a survey of shaped-based registration and segmentation techniques for cardiac images

8/12/2019 A Survey of Shaped-based Registration and Segmentation Techniques for Cardiac Images

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A survey of shaped-based registration and segmentation techniques

for cardiac images

Vahid Tavakoli , Amir A. Amini 1

University of Louisville, Louisville, KY, United States

a r t i c l e i n f o

Article history:

Available online 30 April 2013

Keywords:

Cardiac CT

Cardiac motion

Cardiac MRCardiac segmentation

Cardiac registration

EchocardiographyReview article

a b s t r a c t

Heart disease is the leading cause of death in the modern world. Cardiac imaging is routinely applied forassessment and diagnosis of cardiac diseases. Computerized image analysis methods are now widelyapplied to cardiac segmentation and registration in order to extract the anatomy and contractile function

of the heart. The vast number of recent papers on this topic point to the need for an up to date survey inorder to summarize and classify the published literature. This paper presents a survey of shape modeling

applications to cardiac image analysis from MRI, CT, echocardiography, PET, and SPECT and aims to (1)introduce new methodologies in this field, (2) classify major contributions in image-based cardiac mod-

eling, (3) provide a tutorial to beginners to initiate their own studies, and (4) introduce the major chal-lenges of registration and segmentation and provide practical examples. The techniques surveyed include

statistical models, deformable models/level sets, biophysical models, and non-rigid registration usingbasis functions. About 130 journal articles are categorized based on methodology, output, imaging sys-tem, modality, and validations. The advantages and disadvantages of the registration and validation tech-

niques are discussed as appropriate in each section.2013 Elsevier Inc. All rights reserved.

1. Introduction

The heart is the most energetic organ in our body. Beating aboutevery second, it continuously supplies the body with vital oxygen-carrying blood. Heart disease is the leading cause of death in

modern countries [13]. The mortality rate of CVD is estimatedto be 17 million in 2005 and thus is ranked as the top killer world-

wide[35]. According to the AHA update of 2009, CVD is the causeof 10% of days of lost productivity in low- and middle-incomecountries, and 18% of days of lost productivity in high income

countries. CVD morbidity rates are estimated to rise from around47 million days globally in 1990 to 82 million days in 2020[46].

Analysis of the cardiac function using imaging instruments hasshown to be effective in reducing the mortality and morbidity ofCVD. Myocardial motion analysis is time consuming and suffers

from inter and intra-observer variability. Computerized analysiscan help clinicians to interpret the medical conditions objectively

[1,79]. Cardiac image processing techniques, mainly categorizedas segmentation and registration, have been used widely to assess

the functionality of the heart[1014]. Cardiac image segmentationprovides us with high quality structural information of the heartwhile registration techniques calculate the local functional analy-sis helpful in diagnosis and treatment planning of patients. Model-ing of the cardiac shape, motion and physical structure have played

a major role in the development of the image analysis algorithms.Previously, there have been some review papers in the field ofcomputer analysis of cardiac imaging[15,16]. Some review papershave focused on echocardiography segmentation [17], cine MR

segmentation[18]or Tagged MRI[19,20]. Frangi et al.[16]classi-fied cardiac modeling techniques to three classes: surface models,

1077-3142/$ - see front matter 2013 Elsevier Inc. All rights reserved.http://dx.doi.org/10.1016/j.cviu.2012.11.017

Abbreviations:AAM, Active Appearance Model; ASM, Active Shape Model; CT,

Computed Tomography; CVD, Cardiovascular Disease; MRI, Magnetic Resonance

Imaging; EB, Expert Based; EDV, End Diastolic Volume; EF, Ejection Fraction; EFFD,Extended Free Form Deformation; EM, Expectation Maximization; Endo, Endocar-

dium; Epi, Epicardium; ESV, End Systolic Volume; FE, Finite Element; FFD, Free

Form Deformation; GMM, Gaussian Mixture Model; Four CH, Four chamber; GRPM,Generalized Robust Point Matching; LA, Left Atrium; LADA, Left Anterior Descend-

ing Artery; LAX, Long Axis; LCX, Left Circumflex; LV, Left Ventricle; MI, MutualInformation;MIA, Medical Image Analysis; MRI, MagneticResonance Imaging;MRF,

Markov Random Field; N, Normal; NMI, Normalized Mutual Information; N/A, Not

Applicable; NURBS, Non-Uniform Rational B-Spline; P, Patient; PCA, Principal

Component Analysis; PET, Positron Emission Tomography; PM, Papillary Muscle;

RA, Right Atrium; RPM, Robust Point Matching; RV, Right Ventricle; SAD, Sum

Absolute of Differences; SAX, Short Axis; SM, Sonomicrometry; SPECT, Single

Photon Emission Computed Tomography; SSD, Sum Square of Differences; TDI,

Tissue Doppler Imaging; TEE, Trans-Esophageal Echocardiography; TMI, Transac-tion of Medical Imaging; US, Ultrasound. Corresponding author. Address: Room 410, Lutz Hall, University of Louisville,

Louisville, KY 40292, United States. Fax: +1 502 8764534.

E-mail addresses: [email protected](V. Tavakoli), amir.amini@louisville.

edu(A.A. Amini).1 Address: Room 409, Lutz Hall, University of Louisville, Louisville, KY 40292,

United States. Fax: +1 502 8764534.

Computer Vision and Image Understanding 117 (2013) 966989

Contents lists available at SciVerse ScienceDirect

Computer Vision and Image Understanding

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c v i u
http://dx.doi.org/10.1016/j.cviu.2012.11.017mailto:[email protected]:amir.amini@louisville.%20edumailto:amir.amini@louisville.%20eduhttp://dx.doi.org/10.1016/j.cviu.2012.11.017http://www.sciencedirect.com/science/journal/10773142http://www.elsevier.com/locate/cviuhttp://www.elsevier.com/locate/cviuhttp://www.sciencedirect.com/science/journal/10773142http://dx.doi.org/10.1016/j.cviu.2012.11.017mailto:amir.amini@louisville.%20edumailto:amir.amini@louisville.%20edumailto:[email protected]://dx.doi.org/10.1016/j.cviu.2012.11.017http://crossmark.dyndns.org/dialog/?doi=10.1016/j.cviu.2012.11.017&domain=pdf


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volume models, and deformable models. The review focused on 3Dcardiac modeling techniques based on different modalities namely

angiography, cardiac US, isotope imaging, cardiac CT, and MRI.With the increasing number of the cardiac modeling techniques,a review article to summarize recent efforts is timely.

This survey aims to (1) classify major contributions in the field

of cardiac modeling, (2) introduce the methodologies in this field,(3) tutor beginners to initiate their research, and (4) introducethe major challenges of registration and segmentation with exam-ples. The techniques developed in the last 10 years are classifiedas: statistical models, deformable models/level sets, biophysical

models, and non-rigid registration methods. The articles are classi-fied in different tables describing the method, database, and outputof the technique. The novelties of the methods are described in rel-evant sections and are compared to alternative algorithms. The

advantages and disadvantages of each category are discussed aswell and different approaches to validation are classified.

The surveyed articles in this review are from major journalssuch as IEEE Transaction on Medical Imaging, Medical Image Anal-

ysis, IEEE Transaction on Image Processing, IEEE Transaction onInformation on Biomedicine, Ultrasound in Medicine and Biology,International Journal of Computer Vision, Computer Vision and Im-

age Understanding, IEEE Transaction on Biomedical Engineering,Cardiovascular Magnetic Resonance, and Journal of Magnetic Reso-nance in Medicine.

1.1. Cardiac anatomy

The heart is composed of a muscular contractile organ (myocar-dium) surrounded by two layers of connective tissue inside andoutside called endocardium and epicardium, respectively. Theheart has four chambers and four major valves (Fig. 1). LV, the

prominent chamber of the heart, is the major contractile chamber,and maintains the systemic circulation. Myocardial contraction ismaintained by a circulatory system of coronary arteries that sup-

plies the muscle with oxygenized hemoglobin and nutrients. Coro-nary arteries (right and left) are two branches of the aorta andsupply the myocardium through smaller branches such as LCX,LAD and diagonal arteries[2].

Due to atherosclerosis, the coronary arteries may gradually be-

come occluded and end in CAD (Coronary Artery Disease).

Coronary occlusion leads to disturbance in the cardiac contractilityand causes global or regional dysfunction in the heart and may be

diagnosed using state-of-the-art medical imaging techniques suchas echocardiography, MRI, CT, and nuclear medicine[2]. In study-ing ventricular motion, physicians typically assign a subjective seg-mental function score to different segments of the ventricles:

Normokinesia (0): The myocardial motion and thickening isnormal.Hypokinesisa (1): The affected segment moves slower andthickens less than normal.

Akinesia (2): The infarcted region has totally lost its ability tocontract in the systolic phase and moves passively along withits surrounding myocardial tissue.Dyskinesisa (3): The infarcted region moves paradoxically and

bulges out during systole due to the ventricular blood pressure.Aneurysm (4): The infarcted region undergoes remodeling,becomes thin, bulging outwards during the systolic phase likea balloon, leading to rupture and death[9].

The cardiac blood circulation is an alternation of two phases:diastole (relaxation phase) and systole (contraction phase). Nor-

mally 70% of the whole LV blood in end diastole is ejected out dur-ing systole. The Ejection Fraction (EF) ratio is an index of global LVfunction. EF is calculated as (EDVESV)/EDV where EDV is the vol-ume of the LV at end-diastole and ESV is the volume of the LV dur-ing end-systole. Ventricular walls thicken during systole this is

typically referred to as wall thickening and has been proven tobe a very reliable index of regional myocardial function. Heart fail-ure is characterized by a significant decrease in the EF. An addi-tional index of cardiac performance is myocardial mass which

can be determined from myocardial volume, assuming the myocar-dium to have uniform density[9].

