The British Journal of Radiology 77 2004 S140 S153 DOI 10 1259 bjr 25329214 E 2004 The British Institute of Radiology Non rigid image registration theory and practice W R CRUM DPhil T HARTKENS PhD and D L G HILL PhD Division of Imaging Sciences The Guy s King s and St Thomas School of Medicine London SE1 9RT UK Abstract Image registration is an important enabling technology in medical image analysis The current emphasis is on development and validation of application specific non rigid techniques but there is already a plethora of techniques and terminology in use In this paper we discuss the current state of the art of non rigid registration to put on going research in context and to highlight current and future clinical applications that might benefit from this technology The philosophy and motivation underlying non rigid registration is discussed and a guide to common terminology is presented The core components of registration systems are described and outstanding issues of validity and validation are confronted Image registration is a key enabling technology in medical image analysis that has benefited from 20 years of development 1 It is a process for determining the correspondence of features between images collected at different times or using different imaging modalities The correspondences can be used to change the appearance by rotating translating stretching etc of one image so it more closely resembles another so the pair can be directly compared combined or analysed Figure 1 The most intuitive use of registration is to correct for different patient positions between scans Image registration is not an end in itself but adds value to images e g by allowing structural CT MR ultrasound and functional PET SPECT functional MRI fMRI images to be viewed and analysed in the same coordinate system and facilitates new uses of images e g to monitor and quantify disease progression over time in the individual 2 or to build statistical models of structural variation in a population 3 In some application areas image registration is now a core tool for example i reliable analysis of fMRIs of the brain requires image registration to correct for small amounts of subject motion during imaging 4 ii the widely used technique of voxel based morphometry makes use of image registration to bring brain images from tens or hundreds of subjects into a common coordinate system for analysis so called spatial normalization 5 iii the analysis of perfusion images of the heart would not be possible without image registration to compensate for patient respiration 6 and iv some of the latest MR image acquisition techniques incorporate image registration to correct for motion 7 Historically image registration has been classified as being rigid where images are assumed to be of objects that simply need to be rotated and translated with respect to one another to achieve correspondence or non rigid where either through biological differences or image acquisition or both correspondence between structures in two images cannot be achieved without some localized stretching of the images Much of the early work in medical image registration was in registering brain images of the same subject acquired with different modalities e g MRI and CT or PET 8 9 For these applications a rigid Address correspondence to Professor Derek Hill Division of Imaging Sciences Thomas Guy House 5th Floor Guy s Hospital London SE1 9RT UK S140 body approximation was sufficient as there is relatively little change in brain shape or position within the skull over the relatively short periods between scans Today rigid registration is often extended to include affine registration which includes scale factors and shears and can partially correct for calibration differences across scanners or gross differences in scale between subjects There have been several recent reviews that cover these Figure 1 Schematic showing rigid and non rigid registration The source image is rotated of a different size and contains different internal structure to the target These differences are corrected by a series of steps with the global changes generally being determined before the local changes The British Journal of Radiology Special Issue 2004 Non rigid image registration areas in more detail 1 10 Clearly most of the human body does not conform to a rigid or even an affine approximation 11 and much of the most interesting and challenging work in registration today involves the development of non rigid registration techniques for applications ranging from correcting for soft tissue deformation during imaging or surgery 12 through to modelling changes in neuroanatomy in the very old 13 and the very young 14 In this paper we focus on these non rigid registration algorithms and their applications We first distinguish and compare geometry based and voxel based approaches discuss outstanding problems of validity and validation and examine the confluence of registration segmentation and statistical modelling We concentrate on the concepts common application areas and limitations of contemporary algorithms but provide references to the technical literature for the interested reader With such broad ambition this paper will inevitably fail to be comprehensive but aims to provide a snapshot of the current state of the art with particular emphasis on clinical applications For more specific aspects of image registration the reader is referred to other reviews there is good technical coverage in Hill et al 1 Brown 15 Lester and Arridge 16 Maintz and Viergever 17 and Zitova and Flusser 18 reviews of cardiac applications in Makela et al 19 nuclear medicine in Hutton et al 20 radiotherapy in Rosenman et al 21 digital subtraction angiography in Meijering et al 22 and brain applications in Toga and Thompson 23 and Thompson et al 24 Registration and correspondence Image registration is about determining a spatial transformation or mapping that relates positions in one image to corresponding positions in one or more other images The meaning of correspondence is crucial depending on the application the user may be interested in structural correspondence e g lining up the same anatomical structures before and after treatment to detect response functional correspondence e g lining up functionally equivalent regions of the brains of a group of subjects or structural functional correspondence e g correctly positioning functional information on a structural image A particular