Nonrigid registration methods for myocardial perfusion mri and cerebral diffusion tensor mri 1

NONRIGID REGISTRATION METHODS FORMYOCARDIAL PERFUSION MRI AND CEREBRAL DIFFUSION TENSOR MRI LI CHAO NATIONAL UNIVERSITY OF SINGAPORE 2012... NONRIGID REGISTRATION METHODS FORMYOCARDIAL P

NONRIGID REGISTRATION METHODS FOR

MYOCARDIAL PERFUSION MRI AND

CEREBRAL DIFFUSION TENSOR MRI

LI CHAO

NATIONAL UNIVERSITY OF SINGAPORE

2012

NONRIGID REGISTRATION METHODS FOR

MYOCARDIAL PERFUSION MRI AND

CEREBRAL DIFFUSION TENSOR MRI

LI CHAO(B.Sc.), University of Science and Technology of China

a thesis submitted for the degree of

doctor of philosophy

DEPARTMENT OF ELECTRICAL AND COMPUTER

ENGINEERINGNATIONAL UNIVERSITY OF SINGAPORE

2012

First and foremost, I would like to express my sincere appreciation to mysupervisor, Asst Prof Sun Ying This dissertation is definitely not possiblewithout her guidance and persistent help I would also like to thank mymentor during the exchange in the Chinese University of Hong Kong, Asst.Prof Wang Xiaogang, for his advice

Second, I would like to thank my thesis committee, Prof Ong Sim Hengand Asst Prof Yan Shuicheng and anonymous reviewers for their valuablecomments

Third, I thank Mahapatra Dwarikanath, Jia Xiao, Hiew Litt Teen fortheir enlightening suggestions during our discussions, and I thank FrancisHoon Keng Chuan and other friends in the Vision and Machine LearningLab who have helped me in my study

Last but surely not the least, I would express my heartfelt thanks to myparents and my wife for their precious support and encouragement

i

§ 1.2 Scope and Contributions 5

§ 1.2.1 Pseudo Ground Truth Based Perfusion Sequence

2 Background 9

§ 2.1 Magnetic Resonance Imaging (MRI) 9

§ 2.2 Ischemic Heart Disease and Perfusion MRI 10

§ 2.3 Small Vessel Disease and Diffusion MRI 14

§ 2.4 Introduction to Image Registration 19

§ 2.4.1 Similarity Measures 20

§ 2.4.2 Transformation Models 28

§ 2.5 Registration in Myocardial Perfusion MRI 35

§ 2.6 Registration in Diffusion Tensor MRI 38

3 The Pseudo Ground Truth Method 41 § 3.1 Introduction 41

§ 3.2 PGT-based Registration for General Perfusion MRI 44

§ 3.2.1 Data Fidelity Term 45

§ 3.2.2 Spatial Smoothness Constraint 45

§ 3.2.3 Temporal Smoothness Constraint 48

§ 3.2.4 Energy Minimization 49

§ 3.2.5 Preliminary Results 52

§ 3.3 Registration of Myocardial Perfusion MRI 55

§ 3.3.1 Initial Alignment 55

§ 3.3.2 Heart Ventricle Segmentation 57

§ 3.3.3 Nonrigid Registration 63

4 The Contour-Image Registration Method 67 § 4.1 Introduction 67

§ 4.2 Active Image 71

CONTENTS v

§ 4.2.1 B-spline FFD 71

§ 4.2.2 Energy Functional 72

§ 4.2.3 Energy Minimization 73

§ 4.2.4 Preliminary Results 74

§ 4.3 Free-form Fibers 78

§ 4.3.1 Fiber Model 81

§ 4.3.2 Fiber-to-DTI Registration 82

5 Results 95 § 5.1 Data Acquisition 95

§ 5.2 Perfusion MRI 96

§ 5.3 Diffusion MRI 116

6 Conclusion and Future Work 127 § 6.1 Conclusion and Discussion 127

§ 6.1.1 Cardiac Perfusion MRI 128

§ 6.1.2 Cerebral Diffusion MRI 130

§ 6.2 Future Work 132

§ 6.2.1 Cardiac Perfusion MRI 132

§ 6.2.2 Cerebral Diffusion MRI 134

As the two leading causes of death, ischemic heart disease and cerebrovasculardisease are of great research importance Perfusion Magnetic ResonanceImaging (MRI) and diffusion MRI have emerged as the most effective non-invasive diagnostic tools respectively for ischemic heart disease and cerebralischemic small vessel disease This thesis discusses the nonrigid registrationproblems in these two imaging techniques