2. Cardiac imaging modalities

There are several cardiac imaging modalities that are in wide-spread use. These include MRI, CT, echocardiography, and nuclear

medicine. Each method has advantages and draw backs that are dis-cussedin this section. MRI, CT,and Echocardiographyare amenabletocomputer analysis and much effort has been devoted to automated

processing of images from these modalities. In comparison, nuclearmedicine has seen less effort devoted to computerized analysis.

2.1. MRI

Magnetic Resonance Imaging (MRI) uses a magnetic field toalign the magnetization of hydrogen nuclei in the body. Subse-quently radio frequency pulses change the alignment of this mag-

netization and produce a rotating magnetic field detectable by anexternal RF coil. MRI uses non-ionizing radiation and is considereda non-invasive technique. Contrast may be used for further signalenhancement. Contraindications to use of MRI include pacemakers

and metal implants. With MRI, different segments of the myocar-dium are well visualized and can be easily reconstructed in 4D for-mat. An advantage of MRI is that it is possible to acquire imageswith different orientation with no image processing (no reslicing

is necessary). An advantage of MRI in comparison to other imagingmethods is that it permits evaluation of perfusion (first past perfu-sion), function (cine and tagged imaging), scars (Late-GadoliniumEnhancement imaging), as well as epicardial coronaries. However,

MRI is more costly than other methods, (particularly echocardiog-raphy) and is not available in all cardiac care centers. Cine MR is

able to achieve high resolution images with respect to the cardiacborder but the contrast is not as helpful inside the cardiac wall.

Fig. 1. Anatomical components of the heart labeled separately as LV, RV, LA, RA,

Aortic valve (A), Tricuspidvalve (T), Pulmonic valve (P), Mitral valve(M). (FromYalecardiac atlas: www.yale.edu/imaging/contents.html.)

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An MR imaging protocol named tagged MRI uses spin tagging pre-pulses to produce markers inside the myocardium over time, which

can be tracked, permitting the possibility to compute dense myo-cardial motions and the strain. One drawback of this method isthe fadingof the tag lines over time, which is especially pronouncedin diastole, when imaging with no trigger delay. A solution to this isto apply a trigger delay in order to visualize diastolic function of the

heart. Cardiac cine-MRI is considered the standard MR techniquemainly used for global function measurements and segmentationwhile taggedMR techniques are used for regional analysis andtem-poral registration [7]. MR images acquired with orientation perpen-

dicular to the long axis of the heart (the line which connects theapex to the outflow tract) is called Short Axis plane (SAX) (Fig. 2).Imaging of the heart in cine MRI covers about 1015 slices and1530 frames, depending on the size of the heart, prescribed slice

thickness, the heart rate, and specific approach to image acquisi-tion.Fig. 3shows SAX images in cine and tagged MR series duringdifferent cardiac cycles. Images acquired parallel to the long-axisaxis arecalled Long Axis (LAX) images andare sometimes combined

with SAX images for better visualization of the anatomy as well asfor computing true 3-D motion (including the through-plane mo-tion). Cardiac images are not specific to the heart and certainly in-

clude non-cardiac tissue as well. To decrease the computationaltime, a region of interest (ROI) can be computed that only includesthe heart tissue. On a usual (gradient echo) cine MR image, theblood pools is white and the myocardium is black; however, blackblood imaging renders the blood pool dark [7,19,20]. Other submo-

dalities of CMRinclude Late-Gadolinium-Enhancement(LGE) imag-ing for visualizing scarred tissue, coronary MRA for visualizing thecoronaries, multinuclear spectroscopy for spectroscopic imagingbased on Carbon, Sodium, or Flourine, and first-pass perfusion

imaging to visualize the ischemic myocardium. Flow imaging(e.g., phase-contrast) MRI can also be used to reveal flow and mo-

tion information for blood flowinside vessels which may be locateddeep within the body or to determine ventricular wall motion[7].

2.2. Echocardiography

Echocardiography utilizes the backscattered ultrasound wavegenerated by an array of piezoelectric crystals to acquire images of

different tissues. It has important advantages including, portability,non-invasiveness, use of non-ionizing radiation, real-time, and lowcost. However, echocardiography, in general, suffers from poor con-trast, noisy images, sub-optimal visualization of the cardiac seg-

ments, air/bone interaction problems causing reverberationartifacts, and reproducibility and operator dependence issues. Anadditional disadvantage in the overweight patients is the inabilityto obtain an acoustic window since there is a need to bypass thelungs and the ribcage to image the heart[8,9]. Doppler imaging is

possible with USand may beusedto compute thevelocity of movingparticles(and measureblood flow). However,use of DopplerUS onlypermits computation of the tissue/blood motion in the direction ofthe ultrasound beam (called the angle of insonification)[8,9].

3D echocardiography images can be obtained using recentsophisticated 3D ultrasound transducers by using a miniaturizedarray of piezoelectric crystals. Real time 3D scanners were intro-duced in the early 1990s but in comparison to 2D echocardiogra-

phy, initial images suffered from low spatial resolution. Newhigh-tech transducer arrays have significantly improved spatialresolution and image quality as a result, 3D imaging is enjoyingmore wide-spread use[8,9].

Fig. 2. (a)Illustration of Short-Axis (SAX) andLong-Axis (LAX) cardiac images in a normal subject,(b) cardiac Cine MRI, LAX (C) Cardiac Cine MRI SAX (1:LV,2:RV), (d)A close-up of the SAX image showing the epicardium and endocardium and Papillary Muscles (PMs) shape variability.

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Ultrasound images have a texture pattern usually referred to asspeckle. Speckle formation is the result of the diffuse scattering ofthe ultrasound wave encountering random interference with scat-

terers which are very tiny particles of size comparable to the wave-

length of the ultrasound wave. These scatterer particles do notsimply reflect or refract the ultrasound wave but induce a morecomplex diffuse scattering which is the basic physical concept of

speckle formation. Speckle is considered an inherent property ofthe ultrasound image notorious for having spatial correlated mul-tiplicative noise and making the ultrasound images unreliable.Speckle tracking techniques try to use these same speckle patterns

to detect the cardiac motion in echocardiographic frames. Dopplerimaging is also utilized for computing the velocity of blood as wellas that of the myocardium. When applied to image tissue veloci-ties, the technique is referred to as Tissue Doppler Imaging or

TDI for short[8,9].

2.3. CT

4D cardiac CT allows non-invasive imaging of the detailed car-diac anatomy with high contrast and exquisite resolution; espe-

cially useful for the assessment of coronary artery structure.However, it is not as widelyavailable as echocardiography and usesionizing radiation. Cardiac multi-detector computed tomography(MDCT) is able to acquire moving images of the heart that rivals

cine MRI (though with reduced temporal resolution) as a detailedsourceof information (Fig. 5). Initial generations of CT systems werenot able to provide accurate images of the heart due to its fast mo-tion. Now a days, MDCT scanners such as 64 (128, 256, or 320)

detector-row CT scanners and dual source CT scanner are availablewith multiple gantry rotations in one second acquiring several CTslices (64 slice for a 64 row CT scanner). It is foreseeable that CT

technology will advance to the point of covering the entire heartin a singlerotationand in a singlecardiaccycle. Also, useof iterativereconstruction techniques has thepotential to permit theuse of lowdose, high quality scans. CT angiography (CTA) is very sensitive for

diagnosis of coronary artery, by-pass graft, and stent abnormalities.It is able to acquire unique visualization of the coronary arteriesincluding narrowing, type and degree of atherosclerosis plaque.Additionally, it canalso be used to simultaneously visualizethe pul-

monary andsystemicarteriesas well as the thrombosis. Despite theexpense, cardiac CT is becoming more widely available in cardiaccare centers andmay be an alternative to diagnostic catheterizationwhich is invasive and costly. Recent advances in cardiac CT with

contrast (late enhancement CT) also permit visualization of scarredmyocardium (similar to LGE imaging in MRI) and also the possibil-

ity to utilize a range of X-ray energies to perform tissue character-ization (this is referred to spectral CT)[7,8,10].

2.4. Radioisotope imaging

Nuclear medicine techniques such as Positron Emission Tomog-

raphy (PET) and Single Photon Emission Computer Tomography

(SPECT) use the gamma-ray or positron emission of injected radio-pharmaceuticals in order to image the myocardium. The injectedradiotracers are taken up in particular tissues, such as malfunction-

ing or dead myocardium, and continue to irradiate positrons(which lead to emission of gamma-rays) during decay, permittingvisualization of the metabolism and function of the heart. SPECTstudies, which make use of Thalium or Technetium, are routinely

utilized to image myocardial perfusion. Imaging can be performedat rest or under pharmacologic stress (e.g. adenosine) to measurethe perfusion reserve and defects (Fig. 5). The wash-out of the iso-tope is the long acquisition time which is in the range of 30 min to

3 h while the patient should stay still. Although radio-tracer stud-ies pose some risk to the patient, they have proven to be extremelypowerful with high sensitivity and specificity in the assessment of

patients with coronary artery disease and in determining the terri-tory with perfusion defects. Fluroro-Deoxy-Glucose (FDG) is usedin the case of PET to image myocardial metabolism. In fact, withFDG PET it is possible to distinguish between necrotic vs. stunned

vs. hibernating myocardium. PET is the only modality which canconclusively determine myocardial viability and is typically usedas ground-truth in multimodality studies[1014].

