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A review of segmentation methods in short axis cardiac MR images

A review of segmentation methods in short axis cardiac MR images
A review of segmentation methods in short axis cardiac MR images

Survey Paper

A review of segmentation methods in short axis cardiac MR images

Caroline Petitjean a ,?,Jean-Nicolas Dacher b

a Universitéde Rouen,LITIS EA 4108,BP 12,76801Saint-Etienne-du-Rouvray,France

b

University Hospital of Rouen,Department of Radiology &University of Rouen,INSERM U644,76031Rouen,France

a r t i c l e i n f o Article history:

Received 4May 2010

Received in revised form 23October 2010Accepted 15December 2010

Available online 24December 2010Keywords:Cardiac MRI

Segmentation

Deformable models Survey

a b s t r a c t

For the last 15years,Magnetic Resonance Imaging (MRI)has become a reference examination for cardiac morphology,function and perfusion in humans.Yet,due to the characteristics of cardiac MR images and to the great variability of the images among patients,the problem of heart cavities segmen-tation in MRI is still open.This paper is a review of fully and semi-automated methods performing segmentation in short axis images using a cardiac cine MRI sequence.Medical background and speci?c segmentation dif?culties associated to these images are presented.For this particularly complex seg-mentation task,prior knowledge is required.We thus propose an original categorization for cardiac segmentation methods,with a special emphasis on what level of external information is required (weak or strong)and how it is used to constrain segmentation.After reviewing method principles and analyzing segmentation results,we conclude with a discussion and future trends in this ?eld regarding methodological and medical issues.

ó2010Elsevier B.V.All rights reserved.

1.Introduction

Cardiovascular diseases are the leading cause of death in Wes-tern countries (Allender et al.,2008;Lloyd-Jones,2010).Diagnosis and treatment follow-up of these pathologies can rely on numer-ous cardiac imaging modalities,which include echography,CT (computerized tomography),coronary angiography and cardiac MRI.Today recognized as a reference modality for the non-invasive assessment of left ventricular function,MRI also supplies accurate information on morphology,muscle perfusion,tissue viability or blood ?ow,using adequate protocols.The cardiac contractile func-tion can be quanti?ed through ventricle volumes,masses and ejec-tion fraction,by segmenting the left (LV)and right (RV)ventricles from cine MR images.Manual segmentation is a long and tedious task,which requires about 20min per ventricle by a clinician.Be-cause this task is also prone to intra-and inter-observer variability,there has been a lot of research work about automated segmenta-tion methods.In particular,commercial software packages such as MASS (Medis,Leiden,The Netherlands)(van der Geest et al.,1994)and Argus (Siemens Medical Systems,Germany)(O’Donnell et al.,2006)are today available for automatic ventricle delineation.Even though processing time has been greatly reduced,the provided contour detection still needs to be improved to equal manual contour tracing (Fran?ois et al.,2004;Mahnken et al.,2006).While reviews on cardiac image analysis (Suri,2000;Frangi et al.,2001)and medical image segmentation (Suri et al.,2001;Pham et al.,2000)exist,we have focused on methods dedicated to cardiac MR segmentation:the particular shape of both ventricles,as well as MR characteristics,have required speci?c developments.De-spite more than 15years of research,the problem is still open,as shown by the holding of a segmentation contest on the LV in 2009during the MICCAI conference 1,and remains completely un-solved for the RV.

In the present paper,we will review automatic and semi-automatic segmentation methods of cine MR images of the cardiac ventricles,using the short-axis view,the most common imaging plane to assess the cardiac function.We wish to provide the reader with (i)major challenges linked to this segmentation task,(ii)a state-of-the art of cardiac segmentation methods,including debut methods and current ones,and (iii)future trends in this ?eld.This paper is intended for researchers in the ?eld of cardiac segmenta-tion,but also to image processing and pattern recognition researchers interested to see how different segmentation tech-niques apply for a given application.The remaining of the paper is as follows.Short-axis MR images and the challenge of their seg-mentation are presented in Section 2.In Section 3,a categorization for segmentation methods is proposed and justi?ed.Segmentation methods are presented in Section 4and their results are discussed

1361-8415/$-see front matter ó2010Elsevier B.V.All rights reserved.doi:10.1016/j.media.2010.12.004

?Corresponding author.Tel.:+33232955215;fax:+33232955022.