To compensate patients’ breathing and precisely trace the perfusion nal over time, nonrigid registration of the perfusion sequence is required.This registration was conventionally accomplished by pairwisely mappingimages from different perfusion phases but it often failed to handle the greatmismatch of intensity distributions between the reference and floating imagesdue to the variation of the contrast concentration We propose to register theobserved sequence to a pseudo ground truth (PGT), which is a motion/noisefree sequence that is estimated from the observed one, and having almostidentical intensity variations as the original sequence In contrast to pairs

sig-of images within the observed sequence, the corresponding pairs sig-of imagesbetween the observed sequence and the PGT have similar intensities, and

vii

thus the registration problem is greatly eased Our experimental results on

20 cardiac perfusion MR scans have quantitatively and qualitatively shownthat the method is able to effectively compensate for the elastic deformation

of the heart in the myocardial perfusion sequence

The state-of-the-art DTI analysis frameworks, e.g., Voxel-Based phometry and Tract-Based Spatial Statistics, are based on image-to-imageregistration and cannot analyze brain fiber tracts The brain fiber tracts re-construction, i.e., tractography, is usually accomplished by linking the prin-cipal directions of diffusion tensors, which often early terminates at whitematter (WM) lesion regions Besides, tractography segmentation and estab-lishing correspondences among fiber tracts are challenging We propose anovel fiber-to-DTI registration method which deforms a manually annotatedwhole brain fiber model to diffusion tensor images of new subjects Tractog-raphy, tractography segmentation, and inter-subject fiber correspondencesare automatically obtained by this registration The early termination issue

Mor-is overcome by imposing inter- and intra- fiber regularization To handlesevere WM lesions, we use robust principal component analysis to identifyregions with unreliable registration, and propose a statistical along-fiber pri-

or to automatically rectify the registration of these regions Experimentalresults have shown successful registration on 55 subjects and the registra-tion is robust to WM lesions The DTI measure computed from registeredanatomical fiber bundles have significant correlation with cognitive functions

List of Tables

5.1 The RMS distances (pixels/mm) between the manually drawncontours and the propagated contours for the endocardium,epicardium, and all the contours 108

5.2 Comparisons of the RMS distances (pixels/mm) for respectivedata sets 109

5.3 Correlations between MRI scores and cognitive scores For allthe entries except ‘TBSS’ and ‘whole brain’, the MRI score isthe average FA value along the fibers obtained by the proposedmethod ‘TBSS’ uses the average of skeletonised FA values(Smith et al., 2006) as the MRI score For ‘whole brain’, theMRI score is the average FA for the entire brain region Brainmasks are produced by 3D Slicer 124

ix

List of Figures

1.1 A typical myocardial perfusion sequence 3

1.2 Streamline tractography vs fiber-to-DTI registration 7

2.1 Heart anatomy 11

2.2 The rigid and nonrigid registration in myocardial perfusion MRI 13 2.3 Talairach space: a brain anatomical map 15

2.4 Diffusion tensor imaging 17

2.5 A typical registration process 20

2.6 MRI bias field 24

2.7 Joint histograms 27

2.8 Forward and backward mapping 29

3.1 The PGT-based registration algorithm 42

3.2 Intensity-time curves of pixels located inside the RV, LV, ocardium, and at the boundary between the LV and the my-ocardium 46

3.3 Registration results for a renal perfusion sequence 53

3.4 Registration results for a myocardial perfusion MRI 54

xi

3.5 Initial alignment of a myocardial perfusion MRI sequence 57

3.6 Results of heart ventricle segmentation 62

4.1 Change of topology in multi-object segmentation 69

4.2 Model evolution for synthetic image segmentation 75

4.3 Shape preservation vs flexibility 76

4.4 Occluded hand segmentation 77

4.5 Cardiac MR image segmentation: (a) initial contours con-structed by 3 ellipses, (b) segmentation result 78

4.6 The workflow of the proposed fiber-to-DTI registration scheme 80 4.7 A full brain fiber model 81

4.8 The merged fiber model 82

4.9 The Robust PCA result 88

4.10 The 8 non-local contextual regions 90

4.11 MD images for a patient subject and a healthy subject and similarity maps 92

5.1 PGT-based registration results for synthetic data 101

5.2 Average perfusion signals in the ischemic tissue for the syn-thetic experiment 102

5.3 Contour propagation for one pre-contrast frame and three post-contrast frames from a real patient cardiac MR perfu-sion scan 103

