Deformable Medical Image Registration: A Survey <s> V. DISCUSSION <s> Nonrigid registration (NRR) is routinely used in the study of neuroanatomy and function and is a standard component of analysis packages such as SPM. There remain many unresolved correspondence problems that arise from attempts to associate functional areas with specific neuroanatomy and to compare both function and anatomy across patient groups. Problems can result from ignorance of the underlying neurology which is then compounded by unjustified inferences drawn from the results of NRR. Usually the magnitude, distribution, and significance of errors in NRR are unknown so the errors in correspondences determined by NRR are also unknown and their effect on experimental results cannot easily be quantified. In this paper we review the principles by which the presumed correspondence and homology of structures is used to drive registration and identify the conceptual and algorithmic areas where current techniques are lacking. We suggest that for applications using NRR to be robust and achieve their potential, context-specific definitions of correspondence must be developed which properly characterise error. Prior knowledge of image content must be utilised to monitor and guide registration and gauge the degree of success. The use of NRR in voxel-based morphometry is examined from this context and found wanting. We conclude that a move away from increasingly sophisticated but context-free registration technology is required and that the veracity of studies that rely on NRR should be keenly questioned when the error distribution is unknown and the results are unsupported by other contextual information. <s> BIB001 </s> Deformable Medical Image Registration: A Survey <s> V. DISCUSSION <s> Non-rigid image registration (NIR) is an essential tool for morphologic comparisons in the presence of intra- and inter-individual anatomic variations. Many NIR methods have been developed, but are especially difficult to evaluate since point-wise inter-image correspondence is usually unknown, i.e., there is no “Gold Standard” to evaluate performance. The Non-rigid Image Registration Evaluation Project (NIREP) has been started to develop, establish, maintain, and endorse a standardized set of relevant benchmarks and metrics for performance evaluation of nonrigid image registration algorithms. This paper describes the basic framework of the project. <s> BIB002 </s> Deformable Medical Image Registration: A Survey <s> V. DISCUSSION <s> Abstract We describe the construction of a digital brain atlas composed of data from manually delineated MRI data. A total of 56 structures were labeled in MRI of 40 healthy, normal volunteers. This labeling was performed according to a set of protocols developed for this project. Pairs of raters were assigned to each structure and trained on the protocol for that structure. Each rater pair was tested for concordance on 6 of the 40 brains; once they had achieved reliability standards, they divided the task of delineating the remaining 34 brains. The data were then spatially normalized to well-known templates using 3 popular algorithms: AIR5.2.5’s nonlinear warp (Woods et al., 1998) paired with the ICBM452 Warp 5 atlas (Rex et al., 2003), FSL’s FLIRT (Smith et al., 2004) was paired with its own template, a skull-stripped version of the ICBM152 T1 average; and SPM5’s unified segmentation method (Ashburner and Friston, 2005) was paired with its canonical brain, the whole head ICBM152 T1 average. We thus produced 3 variants of our atlas, where each was constructed from 40 representative samples of a data processing stream that one might use for analysis. For each normalization algorithm, the individual structure delineations were then resampled according to the computed transformations. We next computed averages at each voxel location to estimate the probability of that voxel belonging to each of the 56 structures. Each version of the atlas contains, for every voxel, probability densities for each region, thus providing a resource for automated probabilistic labeling of external data types registered into standard spaces; we also computed average intensity images and tissue density maps based on the three methods and target spaces. These atlases will serve as a resource for diverse applications including meta-analysis of functional and structural imaging data and other bioinformatics applications where display of arbitrary labels in probabilistically defined anatomic space will facilitate both knowledge-based development and visualization of findings from multiple disciplines. <s> BIB003 </s> Deformable Medical Image Registration: A Survey <s> V. DISCUSSION <s> Expert landmark correspondences are widely reported for evaluating deformable image registration (DIR) spatial accuracy. In this report, we present a framework for objective evaluation of DIR spatial accuracy using large sets of expert-determined landmark point pairs. Large samples (>1100) of pulmonary landmark point pairs were manually generated for five cases. Estimates of inter- and intra-observer variation were determined from repeated registration. Comparative evaluation of DIR spatial accuracy was performed for two algorithms, a gradient-based optical flow algorithm and a landmark-based moving least-squares algorithm. The uncertainty of spatial error estimates was found to be inversely proportional to the square root of the number of landmark point pairs and directly proportional to the standard deviation of the spatial errors. Using the statistical properties of this data, we performed sample size calculations to estimate the average spatial accuracy of each algorithm with 95% confidence intervals within a 0.5 mm range. For the optical flow and moving least-squares algorithms, the required sample sizes were 1050 and 36, respectively. Comparative evaluation based on fewer than the required validation landmarks results in misrepresentation of the relative spatial accuracy. This study demonstrates that landmark pairs can be used to assess DIR spatial accuracy within a narrow uncertainty range. <s> BIB004 </s> Deformable Medical Image Registration: A Survey <s> V. DISCUSSION <s> Quantitative evaluation of image registration algorithms is a difficult and under-addressed issue due to the lack of a reference standard in most registration problems. In this work a method is presented whereby detailed reference standard data may be constructed in an efficient semi-automatic fashion. A well-distributed set of n landmarks is detected fully automatically in one scan of a pair to be registered. Using a custom-designed interface, observers define corresponding anatomic locations in the second scan <s> BIB005 </s> Deformable Medical Image Registration: A Survey <s> V. DISCUSSION <s> EMPIRE10 (Evaluation of Methods for Pulmonary Image REgistration 2010) is a public platform for fair and meaningful comparison of registration algorithms which are applied to a database of intra patient thoracic CT image pairs. Evaluation of nonrigid registration techniques is a nontrivial task. This is compounded by the fact that researchers typically test only on their own data, which varies widely. For this reason, reliable assessment and comparison of different registration algorithms has been virtually impossible in the past. In this work we present the results of the launch phase of EMPIRE10, which comprised the comprehensive evaluation and comparison of 20 individual algorithms from leading academic