E-mail addresses:Caroline.Petitjean@univ-rouen.fr (C.Petitjean),Jean-Nicolas.Dacher@chu-rouen.fr (J.-N.Dacher).

1

MICCAI Workshop –Cardiac MR Left Ventricle Segmentation Challenge,http://smial.sri.utoronto.ca/LV_Challenge/,2009.

in Section 5.At last conclusion and Section 6.

2.Cardiac MR image processing 2.1.Description of short-axis MR images

The complexity of segmenting heart chambers mainly relies on heart anatomy and MRI LV function consists in pumping the oxygenated and consequently to the systemic circuit.The LV known shape of ellipsoid (Fig.1)and is dium,whose normal values for thickness range On the contrary,the RV has a complex crescent lower pressure to eject blood to the lungs and times thinner than the LV,reaching the limit of tion.For those reasons,and because its function the LV’s,most research effort has focused on MRI has proven to provide an accurate (Shors et al.,2004).

Let us now describe the data that compose a examination.The standard imaging plane is long (apex-base)axis and called short axis of the heart in MRI covers the whole organ short-axis slices,distance between two from 10to 20mm.As the heart is a moving quired throughout the cardiac cycle,thanks to of MR acquisition to the ECG signal and the namic)MR sequences.In full-size images,the quite a small surface in cardiac MR images and ally restricted to a smaller region of interest phases (or images)can be obtained during one the currently available equipment,yielding a of about 30ms.The number of phases decreases proportionally of gray levels or structure shapes.Gray level intensities can also differ due to the use of different MRI scans or different bFFE se-quences.Fuzziness can be observed on some parts of the images,mostly due to blood ?ow and partial volume effects,aggravated by respiration motion artefacts.This former effect is a consequence of non-zero thickness of MRI slices:in some areas,a voxel can be a mixture of several tissue types.In terms of shape,the ventricle var-ies over patients,over time and over the long axis.This variability must be accounted for in segmentation algorithms.

2.2.Issues in cardiac MR image segmentation

Segmentation of the heart on these images consists in delineat-ing the outer wall,also called epicardium and the inner wall,called endocardium (Fig.2).Each contour to be delineated presents spe-ci?c segmentation dif?culties,as described below.

Epicardium segmentation.The epicardial wall is at the frontier between the myocardium and surrounding tissues (fat,lung),which have different intensity pro?les and show poor contrast with the myocardium.Segmentation of the epicardial wall is thus dif?cult,especially for the RV because of its reduced thickness.Endocardium segmentation.Endocardium surrounds the LV cav-ity.MRI provides quite good contrast between myocardium and the blood ?ow without the need of contrast medium.Still segmen-tation dif?culties exist,that mostly originate from gray level inho-mogeneities in the blood ?ow,and particularly because of the presence of papillary muscles and trabeculations (wall irregulari-ties)inside the heart chambers,which have the same intensity pro-?le as the myocardium (Fig.2).They can thus prevent from clearly delineating this wall.According to clinical standards,they should not be taken into account for endocardial wall segmentation.

Fig.1.LV and RV geometry.

Fig.2.A full size short-axis cardiac MR image and a ROI identifying the heart.

Fig.3.Variability among cardiac images.

170 C.

Because the endocardial wall is less dif?cult to segment that epicardial one,and since it is the only contour required to ventricular volume,some works only focus on the segmentation.

Position along the apex-base axis.Segmentation complexity depends on the slice level of the image.Apical and basal images are more dif?cult to segment than mid-ventricular Indeed,MRI resolution is not high enough to resolve size of structures at the apex and ventricle shapes are strongly close to the base of the heart,because of the vincinity of the Note also that the RV shape varies much throughout the apex-base axis,whereas the LV remains close to a ring shape,as shown in Fig.4.