5.4 PGT estimation with and without segmentation information 104 5.5 Contour propagations for 4 cardiac scans using our method 107

LIST OF FIGURES xiii

5.6 The inverted cumulative histogram for distances between thepropagated contours and the manually drawn contours 110

5.7 Comparison of intensity-time curves before and after nonrigidregistration 111

5.8 Myocardial perfusion maps generated using maximum upslope.113

5.9 Comparison of the statistics of the normalized upslope in docardial region before and after nonrigid registration 115

suben-5.10 Fiber points reconstructed by fiber-to-DTI registration 117

5.11 The MD slices in axial view and overlaid with the results offirst registration, and the second round of registration 118

5.12 Comparison of corpus callosum bundles reconstructed by usingmanual seeding and our method 119

5.13 The average FA images after back-warping From top to tom shows sagittal, coronal, and axial views From left to rightshows the results using no registration, affine registration, andnon-rigid registration 121

bot-5.14 The histograms of pixel-wise FA standard deviations withinthe brain area after back-warping all the subjects to the brainfiber model domain 122

5.15 Comparison of MR measurements between healthy subjectsand patients The top figure shows the results using mean

FA, while the bottom figure shows measurements along ourreconstructed fibers 125

List of Symbols and

Abbreviations

Abbreviations

DTI diffusion tensor imaging

nFiT normalized fiber-tensor-fitnMI normalized mutual information

SVD (cerebral) small vessel disease

xv

g the nonrigidly deformed perfusion sequence

H(·) nonrigid deformation function of a perfusion sequenceTr(D) the trace of tensor (D)

Ifloating the floating image in registration

Iref the reference image in registration

M the affine transformation matrix

Pdef points in the deformed floating image

Pmov points in the floating image

ρ likelihood based on nonlocal contextual prior

V the principal axes of the brain

Chapter 1 Introduction

This thesis tackles nonrigid registration problems in medical imaging, ically, the myocardial perfusion Magnetic Resonance Imaging (MRI) and thecerebral diffusion MRI In Section § 1.1 we introduce the motivation of per-forming nonrigid registration of myocardial perfusion MRI and fiber-to-DTIregistration The scope and contributions of our work are highlighted inSection§ 1.2 Section § 1.3 states the organization of this thesis

To assess cardiac perfusion, a contrast agent is injected into the

patien-t, after which a series of MR images are acquired over time This ing technique is termed perfusion MRI (Kellman and Arai, 2007) in which

imag-1

the damaged heart muscle (ischemia) shows delayed and diminished trast enhancement Although the perfusion images are acquired according toelectrocardiographic-gated (ECG-gated) sequences so as to scan each frame

con-at the same phase of the cardiac cycle, the acquired heart images usuallyundergo position and shape changes caused by patient’s breathing and ar-rhythmia To trace the perfusion signal of each pixel over time, registration

of the perfusion sequence is required

Despite decades of research, general image-to-image registration ods cannot reliably compensate nonrigid heart deformations in perfusion se-quences because the intensity of heart ventricles varies over time due to thewash-in and wash-out of the contrast agent (Fig 1.1)

meth-§1.1 Motivation 3

Figure 1.1: A typical myocardial perfusion sequence (every 5th frame) aftercompensating global translation

Screening the cerebrovascular disease is more difficult than screening chemic heart disease because the brain fibers and cerebral small vessels aremuch smaller than the heart muscle To detect the abnormality of brainfibers, diffusion MRI, and its derivative, diffusion tensor imaging (DTI), arewidely used for their capability of measuring the diffusivity of water molecule

is-in the brais-in

Many registration approaches have been proposed in the literature fordiffusion MRI analysis However, most of these studies focus on the corre-spondences between images and do not directly cope with the brain fibers.Tractography, which refers to the reconstruction of neural fiber tracts, hasemerged as a powerful tool for diffusion MRI analysis Conventional tractog-raphy methods often early terminate at white matter (WM) lesion regionswhich are not the actual end of neural fibers but have low water molecu-lar diffusivity This early-termination issue often results in incomplete fiberreconstruction and hence making the subsequent analysis unreliable for cere-brovascular patients Additionally, since the topology of the brain is verycomplex and different regions correspond to different functions, tractographysegmentation is a necessary but challenging task We propose that brain fiberreconstruction and fiber segmentation can be accomplished by fiber-to-DTIregistration, which overcomes the aforementioned limitations of tractographyand provides inter-subject correspondences