Albeit the importance and prevalence of nuclear cardiology in

clinical care of patients, nuclear techniques (especially PET) arevery expensive and furthermore the resolutions are nowhere nearother modalities. Perhaps, this has contributed to decreased enthu-siasm of computer vision researcher to develop automatic and

quantitative techniques for this modality.

2.5. Cardiac segmentation and registration challenges

Cardiac segmentation consists of the segmentation of the epi-cardium and the endocardium of LV, RV, LA, and RA.Epicardial seg-

mentation: In general epicardial delineation is more difficult thanendocardial delineation due to the similarity and fuzziness of thegray level of the outer tissues and the heart and poor contrast.Endocardial contour has a good contrast due to the large intensity

variation of the blood and the myocardium in all the modalities.Endocardial segmentation: Endocardial delineation is not straight-forward due to the Papillary Muscles and myocardial trabeculationridges visible in MR, echo and CT (Figs. 35). Local image features

such as intensity and gradient do not represent the real contoursnear the Papillary Muscle. Since clinicians consider the Papillary

Muscle as a part of the blood pool, it is usually not segmented inthe current algorithms. Some of the challenges are shown inFig. 6.

Fig. 3. (a) Cine MRI and (b) Tagged MRI data at the basal, mid-LV, and apical sections in different phases of the cardiac cycle in a canines heart (systole to diastole), (1:LV,

2:RV). For the Mid-LV slices good visualization of LV and RV can be achieved due to the larger size of the chamber for these cross section. The apical slices however result in

poor visualizations since these chambers are small or non-existent at the apex. Basal slices on the other hand are complicated with atria and the great vessels.

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2.5.1. RV, RA, LA, and great vessel segmentation

The shape of the RV is also more variable and concave and thusmore challenging than the LV. The RV chamber is present in fewslices and the RV wall is thinner with respect to the LV wall andtherefore the epicardium and endocardium are close to each other

and more difficult to segment. Atria and great vessels are onlypresent in 24 slices. They are especially difficult to delineate inechocardiography images but easier to deal with in CT series dueto the better spatial resolution and visibility.

2.5.2. Apical and basal slices

Additionally apical slices are more difficult to segment in all themodalities due to less information, unpredictable end of the LV andRV cavities, vicinity of diaphragm, more variable shape and motionof the contours and haziness of the tissue. Indeed, even manual

segmentation of the tip of the heart (apical slices) is difficult. Basal

slices are also more cumbersome to segment due to highly variableshape and motion of the LV and RV walls and cavities in the basalslices as well as the vicinity of the atrial and great vessel lumens.

2.5.3. Pixel resolution anisotropyPixel resolution anisotropy is a common issue in MRI and CT

segmentation and registration. The resolution of the pixels in the

spatial direction is not the same as the resolution of the pixel inthe through plane direction.

2.5.4. Motion estimation

With respect to motion estimation, out-of-plane error (through-plane error) is a common issue in any 2D technique and therefore3D motion detection is suggested to cope with the problem. How-ever 3D cardiac imaging usually requires a longer acquisition per-

iod, slice misregistrations, ECG gates, and breath-holding [7].

Fig. 4. Different echocardiographic views with corresponding anatomy (a) transthoracic short-axis view (b) four chamber apical view (From atlas of Echocardiography,http://

www.yale.edu/imaging/echo_atlas/contents/index.htm), (c) a four chamber image, - red boxes show the invisible and dropout regions causing registration and segmentation

challenges. The Papillary Muscles and valve cords can interact with the real endocardial contoursas well (1:LV, 2:RV, 3:LA, 4:RA). (For interpretationof the referencesto color

in this figure legend, the reader is referred to the web version of this article.)

Fig. 5. (a) Cardiac CT SAX image during diastole, (b) cardiac CT SAX image during systole, (c) cardiac SPECT data http://bocaradiology.com/Procedures/cardiac.htm.

Fig. 6. Illustrationof some segmentation challenges in cine MR cardiac images: (a) interaction of the neighboring structures in segmentation of epicardiumin apical views of

caninecine MRI this is because the LV shape is small andfuzzy, (b)interactionof theneighboring structures in segmentation of LV in basal views of caninecine MRI this is

because the other chambers are comparable in size to the LV for basal locations, (c) interaction of the Papillary Muscle intensity causing the Papillary Muscles to be includedas part of the myocardium in human cine MRI.



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Although cine MRI has excellent cardiac contour contrast, itlacks the myocardial contrast inside the cardiac wall and, there-

fore, it is not suitable for dense motion analysis and strain estima-tion. Tagged MRI is suitable for this purpose. The tag line markerscan be tracked through the cardiac frames but they fade outthrough the cardiac cycles and are washed out and less usefulespecially during the diastole.

2.5.5. Special issues in echocardiography images

Since echocardiography is performed by hand, several views

can be acquired using different transducer orientations. Theseviews are not the same especially in the task of segmentation. An-other shortcoming is the fact that in both 2D and 3D echocardiog-raphy data, the contour of the epicardium or endocardium may be

incomplete simply because it is out of the region of the transducercoverage. The endocardial and epicardial contours have even lesscontrast in echocardiography due to the noisy structure of theultrasound images. Different types of ultrasound artifacts contrib-

ute to this problem as well, especially drop out artifact that hap-pens when the tissue contour is in the direction of the ultrasoundbeam. Another feature of ultrasound images is the speckle pattern.

The shift varying PSF in echocardiography makes decorrelation inthe RF signal and the B-mode image which leads to higher errorin the registration methods. Artifacts and the presence of air andbone also contribute to less accurate results.

3. Methodological classification

Calculation of important cardiac indices such as cardiac vol-umes and Ejection Fraction are based on accurate segmentation

of the heart chambers while computation of the regional displace-ments and mechanical indices of cardiac function are related totemporal registration of the imaging data. Segmentation and regis-tration can be performed via techniques that will be discussed in

this section.

Bottom up methods: Such as thresholding, morphological, pixelclassification and edge-based techniques were among the firsttechniques to be used in the field of cardiac image analysis due

to their simple and intuitive nature. However cardiac texture hasa wide intensity range that is not completely detectable by pixel-driven techniques. Additionally, object boundaries do not neces-sarily overlay on the edges. This problem can be tackled by using

additional assumptions derived from the cardiac structure, statis-tics and physics.

A large number of methods have been developed for cardiacfunctional and anatomical modeling. In this section, we classify

the modeling techniques into four categories described in Tables14. These are (1) statistical models, (2) deformable models/levelset, (3) biophysical models, and (4) non-rigid registration using ba-

sis functions. However the boundaries of each class are not exact.Several papers have combined two or more different classes inthe same algorithm. In this situation, the papers are classifiedaccording to the most relevant group. The tables cover about 130

journal article published in the last 10 years.Key to the tables: Each table consists of several columns repre-

senting authors, modality, dimension of the method, vendor, out-put of the algorithm, description of the algorithm, types of

validation, and type of data. The number of cases in the validationdataset is mentioned in parenthesis as normals (N) or patients (P).Most of the papers use 2D or 3D human data for validation butsome papers focus on dogs, or computational/ physical phantom

data. The output of the proposed methods can be the contour ofthe endocardium only (endo), epicardium (+Epi), RV (+RV), atria

(+A), great vessels (+V), Tag lines (+tag) or motion vectors (+M).Since any segmentation method delineating the epicardium or

the RV also delineates the endocardium, the key (endo) is usedfor methods that only segment the endocardium. In some cases,

parameters such as the number of the data and vendor are missing,are incomplete or unclear and are left blank in the table.

3.1. Statistical methods

Since intensity is not a perfect descriptor of the contours in car-diac images, statistical techniques are finding ever increasinginterest in their area. In general, the heart is a convex, and exclud-ing a few conditions such as a cardiac aneurysm, can be modeled as

an ellipsoidal object that moves in- and out-wards [13]. Thereforeuse of statistical priors, including shape, motion or texture, can aidin the cardiac segmentation and registration tasks. Statisticalmethods can be classified based on use of shape prior, Active Shape

Model, Active Appearance Model[21,22]and motion model. Eachsubcategory will be discussed separately in this survey. Table 1contains the statistical articles [2334,22,3570]classified basedon the structure, method, vendor, dataset, and output.

3.1.1. Shape prior

The LV cavity looks like a truncated ellipsoid while the RV cavity

is thinner and crescent shape. The LV wall is three times thickerthan the RV wall. Several authors have tried to use the expectedshape of the heart as a prior in aiding automated segmentationand registration. The prior is typically incorporated as an addi-tional constraint to overcome the failures of intensity or edge

based energy functions to uniquely determine the anatomicalboundaries.

3.1.1.1. Simple shapes as prior. Since the LV contour resembles an

ellipse; a fast approach for building a prior is to use an ellipsoid.Pluempitiwiriyawej et al. [53] utilized an ellipsoid with 5 de-grees of freedom as prior. The five parameters defined the loca-tion, size and scale of the ellipsoid. The distance of the contour

to the ellipsoid was used as the ellipsoid constraint. The authors

also added two additional energy terms for the ellipsoid shapeprior: 1. stochastic region based term based on modeling the dis-tribution of the pixels inside and outside the contour; 2. an edge

based term similar to a snake (latter will be discussed in Sec-tion 3.2) energy function to attract the contour toward theedges. The combined energy functional is used in a level setframework (latter to be discussed in Section 3.2) in order to seg-

ment 2D short-axis cine MR images. The advantage of this meth-od is using five degrees of freedom, which can decrease thecomputation.