2.3.Quanti?cation of cardiac systolic function

Endocardial and epicardial contours are used to quantify the heart function.Physicians are especially interested by the compu-tation of the RV and LV mass and volume at two precise moments of the cardiac cycle:the time of greatest contraction (end systole,ES)and the time of maximum ?lling (end diastole,ED)(Fig.5).Vol-ume is obtained by integrating surfaces obtained on the endocar-dium only,whereas mass computation requires the integration of both endocardial and epicardial surfaces.Volumes at end systole and end diastole are then compared by computing the so-called ejection fraction,de?ned as the ratio of the difference in heart volume during ED and ES times to the ED time.The computation of clinical parameters thus only requires contours at two instants of the cardiac cycle.Full cycle segmentation of the ventricles,although not used currently in clinical routine,allows to assess temporal volume and mass variations and would be of great inter-est as an indicator of cardiac performance (Caudron et al.,2011).It also allows to compute endocardial and epicardial wall motion,as well as myocardium thickening.Note that,because of the aper-ture problem,intramyocardial motion cannot be analyzed from standard cine-MR images but requires dedicated modalities such as tagged MRI (Rougon et al.,2005).3.Overview of segmentation methods

For this review,we have been considering the papers among peer-reviewed publications,that included (i)a segmentation categorization can be used with a few nuances and what criteria is chosen to classify the different methods.

3.1.A categorization of short-axis MR image segmentation methods Numerous segmentation problems require the use of a priori knowledge so as to increase their robustness and accuracy.On one hand,user interaction,an important consideration in any seg-mentation problem (Pham et al.,2000),can be regarded as a pri-ori knowledge.In our application,it can consist in either pointing the center of the LV cavity or manually tracing the ventricle bor-der.These two levels of user interaction do not have the same im-pact in terms of reproductibility,neither require the same level of expertise,and are thus going to be distinguished.On the other hand,as medical expertise is available on cardiac ventricles,it can be used during the segmentation process,with different lev-els of information as well.Prior information can consist in weak assumptions such as simple spatial relationships between objects (for instance,the RV is to the left of the LV)or anatomical assumptions making use of the circular geometry of the LV.The knowledge of the heart biomechanics can also be integrated into the segmentation process,to constrain adequately the segmenta-tion of the different phases.More accurate information regarding the shape of the heart can also be obtained through higher-level information,such as a statistical shape model.On some images,especially at the apex,myocardium borders are very fuzzy and ill-de?ned,and it is very dif?cult to rely on the image alone to perform segmentation.The use of a shape model for example is thereby particularly useful,but at the expense of building a train-ing data set with manually generated segmentations.We will thus distinguish three main levels of information used during Fig.

4.Cardiac images corresponding to 12short-axis slices from apex to base.

Cardiac MR images at end diastole (left)and end systole C.Petitjean,J.-N.Dacher /

including snakes and their variants,on the contrary,offer a great, versatile framework for using either weak or strong prior.They can include anatomical information,as well as high level informa-tion,in the so-called shape prior based segmentation framework, or through active shape and appearance models(ASM/AAM).At last,atlas guided segmentation also make use of a set of manually segmented images.Considering both the usual segmentation method categorization and the level of external information,we propose the following two main categories(Table1):

segmentation based on no or weak prior,that includes image-based and pixel classi?cation based methods,as well as deform-able models;

segmentation based on strong prior,that includes shape prior based deformable models,active shape and appearance models, and atlas based methods.

Methods combining strong and weak priors have been catego-rized in the strong prior section.In the next section,comparison criteria for segmentation methods are detailed.

3.2.Points of comparison for segmentation methods

Segmentation methods are compared in Table2,on the basis of their experimental conditions.Notations and acronyms used in this table are explained below.

LV/RV.This?ag indicates whether segmentation results are pro-vided on both LV(resp.RV)epicardial and endocardial contours (LV,RV),or endocardial only(LVv,RVv).

User interaction(U).User interaction may be used for segmenta-tion initialization.We will distinguish between limited user inter-action(U1),such as pointing the LV center or dragging a circle,and

Table1

Categorization of segmentation methods vs.type of prior information and related sections in the paper.

Region-and edge-based Pixel classi?cation Deformable models ASM/AAM Atlas

No prior Section Section Section

Weak prior 4.2.1 4.2.2 4.2.3

Strong prior Section Section Section

4.3.1 4.3.2 4.3.3

Table2

Overview of cardiac MR segmentation methods presented in70papers.LV/RV:Left and/or right ventricle segmentation,U:User interaction,E:External information,M:Motion information,ASA:Assessment of segmentation accuracy.Please refer to the text(Section3.2)for other acronym meaning.

