme et al. 1999)(Pluim et al. 2003). The number of bins for the evaluation of the joint probability distribution is limited to 64 to improve statistical strength. For the mono-modal multi-temporal registration, four different similarity measures commonly used for rigid and affine registration are evaluated: Sum of squared differences DSSD , correlation coefficient DCC , correlation ratio‡ DCR and normalized mutual information DNMI (cf. (Hajnal et al. 2001) (Roche et al. 1998) and references therein for further details). 2.4. Registration Scenario and Options The registration experiments proceed in two steps. First a series of registrations is performed to align all scans An , Bn , . . . , M n within each time-point, n, (multi-modal, intra-temporal). For these experiments a single image An was nominated as a within-time-point reference. Then a series of registrations across time-points is performed between scans of the same type to a single baseline reference co-ordinate system, b (mono-modal, multi-temporal). A composition of the resulting transformations ϕkn ,An ◦ ϕAn ,Ab , k = B, . . . , M, subsequently allows to map all images to one defined co-ordinate system at baseline b (cf. Fig. 3 for an illustration, where the T1-volume is exemplarily chosen as a within-time-point reference image).
Figure 3: Illustration of the registration scenario. For the intra-timepoint registration, different modalities Bn , ..., M n are registered to a nominated reference image An . This reference image An at timepoint n is then registered to the corresponding image Ab at baseline b, such that the composition of the respective transformations ϕkn ,An ◦ ϕAn ,Ab , k = B, . . . , M, allows us to map all images to a defined reference co-ordinate system at baseline b. The registration algorithm used in this work is an implementation of the linear unidirectional pair-wise registration algorithm described in Studholme et al. (Studholme et al. ‡ Note that DCR (X, Y) , DCR (Y, X) .
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1999). Both, target and source image are blurred using a Gaussian kernel with a standard deviation of .5×[δx, δy, δz]. Further, a multi-resolution search strategy with 3 resolution levels, a reduction factor of 2 and a step length of 1 with 10 steps per iteration is used. The maximum number of iterations is set to 100. Intensity values of neighboring voxels are estimated by trilinear interpolation. The search for the global optimum in the multi-dimensional parameterspace is performed with a downhill descent optimization scheme. No correction for intensity non-uniformity is performed before registration. For the mono-modal, multi-temporal registration of timepoint n to baseline b, the registration parameters and options are kept constant with one exception. The number of intensity bins is adjusted accordingly if non-probabilistic similarity measures D are used for the evaluation of registration consistency. Mono-modal multi-temporal registration is performed using the entire set of low-order parametric transformation models (rigid body 6 dof, similarity 9 dof as well as affine 12 dof registration). 3. Results 3.1. Qualitative Assessment of the Registration Results The rigid and affine spatial alignment of multi-modal data in longitudinal studies reveals vital information for the assessment of changes due to disease progression and/or therapy. Careful visual inspection suggests that in both of the cases studied here (i.e. multi-modal intratimepoint registration and mono-modal multi-timepoint registration) images are well aligned for all similarity measures D and all employed transformation ϕ (6/9/12 dof). h models Scanneri induced linear distortions are found to be small (scalings min s x , sy , sz , max s x , sy , sz ∼ [.99, 1.01] / ∼ [.99, h 1.01] / ∼ [.98, i 1.01]) and skewing angles were found in the range of min s xy , syx , syz , max s xy , syx , syz ∼ [.01◦ , .36◦ ] / ∼ [.01◦ , .93◦ ]°/∼ [.01◦ , .92◦ ] for the T1 / T1-constrast enhanced / T2 images, respectively (values are computed from the set of all permutations between timepoint n and baseline b seen in 12 dof registration based on DNMI ; further details on the degree of motion between images can be found in Tab. A1 in appendix Appendix A.1). For intra-timepoint registrations, the magnitude of the spatial transformations between T1 and T1-enhanced volumes is observed to be small (see Fig. 4 (a), (b) and (e), (f), respectively). This is to be expected, since images are acquired within one scanning session directly after one another. For the T2-to-T1 intra-timepoint registration, despite larger variation in patient positioning, differences in voxel dimensions δx, δy, δz , differences in the FOV, and large anisotropy of the voxel dimensions of the T2-volume (cf. section 2.1), images are still visually well aligned (see Fig. 4 (c), (d) and (g),(h), respectively). 3.2. Analysis of Registration Consistency The full results for each subject are in Tab. A2 – Tab. A7 in appendix Appendix A.2. Values for δrms and σ are, for reasons of clarity, averaged across all permutations between each timepoint n and the corresponding baseline scan b with respect to (i) each modality and (ii) each measure
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(a)
(b)
(e)
(f)
(c)
(d)
(g)
(h)
Figure 4: Results of multi-modal intra-timepoint 12 dof registration. Images are acquired at baseline and registration is performed to the reference space of the T1-weighted images. The first row provides two sets of images before registration. In (a) (axial view) and (b) (coronal view) the baseline T1-enhanced volume is overlaid onto the corresponding T1weighted image. In (c) and (d) the respective T2-volume is overlaid onto the T1-weighted image. The second row provides the same setting after 12 dof parametric registration.