3.1.1.2. Previous contour. Practically, the shape of contours does notchange dramatically, as they move from one cardiac image to thenext in the spatial or temporal direction. Therefore, a simple ap-

proach to modeling and segmenting the cardiac cavity in 3-D isto use the contour already segmented to locate the contour inthe next slice or the next time point. Chenuoune et al. [50] usethe previous frame as the prior incorporated in a level set (Sec-

tion 3.2) technique. In the first step, the endocardial border ofSAX cine MR images are segmented based on a level set method.The previous contour is then registered using morphology opera-tors to the next frame as a shape prior. Using the previous contour

can decrease the computation but can cause local minima problemas well.

3.1.1.3. Learned shape. Another method uses a learned shape de-

rived from a training step with manually delineated images. Tsaiet al.[28]used a shape prior computed by applying Principal Com-

ponent Analysis (PCA) to a collection of signed distance represen-tations of manually segmented data. Subsequently, the shape

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Table 1

Statistical Methods: Shape prior, Active Shape Models and Active Appearance Models.

Method category Reference Modality/dimension/scanner Output Description Validation (# of Data)

Shape based

(Shape Prior,ASM)

Koikkalainen et al.[23] Cine MR, 3D, Siemens Vision/

Sonata

+Epi +RV A s et of different methods 3D human (20), EB

Suinesiaputra et al.[24] Cine MR, 2D, Philips Gyroscan +Epi ICA decomposition 3D Human (N:44, P:45),

EB

OBrian et al.[25] Cine MR, 3D, GE Genesis Signa +Epi PCA, contour coupling for

unseen contour

3D Human (33), EB

van Assen et al. [26] Cine MR, 3D, Philips Gyroscan +Epi Fuzzy feature detection 3D Human, EB

Lorenzo-Valds et al.[27] Cine MR, 3D, Siemens Sonata +Epi+ RV EM incorporated in ASM 3D Human, EB

Tsai et al.[28] Cine MR, 3D, N/A +Epi Shape prior and level set 2D Human (1), EB

Sanchez-Ortiz et al.[29] Echo,3D, Philips Sonos 7500 endo Phase-based acoustic

feature detection

3D Human (9), EF

compared by SPECT

MUGAJacob et al.[30] Echo, 2D, Philips Hewlett

Packard SONOS 5500

endo Dynamic Snake Model 2D Human (N:4, P:5), EB

Esther Leung et al.[31] Echo, 2D, Philips Sonos 7500 endo Shape Model applied to

the invisible regions

3D Human (35), EB

Song et al.[32] Echo, 2D, +Epi Gradient direction

feature

2D Human (N:29, P:45),

EB

Lorenz and von Berg[33] CT, 3D, Philips Brilliance +Epi + RV + A Deformable mesh 3D Human (27), EB

van Rikxoort et al. [34] CT, 2D endo Atlas model 3D Human (29), EB

Frangi et al.[22] Cine MR, 3D, Philips PoweTrak

6000

+Epi B-spline registration 3D Human, EB

Peters et al.[35] CT/ Cine MR Epi + RV + A + V Distance to the model 3D Human CT (28) &MR(42), EB

Zhou[36] Echo, 2D, Multivendor endo Shape regressionmachine

2D Human (527 four CH),EB

Schaerer et al. [37] Cine MR, 3D +Epi Newton dynamic law and

elasticity as energy

3D Human (15), EB

Makela et al.[38] PET/ Cine MR, 3D, Siemens

Magnetom, Siemens ECAT

+Epi + R V Intensity, edge and

elasticity energies

3D Human (10), EB

Tobon-Gomez et al. [39] SPECT, 2D +Epi Mahalanobis distance 3D Human (20),

simulation, Phantom, EB

Ma et al. [40] Echo, 3D endo Distance to the model 3D Human (P: 28), Cine,

EB

Hoogendoorn et al.[41] CT, 3D, Toshiba Aquilion Epi + RV + A+ V Bilinear shape model 3D Human (45), EBCodero-Grande et al.[42] Cine MR, 3D, GE Genesis +Epi MRF 3D Human (43), EB

zmc et al.[43] Cine MR, 2D, PhilisGyroscan +Epi A-priori search space 3D Human (N:2, P:18), EB

Lee et al.[44] Cine MRI,2D, GE Signa +Epi Circular shape prior 3D Human (38), EB

Stalidis et al.[45] Cine MR, 4D, +Epi NN based shape model 3D Human (32), EB

Dietenbeck et al.[46] Echo, 2D, GE vivid E9, Toshiba

Powerstation 6000

+Epi Thickness term 2D Human (20), EB

Ben Ayed et al.[47] Cine MR, 2D endo Overlap prior 3D Human (20), EB

Ayed et al.[48] Cine MR, 2D +Epi Max-flow, Distance to a

shape

3D Human (20), EB

Grbic et al.[49] CT, 3D Valve boundary Constrained multi-linearshape model

3D Human, EB

Chenuoune et al.[50] Cine MRI, 3D, Siemens

Symphony

endo Geometry matching using

the previous frame

3D Human (N:7, P: 11),

Tagged MRFolkesson et al.[51] Contrast MR, 2D, GE Signa CV/

i

+Epi Local Hessian features 3D Human (11), EB

Andreopoulos and Tsotsos

[52]

Cine MR, GE Signa +Epi 2D +T ASM 3D Human (33), EB

Pluempitiwiriyawej et al.

[53]

Cine MR, 2D, Brucker AVANCE

DRX 4.7 T

S + EPI + RV 5 DOF ellipsoid shape

prior

3D Human (48), EB

Hansegrd et al. [54] Echo,3D, GE Vingmed Vivid 7 +Epi Independent AAM 3D Human (36), EB

Mitchel et al.[55] Cine MR, Echo, 3D, Philips

Gyroscan

+Epi PCA based 3D Human MR (56), 2D

Human echo (64), EB

Mitchel et al.[56] Cine MR, 3D +Epi +RV PCA based 3D Human (60), EBMansi et al.[57] Cine MR, 3D, Siemen Avanto/

Philips Achieva

RV growth prediction

in repaired TOF

Diffeomorphism 3D human (P:49), EB

Peyrat et al.[58] DT-MRI, 3D, GE CV/I Fiber direction model Diffusion tensor statistics 3D dog (9, ex vivo), 3D

human (1, ex vivo), EB

Isgum et al.[59] CT, 3D, Philips Mx8000 IDT +Epi +V Multiple Atlas, local

decision fusion

3D Human (29), EB

Carneiro et al.[60] Echo, 3D endo ANN (Deep Learning

Architecture)

3D Human (14

sequences), EB

AAM Zhang et al.[61] Cine MR, 4D, GE Signa +Epi + R V 4D heart model 3D TOF (25), 3D Human

(25), EB

Joint ASM/AAM Bosch et al.[62] Echo, 2D endo 2D AAM +motion 2D human (P:129 FourCH), EB

Motion Models Lekadir et al.[63] Cine MR, 3D, Siemens Sonata endo Inter-landmark measure 3D Human (50), EBDuchateau et al.[64] Echo, 2D, GE Vingmed +M Diffeomorphism by

logarithm of the flow

2D Human (N:21, P:14),

EB



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prior was incorporated into a level set framework in order to seg-

ment cine MR images. Folkesson et al. [51]used the distance to aprior shape in the context of a geometric active contour model(Section3.2). The prior was computed by training the algorithm

using a set of images. Instead of the image pixels, local features de-

rived by Hessian operator were utilized to increase the speed of thealgorithm. In[44], the heart model was constructed in the waveletdomain and used as the prior. The wavelet transform was applied

Table 1 (continued)

Method category Reference Modality/dimension/scanner Output Description Validation (# of Data)

Paragios [65] Echo, Cine MR, 2D endo + M Level set + learned shape-

motion prior

2D Human

Dydenco et al.[66] Echo, 2D, GE Vingmed,Toshiba Power Vision 6000

+Epi + M Regional statistics curveevolution

2D Human, EB, TDI

Punithakumar et al.[67] Cine MR, 2D endo Cavity/myocardium

overlap prior

3D Human (20), EB

Feng et al.[68] PET, 3D +M Center of mass basedrigid registration

Simulated images,phantom

Pednekar et al.[69] Cine MR, 2D +Epi Motion map of the frames 3D Human (N:8, P:6), EB

Myronenco and Song[70] Echo, 3D +M Motion coherence by

temporal regularization

3D Human, EB

The output is classified as endocardium only (endo), epicardium (+Epi), RV (+RV), Atria (+A), great vessels (+V), Tag lines (+tag) and motion (+M). The magnetic field is 1.5T

unless specified. Some fields are missing, incomplete or unclear in the original papers and are thus left blank. EB: Expert Based, N: Normal, P: Patient, SM: sonomicrometry,TOF: Tetralogy of Fallot (a type of congenital heart disease). Since any segmentation method delineating the epicardium or the RV also delineates the endocardium, the key

(endo) is used for methods that only segment the endocardium.

Table 2

Deformable/level set methods: This table classifies the articles that are based on deformable model or level set.

Method category Authors Modality/dimension/scanner Output Description Validation (# of Data)

Deformable model

and level set

Angelini et al.