Authors Basic method principle LV/RV U E M ASA

Segmentation with weak or no prior

(48)

Image-based Gupta et al.(1993)DP LV U2AM P–

Geiger et al.(1995)DP LV U2–P–

van der Geest et al.(1994)DP LV U1AM P EF V

M

Goshtasby and Turner(1995)Thresholding LVv

RVv

A AM–S

Kaushikkar et al.(1996)Thresholding LVv U1––EF V

Weng et al.(1997)Thresholding LVv

RVv

U1–––

Nachtomy et al.(1998)Thresholding LV U1AM–EF V

M

Waiter et al.(1999)Gradient LV U1––EF

Lalande et al.(1999)DP LV U1AM–V

Fu et al.(2000)DP LV U1––P2C

Cassen et al.(2001)Split and merge LV U2–P V

Noble et al.(2003)Non rigid registration LV U2–P EF V

Yeh et al.(2005)DP LVv U1AM–V

Liu et al.(2005)DP RVv–AM––

üzümcüet al.(2006)DP LV U2–M EF V P2C

Katouzian et al(2006)Thresholding LV RVv U1––S

Lin et al.(2006)Thresholding LVv A AM P P2C

Lee et al.(2008)Graph searching LV U1AM–EF V

M

Jolly et al.(2009)Shortest path and minimum

surf.

LV A AM P S P2C

Cousty et al.(2010)MM,watershed transform LV U1AM M EF M P2S

Pixel classif.Boudraa(1997)Clustering(FCM)LVv–AM–EF

Stalidis et al.(2002)Neural networks LV U1–M P2S

Gering(2003)GMM,MRF LV RVv A AM––

Lynch et al.(2006a)Clustering(K-means)LV–AM–EF S P2C

Kedenburg et al.(2006)Fuzzy kNN and graphcut LV A AM–V

Pednekar et al.(2006)GMM and DP LV A AM P EF V

Cocosco et al.(2008)Clustering LVv

RVv

A AM–EF V

Deformable

models

Ranganath(1995)Active contours LVv U1–P EF S

Chakraborty et al.(1996)Active contours+region term LV U1–––

Yezzi et al.(1997)GAC LV U1––V

Pham et al.(2001)3D deformable surfaces+GVF LV U1BM P V

Paragios(2002)GAC+GVF+region term LV U1AM––

172 C.Petitjean,J.-N.Dacher/Medical Image Analysis15(2011)169–184

advanced user interaction(U2),that consists in manually segment-ing the?rst image of the sequence.When no user interaction is needed,most methods start with an automatic localization of the heart(A).Methods for which no user interaction nor automatic heart localization is reported are speci?ed with a hyphen(-).

Use of external information(E).External information incorporated during the segmentation process may be a weak prior,that can be based on anatomical modeling(AM)such as(i)the circular aspect of the LV:transformation into polar coordinates,use of radial lines, (ii)simple spatial relationships,e.g.the RV is positioned on the left side of the LV,or(iii)the use of an ellipsoid,cylinder or bullet-shaped volumetric model.Assumptions based on the heart motion and deformations,such as the myocardium?ber stiffness,can be integrated into a biophysical model(BM).A strong prior(SP), namely a set of manually drawn borders gathered and synthetized into a statistical model,may also be used.Methods making no use of external information at all are speci?ed with a hyphen(-).

Use of motion information(M).As the heart is a moving organ,its motion can be taken into account in the segmentation process.We are not interested in the underlying contour point tracking prob-lem,that would consist in recovering the trajectories of material points,but rather by how the time dimension can help the seg-mentation process(Montagnat and Delingette,2005).We will distinguish between approaches that propagate an initial segmen-tation result(P)on the whole cardiac cycle by repeating their algorithm on each image,and approaches that explicitely take motion into account(M).Methods that do not make use of heart motion at all are speci?ed with a hyphen(-).

