Non-rigid image registration: theory and practiceW R CRUM, DPhil, T HARTKENS, PhD and D L G HILL, PhDDivision of Imaging Sciences, The Guy’s, King’s and St. Thomas’ School of Medicine, London SE1 9RT, UKAbstract. Image registration is an important enabling technology in medical image analysis. The currentemphasis is on development and validation of application-specific non-rigid techniques, but there is already aplethora of techniques and terminology in use. In this paper we discuss the current state of the art of non-rigidregistration to put on-going research in context and to highlight current and future clinical applications thatmight benefit from this technology. The philosophy and motivation underlying non-rigid registration isdiscussed and a guide to common terminology is presented. The core components of registration systems aredescribed and outstanding issues of validity and validation are confronted.Image registration is a key enabling technology inmedical image analysis that has benefited from 20 years ofdevelopment [1]. It is a process for determining thecorrespondence of features between images collected atdifferent times or using different imaging modalities. Thecorrespondences can be used to change the appearance –by rotating, translating, stretching etc. – of one image so itmore closely resembles another so the pair can be directlycompared, combined or analysed (Figure 1). The mostintuitive use of registration is to correct for differentpatient positions between scans. Image registration is notan end in itself but adds value to images, e.g. by allowingstructural (CT, MR, ultrasound) and functional (PET,SPECT, functional MRI (fMRI)) images to be viewed andanalysed in the same coordinate system, and facilitatesnew uses of images, e.g. to monitor and quantify diseaseprogression over time in the individual [2] or to buildstatistical models of structural variation in a population[3]. In some application areas image registration is now acore tool; for example (i) reliable analysis of fMRIs of thebrain requires image registration to correct for smallamounts of subject motion during imaging [4]; (ii) thewidely used technique of voxel based morphometry makesuse of image registration to bring brain images from tensor hundreds of subjects into a common coordinate systemfor analysis (so-called ‘‘spatial normalization’’) [5]; (iii) theanalysis of perfusion images of the heart would not bepossible without image registration to compensate forpatient respiration [6]; and (iv) some of the latest MRimage acquisition techniques incorporate image registra-tion to correct for motion [7].Historically, image-registration has been classified asbeing ‘‘rigid’’ (where images are assumed to be of objectsthat simply need to be rotated and translated with respectto one another to achieve correspondence) or ‘‘non-rigid’’(where either through biological differences or imageacquisition or both, correspondence between structures intwo images cannot be achieved without some localizedstretching of the images). Much of the early work inmedical image registration was in registering brain imagesof the same subject acquired with different modalities (e.g.MRI and CT or PET) [8, 9]. For these applications a rigidbody approximation was sufficient as there is relativelylittle change in brain shape or position within the skullover the relatively short periods between scans. Todayrigid registration is often extended to include affineregistration, which includes scale factors and shears, andcan partially correct for calibration differences acrossscanners or gross differences in scale between subjects.There have been several recent reviews that cover theseAddress correspondence to Professor Derek Hill, Division of ImagingSciences, Thomas Guy House (5th Floor), Guy’s Hospital, LondonSE1 9RT, UK.Figure 1. Schematic showing rigid and non-rigid registration.The source image is rotated, of a different size and containsdifferent internal structure to the target. These differences arecorrected by a series of steps with the global changes generallybeing determined before the local changes.The British Journal of Radiology, 77 (2004), S140–S153E2004 The British Institute of RadiologyDOI: 10.1259/bjr/25329214S140 The British Journal of Radiology, Special Issue 2004areas in more detail [1, 10]. Clearly most of the humanbody does not conform to a rigid or even an affineapproximation [11] and much of the most interesting andchallenging work in registration today involves thedevelopment of non-rigid registration techniques forapplications ranging from correcting for soft-tissuedeformation during imaging or surgery [12] through tomodelling changes in neuroanatomy in the very old [13]and the very young [14]. In this paper we focus on thesenon-rigid registration algorithms and their applications.We first distinguish and compare geometry-based andvoxel-based approaches, discuss outstanding problems ofvalidity and validation and examine the confluence ofregistration, segmentation and statistical modelling. Weconcentrate on the concepts, common application areasand limitations of contemporary algorithms but providereferences to the technical literature for the interestedreader. With such broad ambition this paper willinevitably fail to be comprehensive but aims to providea snapshot of the current state of the art with particularemphasis on clinical applications. For more specificaspects of image registration, the reader is referred toother reviews; there is good technical coverage in Hill et al[1], Brown [15], Lester and Arridge [16], Maintz andViergever [17] and Zitova and Flusser [18], reviews ofcardiac applications in Makela et al [19], nuclear medicinein Hutton et al [20], radiotherapy in Rosenman et al [21],digital subtraction angiography in Meijering et al [22] andbrain applications in Toga and Thompson [23] andThompson et al [24].Registration and correspondenceImage registration is about determining a spatialtransformation – or mapping – that relates positions inone image, to corresponding positions in one or moreother images. The meaning of correspondence is crucial;depending on the application, the user may be interested instructural correspondence (e.g. lining up the sameanatomical structures before and after treatment todetect response), functional correspondence ( e.g. liningup functionally equivalent regions of the brains of a groupof subjects) or structural–functional