Nonrigid Registration using Free-Form DeformationsOverviewIntroduction – image registrationIntrocution – image registrationTasks within medical image analysis I Nonrigid registration using free-form deformations: Application to breast MR imagesNonrigid registration using free-form deformationsGlobal motion modelLocal motion model ILocal motion model IILocal motion model III Regularisation of the local transformationSimilarity measures ISimilarity measures II – Information theoreticSimilarity measures III – Information theoreticFinal Cost functionOptimizationRview warpingRview warpingApplication: Breast MRIBreast MRI without contrast agent No registrationBreast MRI without contrast agent RegistrationSimilarity measuresBreast MRI with contrast agent – tumour detection No registrationComparison of the registration error in terms of SSD for different degrees of volunteer motion. (a) No voluntary movement. (b) Cough. (c) Move head. (d) Move arm. (e) Lift out of coil and back.Comparison of the registration error in terms of CC for different degrees of volunteer motion. (a) No voluntary movement. (b) Cough. (c) Move head. (d) Move arm. (e) Lift out of coil and back. (a) After rigid. (b) After affine. (c) After nonrigid registration. The corresponding difference images are shown in (d)–(f).Breast MRI – with contrast – tumour detection Maximum intensity projectionNonrigid Registration using Free-Form DeformationsHongchang PengApril 20thPaper Presented: Rueckert et al. , TMI 1999: Nonrigid registration using free-form deformations: Application to breast MR images1Overview Introduction – image registration Tasks within medical image analysis TMI paper 1999:– Nonrigid registration using free-form deformations Global model Local model Regularisation Similarity measures Optimisation– Results on Breast MRI2Introduction – image registration Image registration - general definition:– determining a mapping between the coordinates in one image and those in another, – to achieve biological, anatomical or functional correspondence Purpose of image registration in medical image analysis– Monitoring of changes in an individual– Fusion of information from multiple sources– Comparison of one subject to another–Comparison of one group to another3Introcution – image registration Registration of one image to the coordinate system of another image by a transformation, T: (x,y,z) (x0, y 0, z 0) Types of transformation– Rigid – rotation, translation– Affine – rotation, translation, scaling, shearing– Nonrigid – All sorts of nonlinear deformations(x’,y’,z’)Image A Image B(x,y,z)T(x,y,z)4Tasks within medical image analysis I Rigid registration– Bones Affine registration– If scale changes are expected Growth Inter-subject registration  Nonrigid registration– Correction for tissue deformation Breast MRI Liver MRI Brain shift modelling– Modelling of tissue motion Cardiac motion Respiratory motion– Modelling of growth and atrophy Brain development Dementia or schizophrenia– Fusion of different modalities5Nonrigid registration using free-form deformations: Application to breast MR imagesBy D. Rueckert, L. I. Sonoda, C. Hayes, D.L. G. Hill, M. O. Leach and D.J. HawkesIEEE Transactions on Medical Imaging 19996Nonrigid registration using free-form deformations A combined transformation consisting of both a local and a global transformation T(x,y,z) = Tglobal(x,y,z) + Tlocal(x,y,z) Global: Accounts for the overall motion of the object Local: Accounts for local deformations of the object Cost function: C = Csimilarity+λ¢Csmooth7Global motion model Simplest choice: Rigid transformation– Rotation, translation ) 6 degrees of freedom (d.o.f) More general: Affine transformation– Rotation, translation, scaling and shearing ) 12 d.o.f8Local motion model I Free form deformations (FFDs) based on cubic B-splinesBasic idea: To deform an object by manipulating an underlying nx£ ny£ nzmesh of control points Φ, with spacing δ.– Control points can be displaced from their original location– Control points provide a compact parameterisation of the transformation9Local motion model II Birepresents the ithbasis function of the B-splineB0(u) = (1-u)3/6B1(u) = (3u3-6u2+4)/6B2(u) = (-3u3+3u2+3u+1)/6B3(u) = u3/6 B-splines are locally controlled – computationally efficient10Local motion model III Hierarchical approach A hierarchy of control point meshes Φ1,…ΦLat increasing resolutionsAt each resolution we have a transformation Tllocal Represented by a single B-spline FFD– Control point mesh progressively refined– New control points inserted at each level– Spacing is halved in every step11Regularisation of the local transformation Constrain to a smooth transformation– Penalty term:12Similarity measures I How do we know when we have a good fit between two images?? Depends on the type of images you are registering Similarity assumptions– Identity Single-modality, only differ by gaussian noise– Linear Single-modality, differ by constant intensity– Information theoretic/probabilistic  multi-modality, intensity changing, related by some statistical or functional relationship13Similarity measures II – Information theoretic Entropy Joint entropy Mutual information (MI)14Similarity measures III – Information theoretic Mutual information is still sensitive to overlapping Normalised mutual information– Is robust to the amount of overlap between images15Final Cost function16Optimizationcalculate the optimal affine transformation parameters Θby maximising Csimilarityinitialise the control points Φrepeatcalculate the gradient vector of the cost function, C(Θ,Φ) with respect to the nonrigid transformation parameters, Φ: rC = δC(Θ,Φl)/δΦlwhile ||rC||>εdorecalculate the control points Φ= Φ+µrC/||rC||recalculate the gradient vector rCincrease the control point resolution by calculating new control points Φl+1from Φlincrease the image resolutionuntil finest level of resolution is reached17Rview warping•Brain deformation after warping•Images after affine registration•Source image•(Baseline DTI image)•Target image•(T1 weighted MRI)•http://www.doc.ic.ac.uk/~dr/software/Rview warping•Visualization of the deformation with the deformation grid•The grid