Assessment of segmentation accuracy(ASA).The performance of a segmentation method is quanti?ed through validation against a ground truth.Gold standard in this domain is manual delineation by an expert.Although qualitative visual evaluation is sometimes provided in certain studies(speci?ed with a hyphen),segmenta-tion accuracy is usually assessed by computing and comparing quantitative measures such as ventricle surface(S),volume(V) and mass(M),and ejection fraction(EF)based on contours ob-tained manually and automatically.Note that because of error compensation,these measures do not totally ensure accurate error measurement.In order to compare contours(resp.surfaces),error accuracy is better estimated by computing the mean perpendicular distance between them,denoted as point-to-curve(P2C)error (resp.point-to-surface(P2S)error).Correlation between manual tracing and automatic method,as well as inter-expert variability may be estimated through linear regression and Bland–Altman analysis.This latter analysis allows for comparison between two measurements by plotting the difference between the two mea-surements against their mean(Bland and Altman,1986).

We shall now review segmentation methods and explain how issues presented in Section2.2are handled,with a?rst focus on how the heart is roughly localized in the MR image.

Table2(continued)

Authors Basic method principle LV/RV U E M ASA

Zhukov et al.(2002)3D deformable surfaces LV U1AM––

Papademetris et al.(2002)Shape based matching LV U1BM P–

Santarelli et al.(2003)Active contours+GVF LV U2–P V M

Battani et al.(2003)GAC RVv U1––V

Pluempitiwiriyawej et al.

(2005)

Active contours+region term LV RV U1AM P S

Heiberg et al.(2005)3D Active contours LV U1AM P V

Wang and Jia(2006)Active contours+GVF LV U1AM P P2C

Jolly(2006)GMM+Active

contours+splines

LV U1AM P P2C

Hautvast et al.(2006)Discrete active contours LV RVv U2–P EF,V P2C

Gotardo et al.(2006)Active contours+Fourier desc.LV U1–P–

Sermesant et al.(2006)Registration LV RV U2BM P–

Yan et al.(2007)Registration LV RV U2BM P–

El Berbari et al.(2007)MM+Active contours+GVF LV U1AM–S P2C

Lynch et al.(2008)Level sets+temporal def.

model

LV A AM M P2C

Billet et al.(2009)Deformable models LV RV U2BM P–

Ben Ayed et al.(2009)Level sets+overlap priors LV U2AM–S Segmentation with strong prior(22)Shape prior Paragios et al.(2002)Level sets and stochastic

repres.

LV–SP––

Tsai et al.(2003)PCA and energy min.LVv–SP––

Kaus et al.(2004)PCA and energy min.LV–SP–P2S

Sénégas et al.(2004)Fourier desc.+Bayesian

approach

LV RVv–SP M P2C

Sun et al.(2005)PCA+Bayesian approach LV U2SP M–

Lin et al.(2005)Probabilistic map+Graphcut LV–SP–P2C

Lynch et al.(2006b)Level sets+PDF LV U1SP–S P2C

ASM/AAM Mitchell et al.(2000)AAM LV A SP–P2C

Stegmann and Nilsson(2001)AAM LV–SP–S P2C

Mitchell et al.(2001)Hybrid ASM/AAM LV RVv A SP–S P2C

Lelieveldt et al.(2001)2D+time AAM LV A SP M S P2C

Mitchell et al.(2002)3D AAM LV A SP–V M P2C

Ordas et al.(2003)ASM with IOF LV RV–SP–P2C

Stegmann and Pedersen

(2005)

3D bi-temporal AAM LV–SP–EF V

van Assen et al.(2006)3D ASM LV–SP–V P2C

Abi-Nahed et al.(2006)ASM+Robust Point Matching RVv–SP–P2C

Zambal et al.(2006)2D AAM+3D ASM LV–SP–P2S

Zhang et al.(2010)AAM+ASM LV RVv U2SP–V M P2S

Atlas Lorenzo-Valdés et al.(2002)Anatomical atlas+NRR LV RVv–SP P V

Lorenzo-Valdés et al.(2004)Probabilistic atlas+EM+MRF LV RVv–SP P V P2C

L?tj?nen et al.(2004)Probabilistic atlas+NRR LV RV–SP–P2S

Zhuang et al.(2008)Anatomical atlas+NRR LV RVv–SP–V P2C

C.Petitjean,J.-N.Dacher/Medical Image Analysis15(2011)169–184173

4.Ventricle segmentation in cardiac MRI

4.1.Automatic localization of the heart

As mentioned above,a ROI centered on the heart is generally extracted from the original MR image,in order not to process the whole image,thus decreasing computational load.Automatic ap-proaches are twofold:time-based approaches,that take advantage of the fact that the heart is the only moving organ in the images,or object detection techniques.They both have in common the use of the Hough transform,that allows to detect the position of the LV thanks to its circular aspect.Note that works presented in(Cocosco et al.,2004;Huang et al.,2007;Jolly,2008)are entirely devoted to this preliminary step,highlighting its importance.