(a) T1b – T11
(d) T1b – T11
(b) T1b – T12
(e) T1b – T12
(c) T1b – T13
(f) T1b – T13
(g) T1b – T14
Figure 5: Results of the T1-to-T1 mono-modal multi-temporal 12 dof registration. Difference images for two patients (top and bottom row, respectively) between each timepoint n = 1, 2, 3, (4) and the baseline scan b are provided. The intensity window is scaled down in order to better visualize residual differences between images due to tumor progression. D, as stated above. Further, the maximum (max) error is computed for each permutation. After determining these max errors for each individual composition of reverse and forward transformation, the total max error from the entire set of permutations is computed. The mean consistency error hδrms i is well below sub-voxel accuracy for all employed transformation
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models ϕ and similarity measures D, with respect to each data-set (cf. section 2). Especially for the T1 and the T1-enhanced volumes all measures D yield almost identical values for hδrms i. This is again summarized in Tab. 1, where hδrms i is averaged across all measures D in order to depict the small differences in hδrms i arising from different measures D (cf. section 2.3). Table 1. Registration consistency error hδrms i from Tab. A2 – Tab. A7 for 6/9/12 dof parametric registration averaged across the different measures D for each patient p. Values for mean hδrms iD and standard deviation hσiD are in [mm] and rounded to 3 dp.
p 1
2
3
4
5
6
|α| 6 9 12 6 9 12 6 9 12 6 9 12 6 9 12 6 9 12
T1-enhanced hδrms iD ± hσiD .031 ± .010 .060 ± .035 .051 ± .020 .026 ± .011 .039 ± .011 .035 ± .014 .019 ± .004 .044 ± .048 .042 ± .012 .018 ± .003 .028 ± .011 .031 ± .012 .023 ± .010 .035 ± .007 .035 ± .015 .022 ± .005 .045 ± .002 .093 ± .007
T1 hδ iD ± hσiD .024 ± .005 .046 ± .011 .049 ± .017 .027 ± .014 .036 ± .009 .032 ± .015 .021 ± .011 .024 ± .008 .033 ± .012 .026 ± .008 .026 ± .008 .027 ± .004 .033 ± .009 .043 ± .018 .044 ± .020 .024 ± .005 .040 ± .004 .071 ± .006 rms
T2 hδ iD ± hσiD .052 ± .015 .073 ± .014 .133 ± .091 .089 ± .038 .222 ± .208 .137 ± .041 .131 ± .031 .267 ± .124 .153 ± .026 .111 ± .015 .153 ± .026 .158 ± .020 .115 ± .034 .286 ± .279 .507 ± .705 .101 ± .042 .117 ± .037 .170 ± .030 rms
Overall there exists a trend that hδrms i computed from different transformation models ϕ slightly increases with the change from 6 to 9 or 12 dof. For the latter two models, no trend for a systematic change in hδrms i is to be observed. The consistency error is in general largest for the T2-volumes compared to the T1-weighted images, having a maximum of hδrms i = (1.765 ± .897) mm for DCR (Y, X), 12 dof, in patient 5 (Tab. A6). Five other results stand out against the remainder of the computed consistency errors for the T2-volumes: hδrms i = (.292 ± .123) mm (patient 1, 12 dof, DCR (Y, X), Tab. A2), hδrms i = (.585 ± .101) mm (patient 2, 9 dof, DCR (X, Y), Tab. A3), hδrms i = (.425 ± .235) mm (patient 3, 9 dof, DSSD , Tab. A4), hδrms i = (.371 ± .208) mm (patient 3, 9 dof, DCC , Tab. A4) and hδrms i = (.783 ± .117) mm (patient 5, 9 dof, DCC , Tab. A6). To get a better insight into these consistency errors, the results are reported individually in Tab. 2. The least consistency error for the T2-volumes is hδrms i = (.041 ± .013) mm for the 6 dof registration based on DSSD for patient 1 (Tab. A2). In total, there exists no case where the average consistency error for the permutation between timepoints n and the baseline scan b is lower than the respective error hδrms i for the T1 and the T1-enhanced volumes.