§1.2 Scope and Contributions 5

This thesis studies the nonrigid registration problems in myocardial perfusionMRI and cerebral diffusion MRI For myocardial perfusion MRI, the goal is

to address the intensity variation across the perfusion sequences caused bythe contrast agent For cerebral diffusion MRI, we explore the feasibility ofachieving brain fiber reconstruction by performing nonrigid registration be-tween a fiber model and DT images This fiber-to-DTI registration approach

is advantageous in overcoming the early termination issue and is able toautomatically provide fiber segmentation and inter-subject correspondences

To facilitate the registration of perfusion MR sequences, a myocardialsegmentation method is introduced Besides, a generic multi-region segmen-tation method is presented to demonstrate the strength of contour-imageregistration and to elicit our free-form fibers method Nevertheless, the mainobjectives of this thesis are on the registration of myocardial perfusion MRIand cerebral diffusion MRI, and hence extensive validation of the segmenta-tion method is beyond the scope of this thesis

Our contributions towards the registration in perfusion and diffusion MRIare respectively briefed as below

Registration

Unlike conventional registration approaches that successively register twoframes within the perfusion sequence, we propose a Pseudo Ground Truth(PGT) based nonrigid perfusion sequence registration method which effec-

tively overcomes the intensity variation issue caused by dynamic contrastenhancement The PGT sequence is free from motion and noise, and isestimated from the observed sequence by applying spatiotemporal smooth-ness constraints It has almost identical intensity variations as the originalsequence and thus simplifying the multi-modality registration (between dif-ferent perfusion phases) problem into a single-modality registration (betweencorresponding frames of PGT and the observed sequence) problem The cor-responding frames between the PGT sequence and the observed sequence isregistered through an improved demons algorithm which emphasizes defor-mations on edges to avoid over-warping of the image texture.

We also propose a myocardial segmentation method to enhance the PGTestimation of myocardial perfusion sequence Thanks to the myocardial seg-mentation, we are able to define a region-adaptive temporal constraint and

a boundary-aware spatial smoothness constraint Consequently, a more curate PGT estimation is achieved and hence a better registration accuracyfor myocardial perfusion MRI

Applica-tion to Diffusion MRI

In medical image segmentation, preserving the shape and topology is essary in order to anatomically produce reasonable organ boundaries Weachieve this goal by reformulating the segmentation problem into a contour-image registration problem Unlike active contour models that only modelthe transformation of organ boundaries, we use free-form deformations (FFD)

nec-§1.2 Scope and Contributions 7

Figure 1.2: Comparison of corpus callosum bundles reconstructed by usingstreamline tractography (left) and our fiber-to-DTI method (right)

to model the deformation field of the entire image This contour-image istration method is able to simultaneously segment multiple objects and canpreserve their shapes and topologies by locally regularizing the deformationfield through B-spline parameterization

reg-Aiming for a robust brain fiber reconstruction and segmentation method,

we extend our contour-image registration method into a free-form fibers tem which directly maps a manually annotated whole brain fiber model todiffusion tensor images of new subjects Specifically, we design a novel fiber-to-DTI registration method which provides fiber tractography, tractographysegmentation, and inter-subject fiber correspondence in one attempt It en-forces the fiber integrity and hence overcoming the early termination issue.The fiber model is merged from 10 subjects such that the common fiber tract-

sys-s contribute more to the regisys-stration than fibersys-s of individual differencesys-s.Moreover, an automated registration correction method is proposed by usingrobust principal component analysis and a novel non-local contextual prior

§ 1.3 Thesis Organization

The rest of this thesis is organized as follows: Chapter 2 introduces thebackground knowledge of MRI, ischemic cardiac and cerebral diseases, andimage registration techniques, including the registration methods dedicated

to perfusion MR sequences and diffusion MRI respectively In Chapter 3,

we introduce the theory of PGT-based nonrigid registration and our tration system for myocardial perfusion MR sequences Chapter 4 describesour contour-image registration method and the free-form fibers system forbrain fiber reconstruction Our results are presented in Chapter 5 Chap-ter6concludes the thesis and discusses the advantages and limitations of theproposed methods as well as future work

regis-Chapter 2 Background

This chapter provides the background knowledge of magnetic resonance ing and its applications in ischemiac heart disease and cerebral small vesseldisease diagnoses respectively in Sections § 2.1-§ 2.3 The standard imageregistration techniques and the state-of-the-art in registration of perfusionMRI and diffusion MRI is reviewed in Sections § 2.4-§ 2.6