When using time dimension,a difference or a variance image can be computed over all the data.In(Pednekar et al.,2006),a dif-ference image is computed between two images where the heart is the largest,i.e.in basal slices of the LV and at end diastole.The resulting image contains a circular region around the LV bound-aries,which is detected thanks to a Hough transform.Image differ-ence is also used in(Huang et al.,2007)followed by texture analysis and K-means clustering to isolate the heart region.Works proposed in(Cocosco et al.,2004;Gering,2003)rely on variance computation.Starting from a3D+t original image,variability along the time dimension is assessed with standard deviation of each voxel.The maximum intensity of this resulting3D image is pro-jected onto a2D image,binarized using Otsu’s method(Otsu, 1979),and dilated several times.The convex hull of the?nally ob-tained region is the?nal2D ROI(Fig.6).Some authors found that the variance image can be quite noisy and have thus proposed a method based on a Fourier analysis of the image(Lin et al.,2006; Jolly,2008).A pixelwise Fourier transform of the image sequence a Markov chain.The system is trained using positive and negative examples.The detection stage provides a cluster of pixels classi?ed as left ventricle and the?nal choice among these candidates is made using a Hough based voting procedure on the individual pro-?les,allowing for sketching a circle roughly positionned on the LV. The method proposed in(Pavani et al.,2010)is based on a popular face detection approach(Viola and Jones,2001),that consists in a Haar description of the subwindows and a cascade of adaboosted classi?ers.Authors suggest to optimize Haar-like features for a gi-ven object detection problem by assigning optimal weights to its different Haar basis functions.

4.2.Segmentation with weak or no prior

This section gathers segmentation methods with weak or no prior,including image-based,pixel classi?cation-based and deformable models.

4.2.1.Image-based methods

As seen in Section2.2,endocardial and epicardial contours pres-ent speci?c segmentation dif?culties.Many image-based methods propose to process them differently and separately,hence the focusing of certain methods on the LV endocardium only.The?rst step consists in?nding the endocardial contour,usually with thresholding(Goshtasby and Turner,1995;Weng et al.,1997; Nachtomy et al.,1998;Katouzian et al,2006)and/or dynamic programming(DP)(Gupta et al.,1993;van der Geest et al.,1994; Geiger et al.,1995;Lalande et al.,1999;Fu et al.,2000;Yeh et al.,2005;Liu et al.,2005;üzümcüet al.,2006).DP applied to image segmentation consists in searching for the optimal path in a cost matrix that assigns a low cost to object frontiers.Here,the circular geometry of the LV is taken advantage of using polar coor-

Automatic computed ROI from six patients(from(Cocosco et al.,2004),with kind permission from Elsevier). 174 C.Petitjean,J.-N.Dacher/Medical Image Analysis15(2011)169–184

posed,in order not to include papillary muscles:computation of the convex hull of the contour(van der Geest et al.,1994;Lin et al.,2006),applications of mathematical morphology(MM)oper-ations such as opening and closing on the contour(Nachtomy et al., 1998;Cousty et al.,2010),or?tting a parametric curve to the con-tour,allowing it to be smooth(Waiter et al.,1999).

The epicardium is found during a second step,often relying on the endocardial contour,that makes use of a spatial model incorpo-rating myocardial thickness or MM operators,applied on the endo-cardial contour.Note that for their initialization,most of these methods rely on a simple user intervention,such as pointing the center of the LV or dragging circles next to the myocardium contours.