[102]

Echo, 3D, Philips iE 33 endo + RV Level set, Mumford-Shah

function

3D Human (10), EB, EF

(compared to cine MR)

Sarti et al.

[104]

Echo, 2D endo Level set, Rayleigh model 2D Human (15), EB

Wolf et al.

[105]

Echo, 3D, Philips Sonos 7500 endo Feature detection using

edges

3D Human (N:14, P:10), EB

Jolly et al.[106]

Cine MRI, CT, 2D, Siemens Magnetom MR/Siemens Somatom CT

+Epi Distance to the shape prior 3D human (MR:29, CT:18), EB

Hautvast et al.

[107]

Cine MR, 2D, Philps Gyroscan Intera S + Epi + RV Distance to the shape 2D Human (69 SAX, 38 LAX),

EB

Lynch et al.

[108]

Cine MRI, N/A, 2D S + Epi Probabilistic shape prior 3D Human (4), EB

Zhu etal. [109] Cine MR, 3D, GE Signa +Epi 4D shape model 3D Dog (32) & Human (22), EB

Lin et al.[110] Echo,2D, Philips Sonos 7500 endo Probabilistic shape prior

and level set

2D Human, EB

Chen et al.

[111]

Tagged MR, 2D, Siemens Trio 3T Tag

lines + M + Epi

Feature detection using

Gabor

3D Human (N:6, P:11),

Phantom

Chen et al.[112]

Tagged MR, 3D +tag lines + M MRF Human SPAMM data

Debreuve et al.[113]

SPECT endo Local features Simulated images

Zagrodsky

et al.[114]

Echo, 3D, Philps Sonos 7500 endo Gradient Vector Flow,

Deformable mesh

3D Human (10), EB

Montagnat

et al.[115]

SPECT, 3D, +Epi Distance to a mesh,

newtons dynamic law

3D Human, EB

Verres et al.

[116]

Cine MR, 3D, Siemens +Epi FE, Hyperelastic warping 3D Human (1), Simulated

images

Phatak et al.

[117]

Cine MR,3D, Siemens Avanto +Epi Fiber, Hyperelastic warping 3D Human (1)

Fang et al.[118]

Echo, 2D, Yale online database endo GMM 2D Human (N/A), EB

Barbosa et al.

[119]

CT, Echo, 3D, GE vivid 7 endo B-spline 3D Human, EB

Rougon et al.

[120]

Tagged MR, 2D, GE +Epi + M Gradient flow of MI 3D Human (N:12), Simulated

imagesKermani et al.

[121]

Cine MR, 3D +Epi Active mesh model 3D Human, Simulated images

Huang et al.

[122]

Cine MR, 2D endo Metamorph:

texture + shape

2D human, EB

Kaus et al.[123]

Cine MRI, 3D, Philips +Epi Deformable contour 3D Human (121), EB


unless specified. Some fields are missing, incomplete or unclear in the original papers and are thus left blank. N: Normal, P: Patient, EB: Expert Based, SM: sonomicrometry,

since any segmentation method delineating the epicardium or the RV also delineates the endocardium, the key (endo) is used for methods that only segment theendocardium.

http://-/?-


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to the cardiac surfaces in the spatiotemporal domain to extract the

coefficients. A neural network model was generated to combinethe local and global information in order to extract the trainedshape and segment the cardiac boundaries. The Fourier decompo-sition approach was shown to be able to represent different shapes

by their Fourier descriptors. Coarse shape coefficients were com-puted by low-order harmonics, while higher order coefficients rep-resented the fine detail.

3.1.1.4. Thickness term. Practically, the endocardial and epicardialcontour segmentations may overlap due to variable contrast andhaziness of the boundaries. This problem dramatically increases

the error and leads to unrealistic rendered 3D heart images. In or-der to tackle this problem, Dietenbeck et al. [46]used a constraintthat poses a forced distance between the endocardial and epicar-dial contours. The thickness constraint was combined in a levelset framework in addition to a regional intensity term and a dis-

tance term describing the distance of the contour to a learnedshape. This technique was applied to echocardiography images tosegment the LV epicardium and endocardium simultaneously.

3.1.1.5. Other statistical shape prior techniques. Ben Ayed et al.[47]proposed to compute the endocardial and epicardial contourssimultaneously using the first frame. In the first step, three image

region classes were proposed: 1. LV cavity containing blood; 2.Myocardium; 3. Background containing adipose tissue, lungs, etc.

The algorithm assumes that the overlap between the kernel-basedintensity distributions within each region remain the same

through the consecutive frames. The Bhattacharyya coefficient

was used as the overlap measure. The Bhattacharyya coefficientis a popular measure to determine the overlap between two statis-tical samples. This coefficient is generally used to calculate the rel-ative closeness of the two distributed classes. In a novel approach,

the energy term does not assume that the overlap between theintensity profiles within different regions has to be absolutely min-imal. This modification helps to include the Papillary Muscle aswell. The authors were able to achieve competitive results without

using geometric training or preprocessing which leads to higherflexibility in the real clinical setting.

Ben Ayed et al. [48] proposed to use combined energy terms

consisting of the distance to a learned shape in addition to anintensity-matching constraint. The first cardiac frame was utilizedfor training of the model of the histogram. The algorithm was ap-plied to cine cardiac images for segmentation of the epicardial

and endocardial boundaries in cine MR SAX images. The prominentadvantage of the last two articles is reduction of the training time.Since training is only based on the first frame, the training time issignificantly reduced. As a disadvantage, the validation is based on

20 datasets. Increasing the number of the tests set can increase thereliability of the method.

Codero-Grande et al. [42] coarsely delineate the myocardiuminitially. The tissue statistics is modeled using Gaussian Mixture

Model (GMM) according to the intensity and gradient of the LVcontour and the tissue inside the LV. GMM tries to model the tissue

histogram using a weighted summation of Gaussian distributions.Consequently, a center-surround biannular radii is overlaid on the

Table 3

Biophysical methods: This class of techniques is based on the physical priors of the human heart.

Method

category

Authors Modality/dimension/

scanner

Output Description Validation (# of Data)

Biophysicalmodels

Bistoquet et al.[124] Cine MR, 3D, PhilipsIntera

+Epi + RV Deterministic incompressible model 3D Human, Tagged MR, EB

Bistoquet et al.[125] Cine MR, 3D, Philips

Intera

+Epi+ RV Deterministic nearly incompressible model 3D Human (N:3, P:3),

Tagged MR, EB

Garson et al.[126] US, 3D, Visual SonicVevo 770

+Epi Deterministic incompressible model, GradientVector Flow

3D mouse, Simulation

Zhu et al. (MIA)[127] Echo, 3D, Philips iE 33 +Epi Statistical nearly incompressible (Gaussian

assumption), level set

3D Dog (11) & Human (22),

EB

Papademeteris et al.

[128]

Echo, 3D, HP Sonos

5500

+Epi Fiber direction 3D Dog (N;2, P:2), SM

Sermesant et al.(2003)[129]

SPECT, DTI MR, Philips +Epi + RV + M Fiber direction 3D human, EB

Bachner et al.

[130,131]

Echo, 2D +M Fiber direction 2D Human, Simulation,

phantom

Hu et al.[132] Tagged MR, 3D +Epi + RV + M Fiber direction, FEM 3D Human, Dog

Fan et al. [133] CT, 3D, N/A Endo Newton dynamic model for local force 3D Dog (N:16)

Sermesant et al.

(2006)[134]

Cine MR, 3D, Philips +Epi + RV + M Mass-Spring model, Fiber direction 3D Human, EB

Wong et al. [135] Cine MR, 3D, N/A +Epi + RV + M physiome model 3D Human, EB

Klein et al.[136] PET, 2D +M FEM Phantom

Yan et al.[137] Cine MR, Echo, 3D,

Philips 7500

+Epi + M FEM 3D Human, Implanted

markerRemm et al.[138] Cine MR, 3D, Siemens

Vision

+Epi + M FEM 3D Human (13), Tagged MR

Shi et al.[139] Cine MR, 3D +M FEM 3D Human, Implanted

marker

Sinusas et al.[140] Cine MR, 3D, GE Signa +Epi FEM 3D Dog (8), Implanted

markers

Szilgyi et al.[141] Cine MR & CT, 3D +Epi + M Electromechanical model 3D Human (42)

Papademetris et al.

[142,143]

Cine MR, 3D +Epi + M Linear elastic model 3D Human, Implanted

marker

Klein et al.[144] PET, 3D +M Linear elastic model 3D Human (1), Phantom

Gigengack et al.[145] PET, 3D +M Hyper-elastic model, mass preservation Simulation, phantom, 3D

Human (21)

The output is classified as endocardium only (endo), epicardium (+Epi), RV (+RV), Atria (+A), great vessels (+V), Tag lines (+tag) and motion (+M). The magnetic field is 1.5Tunless specified. Some fields are missing, incomplete or unclear in the original papers and are thus left blank. N: Normal, P: Patient, EB: Expert Based, SM: sonomicrometry,

since any segmentation method delineating the epicardium or the RV also delineates the endocardium, the key (endo) is used for methods that only segment the

endocardium.



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circular myocardium of SAX slices. Thereafter, a 3D polar grid isgenerated on the images. A Markov Random Field (MRF) systemincluding the prior and the likelihood terms is defined over that

grid. A Markov random field is a graphical model of a set ofmemoryless random variables represented by an undirected graphthat works similar to a Bayesian network. The intensity and the

gradient likelihood over different image subsets are constructedusing the previous grid and finally the parameters of the MRF arerecursively estimated and used for segmentation of cine MRimages.

