Medical Image Registration *

Basic conception of registration Image registration, also called image matching or alignment, is a process to register one image to others, so that the transformation matrix between two of them are determined so that they are corresponding each other in space.

Image registration is the process of estimating an optimal transformation between two images.

q = T(p)R FT: T = arg max S(R,T(F)) T

Digital subtraction angiographyDSA 1977NudelmanDSA

Li Qiang, etc, Improved contralateral subtraction images by use of elastic matching technique , Med. Phys. 27 .8., August 2000(a)

2005

PET

Talairach Ono

Transform Metric: OptimizerInterpolatorRegistration is treated as an optimization problem with the goal of finding the spatial mapping that will bring the moving image into alignment with the fixed image.

3.1

3.2

3.2 B Windowed Sinc

3.3

Mean squares Normalized correlation Mean reciprocal squared difference Mutual information by Viola and Wells Mutual information by Mattes Kullback Liebler distance metric Normalized mutual information Mean squares histogram Correlation coefficient histogram Cardinality Match metric Kappa Statistics metric Gradient Difference metric3.3

3.4 Amoeba: Nelder-Meade downhill simplex. Conjugate Gradient: Fletcher-Reeves form of the conjugate gradient with or without preconditioning.

Gradient Descent: Advances parameters in the direction of the gradient where the step size is governed by a learning rate

3.4 Powell Arent Levenberg-Marquadrt Newton-Raphson hash

4.1 ()

4.2 Subject IntraSubject InterSubject Atlas4.3 (Modalities) Monomodal Multimodal Modality to modal Patient to modality

4.3 XCT (Computed Tomography)MRI (Magnetic Resonance Imaging)US (Ultra Sound)MRA (Magnetic Resonance Angiography)DSA (Digital Subtraction Angiography)

SPECT (Single Photon Emission Computed Tomography)PET (Positron Emission Tomography )fMRI (functional MRI)EEG (Electro-EncephaloGraphy,)MEG (Magneto-EncephaloGraphy) 4.3

4.5 4.4 Object Head (Brain or skull, Eye, Dental) Thorax (Entire, Caridac, Breast) Abdomen (General, Kidney,Liver) Limbs (General, Femur, Humerus, Hand) Spine and vertebrate Pelvis and perineum

4.6

72 4.6

r 4.6

BrownRobertsWells (BRW)Cosman-Roberts-Wells (CRW)Gill-Thomas-CosmanGTC

4.6

2004.3 4.6

Matthew Y. Wang, An Automatic Technique for Finding and LocalizingExternally Attached Markers in CT and MRVolume Images of the Head,IEEE transactions on Biomedical Engineering.Vol.43, No. 6, 1996

4.6

, 2003,No.5 4.6

4.6

4.6

4.6 (Anatomic Landmarks) (umbilic point)

4.6 Igor D. Grachev,etc,A Method for Assessing the Accuracy of Intersubject Registration of the Human Brain Using Anatomic LandmarksNeuroImage 9, 250268 (1999)

4.6

4.6 Detected point landmarks in a 2D sagittal MR image of ahuman brain

Karl RohrOn 3D differential operators for detecting point landmarksImage and Vision Computing 15 (1997) 219-233

4.6 Vo l. 14,No. 72002

4.6

4.6

4.6

4.6

4.7

4.9 4.8

5.1 /I1(x1,y1,z1)I2(x2,y2,z2)P (x1,y1,z1) I2(x2,y2,z2)I1I2P

5.1.1 Rigid Body Transformation x: x=x+p, y=y y: x=x, y=y+q : x=xcos +ysin y=- xsin +ycos 5.1

5.1.1 Rigid Body Transformation5.1 xpyq

5.1.1 Rigid Body Transformation5.1 xp,yq,

5.1.1 Rigid Body Transformation5.1 , xp, yq

5.1.1 Rigid Body Transformation5.1 pq ,

5.1.1 Rigid Body Transformation5.1

5.1.1 6 x p y q z r x y z :125.1

5.1.1 P(u) = Au+BU=(x,y,z)AB

A ATA=IATAI5.1

5.1.2 Affine Transformation CT MR5.1

5.1.2 9 x p y q z r x y z x mxy myz mz5.1

5.1.2 612

xyz1e11 e12 e13 e14e21 e22 e23 e24e31 e32 e33 e34 0 0 0 1xyz1=eij15.1

5.1.2 5.1 657 (2)(1,3)1234567

5.1.3

(1) (2)

Perspective or Projective Transformation5.1

5.1.3 xy1e11 e12 pe21 e22 q f g 1xy1=x= (e11*x+e12*y+p) / (f*x+g*y+1)5.1

5.1.4 Nonlinear Transformationcurved transformation

5.1

5.1.4 x=e00+e01x+e02y+e03z+e04x2+e05xy+e06xz+e07y2+e08yz+e09z2 y=e10+e11x+e12y+e13z+e14x2+e15xy+e16xz+e17y2+e18yz+e19z2 z=e20+e21x+e22y+e23z+e24x2+e25xy+e26xz+e27y2+e28yz+e29z2 n f(X)=AX+B+ Wi U (|Pi-X|) i=1B5.1

5.1.5 5.1

5.1.5 5.1

5.1.5 5.1

Hausdroff , 5.2

(Correlation ratio) (Correlation coefficient) PIU(Partitioned intensity uniformity) , 5.2

5.2

5.3 (ICP) WGF

5.3 head-hat methodPelizzariChenhathead Powell

5.3 ICP ICPBesl Mckay ICP """"""""""