Magnetic resonance imaging (MRI) is a radiology technique that can imageinternal structure of the body It uses a strong magnetic field to alter themagnetization of the atoms in the body and produce a detectable rotationmagnetic field The rotation speed varies among different tissues and results

in MR images with good contrast between soft tissues such as fat, blood,muscles, brain matters, etc Although a typical MRI exam is more expensivethan a computed tomography (CT) or X-ray exam, MRI uses no ionizingradiation and is therefore much safer than CT and X-ray Moreover, MRI

9

provides better contrast for soft tissues than CT Further, some variations

of MRI have demonstrated the capability of revealing the dynamics of bloodflow and the microstructure in deep brain For these reasons, MRI has be-come a very important medical imaging technique especially in cardiovascularimaging and neuro-imaging

MRI

Ischemic heart disease is a kind of heart disease that refers to the reducedblood supply (i.e., ischemia) of the heart muscle (i.e., myocardium) It isreported to be the most common cause of death in Western countries asshown in (Kishore and Michelow, 2011, Fig 1.4) Therefore, the earlydetection of myocardial ischemia is of great importance

§2.2 Ischemic Heart Disease and Perfusion MRI 11

Myocardium

Left Ventricle

Right Ventricle

http://www.yale.edu/imaging/anatomy/heart_anatomy/index.html,while the right image is a real perfusion MRI scan, which is scanned alongthe short axis of the left ventricle as illustrated in the left image

First-pass myocardial perfusion MRI is a promising non-invasive tool forevaluating perfusion abnormalities and screening myocardial ischemia Theheart anatomy is shown in Fig.2.1 In a myocardial perfusion MRI study, theheart is scanned along short-axis slices immediately after a bolus injection of acontrast agent, and the concentration of the contrast agent is proportional tothe MR image intensity It is proven that ischemic myocardial muscle showsdelayed and diminished perfusion enhancement Hence, myocardial ischemiacan be identified and detected by assessing the intensity-time signals of allthe pixels.

Although the perfusion images are acquired using ECG-gated sequencessuch that the slice is scanned at the same phase of the cardiac cycle, the heartusually undergoes position and shape changes caused by patient’s breathingand arrhythmia To precisely trace the perfusion signal of each pixel overtime, accurate registration of the perfusion sequence is required

Figure 2.2 compares the myocardial perfusion signals before and afternonrigid myocardial perfusion registration Without nonrigid registration(yellow and pink plots), the heart undergoes shape change during scanning,and therefore the intensity-time profile of a pixel around the boundary be-tween tissues is a combination of the perfusion signals of neighboring tissues.Consequently, the perfusion map shows ghosting around boundaries (see thetop right image of Fig 2.2), and the signals do not reflect the actual my-ocardial perfusion To monitor the real intensity-time profile, and hencethe concentration of the contrast agent over time, nonrigid registration isnecessary

§2.2 Ischemic Heart Disease and Perfusion MRI 13

Global Translation

Proposed Method Intensity-time profiles for a pixel

Figure 2.2: The rigid and nonrigid registration in myocardial perfusion MRI.The left figure plots the intensity-time profiles of a pixel The intensity-time profile before nonrigid registration exhibits significant oscillations due tomyocardial wall motion and therefore the signal is a combination of differenttissues On the contrary, the profile after nonrigid registration is smooth Onthe right shows the myocardial perfusion maps generated using maximum up-slope The top image shows the perfusion map before nonrigid registrationwhich exhibits ghosting effects due to the misalignment between differentperfusion phases The bottom image shows the perfusion map after nonrigidregistration which is free of ghosting

§ 2.3 Small Vessel Disease and Diffusion MRI

Cerebral ischemic small vessel disease (SVD) refers to the damage to tinyblood vessels lying deep in the brain SVD is common in older people and

is the leading cause of vascular dementia (Joutel et al., 2010) which maylead to cognitive dysfunction such as slow information processing or memoryproblem (Roman et al., 2002; Prins et al., 2005) SVD is also a major con-tributor to stroke (Joutel et al., 2010) which may lead to rapid loss of brainfunctions and permanent neurological damage, or even death Therefore,early detection of cerebral ischemic SVD is very important