3.1.2. ASM

The intensity, probability, and estimated contours from previ-ous spatial and temporal locations may not represent the cardiac

boundaries well; this is especially true in cardiac US images sinceat times, the contours are not complete and the cavity cannot befully visualized. The main advantage of the ASM methods is theirability to overcome the noisy structure and drop outs of the cardiac

images based on probabilistic knowledge of the object which isindependent of the intensity [13,14]. ASM builds a whole shape

model using manually segmented data. Subsequently, the modelis registered on the images as will be discussed. A shape model is

defined as a structure which reflects the typical structure of a spe-cial set of anatomical objects of interest; i.e., the shape model isinvariant to transformations. There are several ways to represent

a shape: 1. cloud point, 2. surface, 3. mesh/triangulation (a set ofpoints with connectivity), 4. skeletonization, 5. parameterizationvia a set of basis functions such as B-spline or NURBS. In computa-

tional cardiac studies, surface and mesh models are utilized morefrequently. Since most Active Shape Models have the same generalstructure, below, the ASM is discussed in general terms and the dif-ferences among the methods are described. Basically, there are five

steps in use of ASM for segmentation:

1. Contour extraction and spatial alignment: A database containingadequate number of examples is manually segmented in the

training phase. Several landmarks are selected on the contoursof the manually segmented training set. Subsequently, thedetected landmarks are aligned to a defined coordinate usingrigid registration techniques such as the Procrustes method

[71]. One shape is arbitrarily selected as the reference.

This step is usually the same in most papers but some variationsexist. Lekadir et al.[63]used inter-landmark measure as an invari-

Table 4

Non-rigid registration methods using basis functions. In this section basis functions such as B-spline are utilized to model the cardiac surfaces and motion.

Method category Authors Modality/dimension/scanner Output Description Validation (# of Data)

Non-rigid registration

using basis function

Amini et al.

[152,153]

Tagged MR, 2D +tag + M B-splines snake 3D Human (5), Simulated

imagesRedeva et al.

[154]

Tagged MR, 3D +Epi + tag + M B-splines snake 3D Human, Simulated

images

Huang et al.

[155]

Tagged MR, 4D +Epi + tag + M B-splines snake 3D Human, Simulated

imagesTustison et al.,

2003[156]

Tagged MR, 3D, Siemens Sonata +Epi + RV 3D B-spline FFD 3D Dog, simulated images

Tustison and

Amini[157]

Tagged MR, 4D, Siemens Sonata +Epi + RV + tag+ M NURBS biventricular model 3D Dog, Simulated images

Deng and

Denney[158]

Tagged MR, 3D +Epi + tag + M B-splines registration 3D Human (10), Simulated

imagesChandrashekara

et al.[159]

Tagged MR, 3D, Siemens Sonata +Epi + tag + M FFD 3D Human (12), EB

Lin et al. [160] Cine MR, 2D +Epi + tag + M B-spline 3D Human, EB

Sundar et al.

[161]

Cine MR, 3D, Siemens Sonata +Epi + tag + M Cubic spline 3D Human (3), Tagged MR

Perperidis et al.

[162]

Cine MR, 3D, 7T (GE Excite

Console, magnex Magnet), Epic

12.4

+Epi B-spline registration 3D mouse, EB

Ledesma et al.

[163]

Echo, 2D, Siemens ACUSON +M B-spline 2D Human (N:6, p:6),

Simulated images

Ledesma et al.[164166] Echo, 2D +M B-spline 2D Human, Simulatedimages, TDI

Elen et al.[167] Echo, 3D, GE Vingmed +M Elastic registration 3D Human (N:3, P:1),Simulated images

Chen and Guan

[168]

MR, 3D +Epi + RV NURBS 3D Human

Metz et al. [169] CT, 3D +M B-spline FFD 3D lung and heart

Zheng et al.

[170]

CT, 3D +Epi + A + V Thin Plate Spline 3D Human

De Craene et al.

[171]

Echo, 3D, GE Vivid 7 +Epi Diffeomorphic B-Spline FFD 3D Human (N:9, P:13)

Peyrat et al.,

2010[172]

CT, 4D +Epi,+RV,+M Diffeomorphic demon 3D Human, post RF-ablation

data, Simulated images,Suhling et al.

[173]

Echo, 2D +M B-spline moments, Optical

flow

2D Dog (6), Simulated

images, Phantom

Yue et al.[174] Echo (intracardiac), 2D, Model

Ultra ICE, Bos ton Scientific

+M Maximum Likelihood, Spline

based control points

2D Dog (4), SM

Zhuang et al.

[79]

Cine MR, 3D, Philips +Epi + RV+ A Locally Affine Registration,

Adaptive Control Point status

3D Human (37)


unless specified. Some fields are missing, incomplete or unclear in the original papers and are thus left blank. N: Normal, P: Patient, EB: Expert Based, SM: sonomicrometry,

since any segmentation method delineating the epicardium or the RV also delineates the endocardium, the key (endo) is used for methods that only segment the

endocardium.

http://-/?-http://-/?-


11/24

ant shape representation that allows the decomposition of the glo-bal prior as well as constraining each individual landmark. The in-

ter-landmark measures rely on barycentric coordinates based onthree coefficients to describe the relative position of each landmarkwith respect to two neighbor triangles of different shapes andposes. The barycentric coordinate system is a homogeneous coor-dinate system in which the location of each point is represented

with respect to the center of mass, or the barycenter. The authorssuggested that inter-landmarks carry larger proportion of theshape difference with respect to the other and this leads to inaccu-rate alignment.

2. Temporal alignment: Different datasets have different numbersof frames. In that case, an interpolation (such as spline or bilin-ear) in time is necessary in order to make the number of frames

similar in the temporal direction [57,60]. Here again one datasetis arbitrarily selected as the reference.

3. Construction of the shape model: A set of selected points distrib-uted on the surface known as PDM (point distribution model)

can be formulated as:

x

x1;y

1;z

1; . . . ;x

n;y

n;z

nT

1

Each 3D shape data has a surface and a particular PDM distributedover the surface. The key is that the PDMs for data in the trainingdatabase should have anatomical correspondence. Probabilityshape models try to derive a statistical map of these points in the

form of mean xand covariance S of the PDM as:

x1N

XNi1xi 2

S 1N 1

XNi1

xixxixT 3

4. Dimensionality reduction: Dimensionality reduction of the train-ing set is usually performed by using Principal ComponentAnalysis (PCA) to find a small set of values that best representthe observed variation. PCA extracts the eigenvalue decomposi-

tion of the covariance matrix, providing the principal eigenvec-tors. Principal eigenvectors show the variability in the data. Inpractice, the eigenvalues that describe 9599% of the total var-iance are kept and the rest are discarded. Subsequently, each

shape may be represented as:

xxub 4where u is the selected eigenvectors and b is the vector of shape

parameters.Instead of the above-mentioned linear equation, Hoogendoorn

et al. [41] used a bilinear model to segment the ventricles, atriaand great vessels in CT images. In the bilinear mode, an additionalparameter (b) was added to provide a better model of the point set.The bilinear model represented an extension of the linear model by

using two factors (Aand b) while removing each factor leads to alinear model. The bilinear model is formulated as:

xATWb 5where X is a scalar observation defined by the point set,A andb areparameterization vectors, andWis similar to the eigenvalue matrix

PCA is based on the assumption that the data are Gaussian dis-tributed which may not be true. To cope with this problem, some

authors have used Independent Component Analysis (ICA) [72]which assumes statistical independence[24,43]. ICA is a technique

to separate set of data into additive non-Gaussian subcomponentsprovided that the subcomponents are mutually statistically

independent. However, ICA increases the computational burdenin comparison to the PCA. Several other variants of PCA have been

developed in the literature. In[24], temporal dynamics and inter-subject variation is tackled using Multilinear PCA (MPCA) and Mul-tilinear ICA (MICA). Bosch et al.[62]performed the PCA techniquein smaller regions to give more local versatility to the generalshape model. Therefore, the local landmarks achieve regional inde-

pendence with regard to the global shape.

5. Shape correspondence: Shape correspondence computes thetransformation (T) that relates the object (x0) to the shape model

as:

x0Txub 6

This is the most important and distinctive part of statistical shapemodeling. Correspondence is performed by overlapping the statisti-

cal model on the test object (object to be segmented) and subse-quently the transformation of the point sets that leads to themaximal overlap is estimated. In the case of cardiac segmentation,if the model contains both LV and RV, they can simultaneously be

modeled and segmented. It is noteworthy that the manual delinea-

tion is limited to the training step and the first frame (in semi-auto-matic techniques). Fully automatic techniques try to find the imagecorrespondence without any initial contour.

Several techniques have been used for the correspondence ofthe point sets. One of the major techniques is Iterative closest point

technique (ICP)[73]. ICP iteratively estimates the global transfor-mation T and then applies that transformation (T) on the currentposition of the point distribution. The transformationTis updatedbased on the minimization of a least squares cost function that is

the distance between the expected point distribution positionand current estimate of image boundary points. In practice, ICPconsists of four steps: (1) using the nearest neighbor criteria tomap the points of the object to the points of the model, (2) Estimat-

ing transformation parameters applied to the point set (pi,t) based

on a minimizing the mean square cost function such that:

fT Xm1i0

kTpi;t pi;t1k2 7

(3) Transforming the point set using the estimated parameters, (4)

the first three steps iterates recursivelyuntil thecost function is lessthan a small predefined value[73].