and industrial research groups. All algorithms are applied to the same set of 30 thoracic CT pairs. Algorithm settings and parameters are chosen by researchers expert in the con figuration of their own method and the evaluation is independent, using the same criteria for all participants. All results are published on the EMPIRE10 website (http://empire10.isi.uu.nl). The challenge remains ongoing and open to new participants. Full results from 24 algorithms have been published at the time of writing. This paper details the organization of the challenge, the data and evaluation methods and the outcome of the initial launch with 20 algorithms. The gain in knowledge and future work are discussed. <s> BIB006 </s> Deformable Medical Image Registration: A Survey <s> V. DISCUSSION <s> The accuracy of nonrigid image registrations is commonly approximated using surrogate measures such as tissue label overlap scores, image similarity, image difference, or transformation inverse consistency error. This paper provides experimental evidence that these measures, even when used in combination, cannot distinguish accurate from inaccurate registrations. To this end, we introduce a “registration” algorithm that generates highly inaccurate image transformations, yet performs extremely well in terms of the surrogate measures. Of the tested criteria, only overlap scores of localized anatomical regions reliably distinguish reasonable from inaccurate registrations, whereas image similarity and tissue overlap do not. We conclude that tissue overlap and image similarity, whether used alone or together, do not provide valid evidence for accurate registrations and should thus not be reported or accepted as such. <s> BIB007
Deformable registration is a mature field that has been extensively studied. As a consequence, an important body of research work has been devoted to its improvement and application in clinical settings. In this review, we have made an effort to provide a comprehensive survey of the recent developments in the field of deformable medical image registration. Our approach was structured around the three core registration components, 1) deformation models, 2) matching criteria, and 3) optimization methods. For every component, particular emphasis was placed on classifying the methods appertaining to it according to their theoretical foundations. We focused our presentation on giving an account of recent approaches that have not be be covered in previous reviews. Let us now summarize the contents of this paper. In Section II we have presented the transformation models for deformable image registration. We discussed physics-based models (see Section II-A) which provide transformations that comply with a physical model. The transformation is estimated through the solution of a PDE that can be computationally demanding. Interpolation-based methods were presented in Section II-B). These models do not assume, in general, that the deformed object behaves according to a natural law. Instead, they exploit interpolation and approximation theory to construct the deformation field. In Section II-C we discussed knowledge-based approaches that exploit our knowledge regarding the problem through the use of more informed priors at the cost of being constrained to well-defined settings. We concluded this section by presenting constraints (see Section II-D) that have been devised to enforce certain properties on the resulting transformation. In Section III we have classified similarity criteria based on the type of information they exploit. We have presented intensity-based matching criteria in Section III-B according to whether they tackle mono-modal or multi-modal registration problems. In the mono-modal case, the use of standard similarity criteria (e.g., SSD or SAD) involving either intensities or multi-channel data extracted from the image through the application of filters is well-accepted by the community. In the multi-modal case, the use of information theoretic measures has become the prevalent solution. In Section III-A, we presented registration approaches that exploit geometric information. The presentation was organized according to the unknown variables the methods estimate. We concluded the section by presenting coupled approaches that opt to bridge the gap between the iconic and the geometric methods (see Section III-C). The third component of registration, optimization, is discussed in Section IV. Registration is an inherently continuous problem. As a consequence, continuous optimization methods have been the main driving force behind registration algorithms. These methods are presented in Section IV-A. Recently, discrete optimization techniques have been proposed to tackle deformable registration. We discuss these approaches in Section IV-B. Heuristic and metaheuristic approaches are briefly introduced in Section IV.C. Image registration is a particularly active field of research. New methods, spanning all aspects of registration, are devised that tackle the shortcomings of the existing ones resulting in a fluid research domain. In this review, we opted to map the research field by reporting the recent advances related to the methodological aspects of registration. An important topic that was not covered is the evaluation of registration methods. Evaluation of registration methods is a particularly difficult problem because of the lack of a "ground truth." The absence of knowledge of correspondences between images makes the quantitative validation of the registration performance a challenging task. Moreover, because of the different requirements of the applications that are based on deformable registration, the notion of correspondence should vary according to application context, aiming to properly characterize error BIB001 . Nonetheless, the increasing availability of annotated data sets (e.g., the LONI Probabilistic Brain Atlas BIB003 , the Internet Brain Segmentation Repository -IBSR  , the CUMC12 dataset 2 acquired at the Columbia University Medical Center, the MGH10 dataset 2 scanned at the MGH/MIT/HMS Athinoula A. Martinos Center for Biomedical Imaging) has made possible evaluation studies like the one by Klein et al. [449] . Moreover, the development of evaluation projects for image registration (i.e., nonrigid image registration evaluation project-NIREP BIB002 ) and the increasing understanding regarding the use of surrogate measures for the measurement of the accuracy of registration BIB007 will further facilitate the comparison between different algorithms. Landmark correspondences can also be used for the evaluation of registration accuracy. Manual identification and matching of landmarks across scans is a tedious task. As a consequence few datasets are available providing such reference standards. One may cite the POPI model  containing 40 landmarks in every frame of a lung CT acquisition, or the CT dataset made available by Castillo et al. BIB004 with landmarks in the maximum inhale and exhale phase. The development of dedicated methods for reference standard construction BIB005 and the organization of registration challenges BIB006 create the necessary conditions for objective comparison of registration methods. The increased availability of data along with the publication of the source code of the methods will lead to evaluation studies that will allow us to quantify the performance of the registration components and draw conclusions regarding their applicability in specific registration settings.