Assessing cerebral ischemic SVD with conventional MRI techniques isdifficult due to the small scale of vessels and the complex topology of thebrain (see Fig 2.3) Moseley et al (1990) found that the water diffusiondecreases in the early stage of the cerebral ischemia and since then diffu-sion MRI has demonstrated strength in capturing such decrease in cerebralischemia (Warach et al., 1992)

§2.3 Small Vessel Disease and Diffusion MRI 15

Figure 2.3: Talairach coordinate system of the human brain (Lancaster et al.,

1997, 2000) Top sagittal view; bottom left coronal view; bottom right axial view

-Diffusion MRI or diffusion weighted MRI uses bipolar magnetic field dient pulses to capture the random translational motion of molecules, i.e.,the molecular diffusion During diffusion MR scanning, the movement ofwater molecule, which is about 10 µm, in the direction of the input magneticfield gradient is perceived and results in a diffusion MR image with voxelsize of several mm3 Repeating such a procedure with n different directionsresults in a 3D-image, of which each voxel is an n-D vector recording the wa-ter molecular diffusivity It is important to note that the water motion is aBrownian motion, rather than the real water flow This diffusion information

gra-of water molecules provides the structural and geometrical cues gra-of the tissue

it belongs to Such diffusion information is not available in conventional T1

or T2-weighted MRI (Le Bihan et al., 2001)

The most important and unique information provided by diffusion MRI

is the directional information when the molecular mobility in tissues variesamong different directions Such directional property is termed anisotropy.Since the molecular diffusion in fibers’ direction is faster than that in theperpendicular direction, one can infer the fiber direction through diffusionMRI As the diameter of brain fiber is much smaller than the voxel size ofMRI, this fiber direction is the overall direction for the axons within thevoxel

§2.3 Small Vessel Disease and Diffusion MRI 17

Figure 2.4: Diffusion tensor imaging which uses a tensor for each voxel todescribe the water molecular diffusivity

A diffusion MRI can have up to more than 100 channels which are dundant and difficult to process To simplify the processing, the diffusivity

re-of each voxel is usually represented by a 3 × 3 matrix

where Tr(D) is the trace of tensor D

Brain fibers reconstruction, i.e., tractography, is important in diffusionMRI analysis Conventional methods (Ducreux et al.,2005;Calamante et al.,

2010) reconstruct the brain fibers by linking the principal directions (a1

§2.4 Introduction to Image Registration 19

in (2.2)) of tensors This streamline algorithm starts from a seed input andgrows by linking the principal directions of tensors as long as the FA value

is above a predefined threshold When it reaches a voxel that has a verylow FA value (lower than the threshold), it assumes the end of the fiber isreached and stops growing

The streamline tractography method generally works well for healthy jects, but suffers from an early termination issue for SVD patients (the yel-low rectangle in Fig 1.2) As we previously introduced, cerebral ischemiadecreases water molecule diffusivity and hence leads to a low FA value (Mose-ley et al., 1990) Once the FA value is reduced to lower than the threshold,

sub-it stops the fiber reconstruction and all the rest parts of the fiber are missed.Besides, any inaccurate estimation of the principal direction of a single ten-sor along the fiber may result in an outlier fiber branch in the reconstruction(the red rectangle in Fig 1.2)

The standard image registration (Hajnal et al., 2001; Zitova and Flusser,

2003) approach deals with two images capturing the same, or similar, tent The two images are usually acquired at different circumstances Forinstances, at different times, in different viewpoints, or by different types ofscanners like MRI vs CT Therefore, the corresponding objects in the twoimages are usually misaligned and may be different in size, orientation, orshape To find the corresponding regions/objects within these two images,one image is deformed, either rigidly or nonrigidly to match the other The

con-The floang image

The reference image

Nonrigid Affine

Aligned? No

Yes

Output

Figure 2.5: A typical registration process The nonrigid registration is formed by the free-form deformation demo using mutual information as thesimilarity measure (Kroon, 2011)

per-image being transformed is called the moving per-image or the floating per-image,while the image used as the reference is called the static image or the refer-ence image A typical registration process is illustrated in Fig 2.5

To evaluate the quality of match between the transformed floating image andthe reference image, a similarity measure is necessary The similarity measure