However ICP is computationally costly and cannot handle dif-ferent energy functions for correspondence computations. Opti-mized matching techniques can be utilized instead of brute-forcepoint set matching. Non-rigid registration techniques such as B-

spline registration (described in Section 1.3.4) have also been usedfor shape correspondence since they are inherently smooth andcan handle different energy functions. Besl and McKay [73] and

Frangi et al. [74] used the landmarks extracted from manuallydelineated images to build a cardiac model. The landmarks werepropagated using volumetric B-spline registration due to severaladvantages. B-spline non-rigid registration is less restrictive

regarding the structure which is due to the faster implementationand inherently smooth nature of the spline basis functions. Nosearch space or point to point mapping is needed either. It is pos-sible to achieve smooth results and handle multiple point set mod-

els at the same time. The B-spline registration will be discussed indetails later in this survey. In an additional article, Frangi et al. con-structed an atlas of binary volumes based on quasi-affine registra-tion using the Normalized Mutual Information (NMI) metric [75].

ASM and AAM are mostly used for segmentation purposes. Nev-ertheless, since the correspondence among the point sets is com-

puted, the motion of the point set can be subsequently analyzed.If the point set is positioned on the contours (endocardium or epi-



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cardium), the derived motion will be sparse. However, the point setcould be positioned on the heart as a 3D mesh to cover the inside of

the myocardium in order to achieve a measure of dense motion.

3.1.2.1. Handling multiple objects or atlases. An Atlas can representone object or a set of normal or abnormal objects. Multi atlas prop-agation and segmentation (MAPS) techniques have become popu-

lar recently in the field of medical image segmentation [76,77].MAPS combines object intensity and object label (contour) whilethe intensity is used for registration and the label is used for thepropagation of the contours or the prior model. Modified versions

of MAPS are also proposed. MUPPS (MUltiple Path Propagation andSegmentation) uses a set of atlases as well as a set of paths of prop-agation similar to a multiple classifier strategy[78]. The selectionof the optimal atlas and path is based on MI as the similarity crite-

rion. In similar work, Isgum et al. [59]argued that a single atlasmay not be a good representation of the whole population and pro-posed a multi-Atlas model that uses decision fusion to select theoptimal atlas. In the first step, an affine registration was used to

align the global image. Subsequently, nonrigid registration basedon B-spline was performed using a gradient descent technique.MI was utilized as a measure of image matching. To cover thewhole range of transformation and in order to increase the speed

of the algorithm, multi-resolution and multi-grid strategies wereadopted. Finally, the atlas that gives the best registration successis given an increased weight. The algorithm outperformed the sin-gle best atlas strategy and averaged shape-atlas strategy.

Zhuang et al. [79] used LARM (Locally affined RegistrationMethod) to transform each substructure (LA, LV, RA, RV and ves-sels) of the heart in a separate step. LARM was able to provide aninitial registration of the images to align the cardiac subcompo-

nents. In order to refine the registration, FFD registration was usedin the next step. The novel aspect proposed by the authors in thisstep was Adaptive Control Point Status (ACPS) that turns the con-trol point status of the object on or off based on the performance

of the registration. The status of the control points was updated

adaptively to guarantee that the active control points were notinactivated. The proposed technique was able to overcome theshape complexity of the heart in cardiac MR images by decompos-

ing the problem into several smaller structures and was able toachieve a better computational speed.

In order to handle different structures such as ventricles and at-

ria more efficiently, multiple-shape model and piecewise registra-tion methods have been proposed. Instead of a single global shapemodel, van Rikxoort et al.[34]used multiple shape models that actlocally using a method called ALMAS (Adaptive Local Multi Atlas

Segmentation). Atlas is a point set model that represents an ana-tomic structure. ALMAS finds the number of necessary atlases toefficiently reconstruct the cardiac model. It locally and automati-cally selects the most appropriate atlases ui(Si) to make the final

combined atlas (S). In ALMAS,nregistrations (Ti) are applied to dif-ferent atlases such that:

S1n

XNi1

uiSi 8

The method was applied to cardiac CT images to segment the ven-tricles and atria and great vessels in 3D. It was shown that the mul-tiple-shape model provides more local autonomy in the atlas.Ecabert et al. [80]developed a model-based approach for the seg-

mentation of the four chambers and great vessels using 3D CTimages. Hough transform was applied first to automatically localizethe heart. ASM was utilized to construct the cardiac model fromcoarse to fine scales using PCA dimensionality reduction. Piecewise

affine transformation was used to handle the shape variability andmatch the model to the objects. The shape model was adjusted by

changing the degrees-of-freedom of the allowed deformations. Toensure that the mesh remains continuous in-between the cham-

bers, a weight was assigned to each local model. The user can alsomanually change the continuity as well.

3.1.2.2. Handling incomplete objects. Esther-Leung et al. [31] pro-posed two different methods (model-driven and edge-driven) fortracking the myocardium in echocardiography images. The ap-proach was motivated by the fact that in echocardiography, visibil-

ity of the myocardium depends on the view. The technique reliedon a local data-driven tracker using optical flow (a temporal regis-tration technique that for the most part uses the intensity con-stancy assumption between corresponding pixels in successive

frames[81,82]) applied to the visible parts and a global statisticalmodel applied to the invisible parts of the myocardium. It was con-cluded that the shape model can handle the invisible tissue inultrasound images as well as the missing boundaries. Another

shape based tackling of drop outs in echocardiography imageswas described in Zhou[36]. The authors use Shape Regression Ma-chine (SRM) as a method to overcome the fuzzy boundaries in 2Dechocardiography images without using the initial delineation. The

SRM uses statistics of the shape, appearance, and anatomy in the

training step to construct a model. Subsequently an automatic ini-tialization was derived using a rigid shape. The initial contour isupdated using a nonlinear regressor to directly associate the non-

rigid shape with the image appearance.

3.1.2.3. Training volume size considerations. The number of datasetsin the training set should be large enough to cover different typesof diseases and dysfunctions. Any undertrained shape model can

theoretically lead to false results and over-fitting[83]. In the caseof 3D and 4D shape modeling; very large datasets are needed, lead-ing to the curse of dimensionality. Therefore, the extracted heartmodel may be unable to cover different cardiac morphometrics.

Zhang et al.[61]used the manual segmentation of the first frameof the test dataset as an adjunct to the shape model to overcome

the limited training dataset problem. Koikkalainen et al. [23]de-scribed several methods to artificially increase the size of the data-

base using different techniques such as nonrigid movement andcombination of Principal Component Analysis (PCA) and Finite Ele-ment Model (FEM). In a separate work, Ltjnen et al. [84] pro-posed several methods to generate synthetic training data to

increase the size of the training dataset. Andreopoulos and Tsotsos[52]argued that ASMs are unable to rely on a small training set tocapture the full range of biological shape variability. They handledthe problem of training 3D ASM through use of wavelets. Wavelets

can decompose the data into several sub-bands having differentamount of detail. Intuitively, wavelets can discard unnecessary de-tails of the manually segmented boundary and keep the coarse andstable parts. The technique was performed in four steps: (1) the ob-

ject was aligned to the shape model; (2) 2D wavelet was performedin two steps on the coarse band and thus leaved seven imagebands; (3) the shape model was constructed in the wavelet domainbased on the coefficients of the wavelet transform; (4) inversewavelet transform was used to recover the shape in the space

domain.

3.1.2.4. Extension to the temporal dimension.The incorporation oftemporal data can be tricky due to the different resolutions ofthe time dimension, higher variation of the motion, and computa-tional expense. Extension of ASMs temporal modeling has been

performed in[52,62].

3.1.2.5. Diffeomorphism. One of the limitations of most image regis-

tration techniques is lack of explicit constraints to ensure that thecomputed transformation is invertible. Folding of the grid over

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itself can lead to the corruption of the neighboring structures of themodel or triangular flipping [85]. Therefore, diffeomorphic tech-

niques are of interest due to the smooth invertible transformationswith smooth inverse solutions. Since diffeomorphism has been al-most exclusively used in the context of ASM in the cardiac segmen-tation and registration field, it is categorized in this section.Diffeomorphic registration algorithms [8688] guarantee an

invertible continuous differentiable mapping between the objectfeatures in order to preserve the topology and orientation of theanatomical structures over time. The log transform of the motionfield was incorporated in the shape model to conserve homeomor-

phism in[60]since the logarithmic transform can decrease the va-lue of the motion. In another work, Beg et al. proposed a variationaldiffeomorphic model based on cardiac fiber elements in DT MRIcardiac images of postmortem biopsies[76].

3.1.2.6. Shape variability. The differences in the anatomic variabilityof the heart originate from three sources: (1) subject variabilitydue to the heart motion; (2) inter-subject variability due to theshape differences among different humans; (3) pathological vari-

ability due to the abnormal cardiac size or function. In order toovercome this problem, some authors have proposed combined in-ter and intra-subject atlases that considers the huge shape varia-tion of the heart[48].

3.1.2.7. Drawbacks of ASM. The probabilistic knowledge is usuallyderived from a training step. This method mandates a comprehen-

sive database, tedious human effort, and high clinical and technicalexpertise. The adequate size of the training set that includes differ-ent pathologies can be a huge problem. This problem can be cum-bersome since the cardiac chambers can vary widely in size and

motion, especially if uncommon diseases are also considered. Thelearned template is limited to recognize a specific group of imageswith similar properties and may miss others. Different training

steps should be used for each echocardiography or MR imagingview in 2D techniques. Additionally, the traditional shape modelis a global structure while local landmarks do not have self auton-omy to fit to the local edges. ASM requires good initialization as

well. If the point distribution set is large, the computational timecan also be problematic in ASM[55,56].