When contours are processed identically,the segmentation pro-cess is initialized with manually drawn borders on the?rst image (Cassen et al.,2001;Noble et al.,2003;üzümcüet al.,2006).Man-ual contours are then propagated through all subsequent images, using split-and-merge(Cassen et al.,2001),non-rigid registration (Noble et al.,2003),or multidimensional DP:in(üzümcüet al., 2006)the initial contours provided by the user are resampled to 32landmarks.Each sample is tracked separately over time by de?ning a search space around each landmark.Cost hypercubes are then?lled with image-feature derived cost function values. The optimal connected path is tracked through cost hypercubes using DP.

4.2.2.Pixel classi?cation based methods

In medical image segmentation,pixel classi?cation is mostly used when multiple images of the same scene are available,as for instance with multispectral MRI or multimodality imaging, e.g.PETscan images(Dawant and Zijdenbos,2000).Each voxel can be described by several complementary features,and is consid-ered as an item to be classi?ed into a single class among several. The image is partitioned into regions or classes,composed of pixels that have close feature values,using either supervised techniques (with learning samples)or unsupervised ones.In our application, features are usually gray level values and segmentation is very of-ten performed using two standard unsupervised techniques which are Gaussian Mixture Model?tting(GMM)and clustering.During the segmentation process,methods use geometrical assumptions regarding the location of the ventricle,in order to compensate the lack of spatial information,inherent to classi?cation based methods,but do not require user interaction in general.As for im-age-based methods,both contours may be processed differently,as shown below.

The principle of GMM is to?t the image histogram with a mix-ture of gaussians using the Expectation-Minimization(EM)algo-rithm(Dempster et al.,1977).The number of gaussians,that corresponds to the number of modes in the histogram,must be ?xed a https://www.sodocs.net/doc/bc4080956.html,ually,between two and?ve modes corresponding to encountered tissue types(myocardium,fat,background,blood pool for example)are chosen.Partial volume effect may be ac-counted for by adding gaussians representing partial voluming be-tween myocardium and blood,myocardium and air(Pednekar et al.,2006).Papillary muscles can be taken into account by assign-ing a mixture of two gaussians to the ventricle cavity:the blood pool and the myocardium(Sénégas et al.,2004).The EM algorithm can be initialized by using the preliminary step of heart localiza-tion(Pednekar et al.,2006)or using an atlas(Lorenzo-Valdés et al.,2004,see Section4.3.3).The EM segmentation result can be embedded in a cost matrix for dynamic programming(Pednekar et al.,2006),or precedes a step based on Markov Random Fields (MRF)in order to incorporate spatial correlations into the segmen-tation process(Gering,2003).The clustering approach consists in aggregating data in clusters in a feature space.Clustering can be performed through K-means algorithm(Lynch et al.,2006a)or fuz-zy C-means,a generalization of K-means allowing partial member-ship in classes(Boudraa,1997).After obtaining separate cluster regions,the LV cavity is identi?ed by computing the distance to a circle(Lynch et al.,2006a).The closest blood pool being the one of the RV,the wall between these two cavities is measured to assess the myocardium thickness,which acts as a guide for seg-menting the epicardium,using edge information.The epicardium contour is closed using a spline.

Only a few supervised approaches have been proposed,since they require a tedious learning phase,that consists in providing the algorithm with gray levels of labeled pixels.The learning can be performed manually,by clicking on a few sample pixels belong-ing to myocardium,blood and lung(Stalidis et al.,2002).Theses samples are provided to a generating-shrinking neural network, combined with a spatiotemporal parametric modeling.In this work,the epicardial boundary is found through a radial search, using the previously de?ned endocardial model.The learning phase may also be automatic,by designing a spatial mask that is applied onto the image,thus providing tissue samples.A k-nearest neighbor algorithm is then used to classify the image pixels,which yields a cost map for graphcut segmentation(Kedenburg et al., 2006).

4.2.3.Deformable models

Deformable models have been made popular through the sem-inal work by Kass et al.(1988),who introduced active contours,or snakes.Thanks to their?exibility,active contours have been widely used in medical image segmentation(Xu et al.,2000).There are iteratively deforming curves according to the minimization of an energy functional,comprising a data-driven term,that provides information about object frontiers and a regularization term,that controls the smoothness of the curve.This energy functional is minimized by implementing the Euler–Lagrange equations in a partial differential equation(PDE).In problems of curve evolution, the level set framework has been widely used because it allows for topological changes(Osher and Sethian,1988).It consists in considering the deforming contour as the zero level of a higher-dimensional function.This implicit representation of the contour allows in particular the segmentation of multiple objects(Caselles et al.,1993).Deformable models have widely been applied to the ventricle segmentation problem either in the parametric framework or in the implicit one using level sets(Yezzi et al., 1997;Battani et al.,2003).