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Table 2. Consistency error δrms for prominent values of hδrms i. Values are given in [mm] for each patient p wrt. individual permutations between timepoint n and baseline b (rounded to 3dp).
p 1
options 12 dof, DCR (Y, X)
2
9 dof, DCR (X, Y)
3
9 dof, DSSD 9 dof, DCC
5
9 dof, DCC
12 dof, DCR (Y, X)
n 1 2 3 1 2 3 1 2 1 2 1 2 3 1 2 3
δrms .073 .132 .671 .072 .120 1.563 .137 .712 .091 .651 2.052 .107 .191 .083 1.369 3.845
σ .016 .061 .293 .032 .062 .209 .067 .403 .045 .371 .202 .047 .101 .016 .726 1.952
max .121 .286 1.484 .138 .248 2.051 .324 1.793 .236 1.653 2.490 .231 .449 .122 3.158 7.958
min .040 .002 .010 .005 .002 1.057 .010 .078 .004 .042 1.574 .000 .002 .045 .018 .075
The maximum consistency error hδrms i = .129 ± .049 mm for the T1-enhanced volumes is found for 12 dof registration using DNMI (patient 3, Tab. A4). The lowest mean error for the T1-enhanced volume is hδrms i = (.012 ± .004) mm seen in patient 3, 6 dof, DSSD (Tab. A4) and hδrms i = (.012 ± .003) mm seen in patient 5, 6 dof, DSSD (Tab. A6). We note that the smallest average root mean squared consistency error hδrms i is achieved 10 times out of 18 (3 transformation models per patient) for DSSD and 5 times for DCC , though differences in hδrms i are subtle. Considering the T1-weighted images, results are similar to those observed in the T1enhanced volumes. The smallest consistency error hδrms i = (.012 ± .004) mm is for the 6 dof registration using DCR (Y, X) for patient 2 (cf. Tab. A4). In general, both, DSSD and DCC , perform well having 5 and 4 times the smallest hδrms i, respectively. Further, DCR (X, Y) demonstrates quite low consistency errors. Remarkably, DNMI never outperformed the other similarity measures D, neither for the T1 nor for the T1-enhanced volumes, though again we note that differences in hδrms i are marginal. 4. Discussion Accurate registration is vital for the detection of subtle changes observed in medical images. In this work, analysis of registration consistency of the low-order alignment (6/9/12 dof) of MR images in multi-temporal MR imaging studies of glioma brain tumor was presented. Assessment of absolute accuracy is difficult in this application as appropriate gold standard transformations are difficult to establish independently, particularly in real clinical data. The
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validation of registration is therefore challenging and usually needs to be done via visual assessment. In contrast, consistency, convergence and robustness provide an estimation of how an algorithm behaves in a particular setting and are useful and desirable properties of any registration algorithm. However, these methods are neither applicable to quantify a registration error in general nor can they be applied retrospectively to identify misregistration (Crum et al. 2003). Therefore, the presented results have to be interpreted with care. Intensity based registration generally requires consistent, well-defined image features to work effectively. The T1 scans satisfy this requirement. Increased vascularity resulting from the progression of glioma tumors might change information seen in T1-enhanced modalities resulting in ill-defined correspondences between subsequent timepoints. Correspondingly, the T1 volume is probably the data set of choice in order to register the subsequent timepoints to one reference space for further analysis. Therefore for our registration protocol, the T1-weighted image is chosen as a withintime-point reference modality. It is apparent that registering across time with other modalities or even registering combinations of modalities across time would all result in less consistent and therefore less robust registration protocols. As shown in section 3, visual inspection suggests that for the intra-timepoint registration images are well aligned. A rigid model should suffice to align all images at a single timepoint provided there is no sequence-specific distortion. However, 9 and 12 dof registration qualitatively perform equally well, and offer protection against subtle cross-sequence effects. This however does not hold for registration between timepoints. Firstly, the employed transformation model should not be limited to a rigid body registration. Instead, 9 dof should at least be used to compensate for differences in patient positioning and to guard against scanner induced drifts in voxel size as proposed in (Freeborough et al. 1996)(Lemieux et al. 1998). Visual inspection as well as the computed consistency errors further suggest that incorporation of scaling and shearing, i.e. a 12 dof affine registration model, yields good results. We have shown that the algorithm performs with good precision for both, the T1 and the T1-enhanced volumes for all employed similarity measures D as well as all transformation models ϕ. We have demonstrated that the registrations are highly consistent. Results are reported down to 3dp to show that, while most cases are highly consistent, there is some systematic variation in the results across the different registration scenarios. In human observer studies it has been shown that one can visually detect a mean voxel shift of ∼ 0.2mm (Denton et al. 2000). For the application, a mean consistency error