3.1.3. AAM

Active Appearance Models use the same platform and steps of

ASMs but include the texture (intensity variations) appearanceof the object as well. The object intensity or gradient perpendicularto the boundaries is usually considered as the appearance texture.The shape data (s) and the appearance data (g) are combined to

make a joint linear system as:

xx/shapeWshapeQshapecg g/AppearQappearc 9where/shapeand/Appearare independent eigenvectors of shape andappearance, Wshapeis a diagonal weight matrix, Qshapeand QAppeararethe eigenvector matrices of the combined shape and appearanceandcis the combined shape appearance parameter vector. The ob-

ject data normal to the boundary contour (also known as profile)are mainly computed by interpolation of the intensity or intensitygradients in the direction of the contour normal [8992]. It isshownthat the normalization of the profile leads to more accurate results.

Two methods are linear normalization using an initial offset[89]and non-linear normalization [62] to handle non-Gaussiandistributions.

Different object profiles can be computed using several other

techniques such as Gabor filters[93], gradient strength and direc-tion[8083], regional features[94],color features[95]and combi-

nation of several profiles [96]. In another work, Song et al. [32]used pixel feature vector as a combination of the smoothed inten-

sity values and the second directional derivative to construct theshape model.

3.1.3.1. Advantages and drawbacks of AAM. ASM is faster and

achieves more accurate local point location than the AAM, butthe AAM also models the texture. Since the internal structure ofthe heart is taken into account, memory problems can be a big is-sue especially in 3D and 4D AAM methods. Decomposing the largematrix into a smaller one is a preliminary solution. Decreasing the

resolution[55,62]and sparse regional analysis of the profile [94]were proposed as well.

3.1.4. Motion models

The heart has an approximately periodic motion that is congru-ent in space and time. Each region of the heart moves on a more orless periodic curve called regional motion trajectory[2,3]. Motiontrajectories can be used as diagnostic tools in medical imaging.

The motion trajectories relevant to a region should be congruentin time and make an almost closed path. There are several strate-gies to make the motion smooth such as shape-motion models,

Kalman filters, and Markovian systems. Motion prior is a modelthat can simulate the spatial and temporal changes of the displace-ments by taking the motion pattern of the cardiac cycle into ac-count as an additional constraint. Several papers that haveconsidered motion models are reviewed in this section.

Dydenco et al. [66]applied a level set algorithm which madeuse of shape and motion prior, for both segmentation and trackingof echocardiographic images. The method is based on three steps:(1) the trained shape is aligned to the image using a rigid registra-

tion technique; (2) the aligned shape is used as an initial contourfor the level set method. The level set uses the data from thelearned shape prior and the statistics of the inside and outside ofthe evolving curve to update the endocardial and epicardial bor-

ders; (3) the evolution of the level set is used to train the motion

prior.Paragios[65]embedded a motion prior and a shape prior in a

level set function. The motion prior minimized the sum of absolute

difference of the corresponding images in the time dimension. Theprior shape was based on distances of the point set to a model. Thedistribution of the distances was assumed to be Gaussian. Puni-thakumar et al.[67]proposed to minimize an energy function con-

sisting of the distance of the transformed shape to a prior shape (atrained shape) as the geometric constraint. A graph cut distributionmethod was utilized in the minimization of the energy functionand delineation of the LV cavity in cardiac MR images. Since a sin-

gle Markovian cannot handle the complex heart motion, a set ofweighted models were combined together to handle the differenttypes of motion of the heart. The multiple model system was able

to automatically switch between the models and identify theappropriate multiple model that matches the cardiac motion basedon a training process. Finally the technique was applied to the cineMR SAX images for the segmentation of endocardial shapes as well

as to define the trajectories in time through different frames.Myronenco and Song [70] developed the Coherent Point Drift(CPD) technique, constraining the motion of the point set in thetemporal direction for both rigid and nonrigid point set registra-

tion. The point set distribution was modeled with a Gaussian Mix-ture Model (GMM). The GMM centroids were updated coherentlyin a global pattern using maximum likelihood to preserve the topo-logical structure of the point sets. The algorithm was used for both

rigid and non-rigid applications. In the nonrigid case, the motioncoherence constraint was added based on regularization of the dis-

placement fields. The purpose of regularization is to increase themotion smoothness. The motion is defined to be smoother if it



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oscillates less which means that it has less energy at high frequen-cies. The method was applied to 3D echo images of the LV in order

to compute displacements.

3.2. Deformable models

3.2.1. Parametric active contours

Deformable models, or active contours (also known as snakes)technique which was first described by Kass et al.[97], is a popular

physically inspired, model-driven technique based on parametriccurves, surfaces or volumes, that deform under internal and exter-nal forces. The external energy forces the contour to move towardthe image data (such as an edge). The internal energy controls the

contour based on a regularizing smoothness constraint. Additionalenergy terms can constrain the deformable model to achieve betterresults. The general deformable model energy function can be writ-ten as:

EEextEint 10External energy is usually defined as:

Eext

krjGr

x;y

I

x;y

jk2

11

where Gr(x,y) is a two dimensional Gaussian function with stan-dard deviation rand I(x,y) is the intensity at pointv(s) = [x(s),y(s)].Internal energy is defined as

Eint12

askvssk2 bskvsssk2 12

wherea and b are weights, the first order term (membrane term:kvs(s)k

2) defines the stretching and the second order term (thin-plate term: kvss(s)k

2) defines the curvature.This energy function was minimized within a variational energy

minimization. The numerical optimization was improved by Aminiet al. [98]who cast the optimization within a dynamic program-ming framework and introduced the concept of soft and hard con-straints. Further improvements to this framework was proposed by

Klein et al. who introduced DP B-spline snakes[99].Some studies have incorporated other terms such as shape prior

and physical constraints as will be discussed later. Deformablemodels have been widely used for the segmentation and tracking

of cardiac images in both MRI and echocardiographic images.Since the edge map of the image can be misleading due to the

noise and missing data, GVF (gradient Vector Flow) was proposedas a new external energy function to handle the edge function

smoothly. GVF is derived based on the minimization of the energyfunction proposed in Eq. (13) where vis the Gradient Vector Flow,l is the smoothing weight, rI is the image gradient, and krI2kpenalizes the edge information[100].

EGVF Z Z lkvk2 k

rI2k kv

rIk2 13

3.2.2. Geometric active contours

Level-sets, first introduced by Osher and Sethian[101], repre-

sents an implicit function which deforms based on regional inten-sity or edge-based feature and is able to develop topologicalchanges. The initial contour at time zero (C0) corresponds to the

zero level set of the function /:

C0 x;yj/x;y;0 0gf 14If we represent a continuous speed function asF then the general-

ized level set equation dynamics can be parameterized as:

/tFjruj 0 15

whereFrepresents the speed function for the curve evolution. Thespeed function depends on internal properties such as geometry

(e.g. curvature) of the interface and external properties such as im-age gradient. Given an initial contour (or contours), an implicit

function is defined and deformed at each pixel where the zero-levelset determines the actual position of the curve(s) as a function oftime. Level set approaches are stable but are computationallycostly. Deformable models are mostly used for segmentation tasks.

However, a measure of cardiac motion can be calculated by com-puting the displacements of the contour or the mesh.

Table 2describes the related articles using this class of tech-niques[102123]. Angelini et al. [102]proposed a level set tech-nique to segment Ultrasound echocardiography images. It is

beneficial to describe the method utilized in this paper, since itwas based on Chan and Vese [103], which is a classical levelset algorithm that can be utilized for other purposes as well. Theauthors minimized an energy function that contained area, length,

and intensity variations inside and outside a contour (the image isconsidered piecewise smooth inside and outside the contour) suchthat:

EaLcontour bVinsideofcontour cZX

jI

c0

j2

H/dX

q Z

X jI

c1j2

1

H

u

dX

16

wherea, b, c, q are the weighting parameters, Iis the intensity, c0andc1represent a fixed intensity level that represent the mean dis-tribution of the intensity inside and outside the curve. H(/) is theHeaviside function defined as:

Hu 1 uP 00 u< 0

17

The length of the contour can be written as:

Lcontour ZX

jrH/jdX ZX

jr/jd/dX 18

where d(/) is the Dirac function and the area inside the contour canbe written as:

Ainside of contour ZX

jHujdX 19

The authors extended this method to delineate the endocardium of

both LV and RV cavities.Sarti et al. [104]used the Rayleigh distribution of the speckle

statistics to segment cardiac US images in a level set framework.The Rayleigh distribution is defined as:

pIRaileighIx;y=r2 exp Ix;y2=2r2

20

where r is the standard deviation. The authors assumed that theintensity distribution of the tissue inside and outside the endocar-

dial curve is similar through the cardiac frames since they represent

the texture of the blood and the myocardium.Barbosa et al. [119]developed a level set technique based on

the global intensity inside and outside of the object boundariesand an additional local regional intensity term. The energy func-

tional was handled in spherical coordinates to match the anatomicshape of the LV. The level-set was evolved based on B-spline con-trol points to increase the smoothness of the curve evolution. Itwas shown that the algorithm is able to effectively segment the

endocardium in echocardiography images. Wolf et al. [105]usedan energy function consisting of region-based inform

a survey of shaped-based registration and segmentation techniques for cardiac images

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