In most of the studies,the regularization term does not change much and is often curvature-based.The contributions regarding ventricle segmentation using deformable models have mainly dealt with the design of the data-driven term.Initially gradient-based(Gupta et al.,1993;Ranganath,1995;Geiger et al.,1995) and thus sensitive to noise,region-based terms have been introduced,that are based on a measure of region homogeneity (Paragios,2002;Pluempitiwiriyawej et al.,2005;Chakraborty et al.,1996).In(Ben Ayed et al.,2009),the authors take into account the intensity distribution overlap that exists between myocardium and cavity,and background and myocardium,and introduce a new term in the functional that measures how close the overlaps are to a segmentation model,manually obtained in the?rst frame.The Gradient Vector Flow(GVF)has also been widely used(Xu and Prince,1998).Initially designed to pull the contour into the object concavities,the GVF consists in diffusing the gradient of an edge map.Authors have noticed that it increases ef?ciency regarding initialization and convergence,hence its wide use(Pham et al.,2001;Santarelli et al.,2003;Wang and Jia,2006; El Berbari et al.,2007).Other energy terms have been introduced: in particular,Paragios proposes a coupled propagation of the epi-cardial and endocardial contours that combines both GVF and level sets(Paragios,2002)(Fig.7).The relative positions of the endocar-

C.Petitjean,J.-N.Dacher/Medical Image Analysis15(2011)169–184175

dium and the epicardium are constrained inside the process.In or-der to ensure the smoothness of the contour,a parametric shape model(circle,elliptic,spline),e.g.the direct Fourier parameteriza-tion of the contour(Staib and Duncan,1992),allows for compact representation and facilitates the formulation of energy(Chakr-aborty et al.,1996;Gotardo et al.,2006).Note that contour initial-ization,a crucial step with deformable models,can be carried out through image preprocessing,such as MM operations(El Berbari et al.,2007)or the EM algorithm(Jolly,2006),or else user interac-tion,as shown in Table2.

Deformable models offer a great framework for3D extension (Pham et al.,2001;Zhukov et al.,2002;Montagnat and Delingette, 2005;Heiberg et al.,2005)2,thanks to3D mesh models,but also to obtain ventricle contours throughout the entire cardiac cycle.A?rst approach to temporal extension is to apply the segmentation result obtained on the image at time t on the following phase image at time t+1.Whereas it has the advantage of low complexity,this sequen-tial approach does not integrate motion information and does not really exploit the temporal aspect of heart motion.Recent ap-proaches have been developped,that apply constraints on temporal evolution of the contour or surface points:it can be a weak con-straint such as averaging point trajectories or a strong constraint such as encoding prior knowledge about cardiac temporal evolution (Montagnat and Delingette,2005;Lynch et al.,2008)or use a seg-mentation/registration coupled approach(Paragios et al.,2002).

Volumetric modeling is particularly useful for tracking the LV cavity over time,using a biomechnical model to constrain the seg-mentation(Pham et al.,2001;Papademetris et al.,2002;Sermesant et al.,2006;Yan et al.,2007;Billet et al.,2009;Casta et al.,2009). The LV myocardium is modeled as a linear elastic material de?ned by several parameters(Poisson’s ratio and Young’s modulus,or equivalently Lamé’s constants),integrated into the so-called stiff-ness matrix,that de?nes the material properties of the deforming body in three dimensions.(Pham et al.,2001;Papademetris et al., 2002).The contractility of the myocardium is linked to the muscle ?ber directions,which is not isotropic.Fiber orientation can be taken into account by considering different stiffness values for the different material axes(Papademetris et al.,2002).In(Billet et al.,2009),the?ber orientation is part of an electromechanical model,that simulates the cardiac electrophysiology.This model is used to regularize the deformations of the volumetric model. This volumetric meshing is usually initialized with2D contours manually obtained on the?rst phases.The mesh is then deformed using an image force and an internal force derived from the biome-chanical model as the regularizing term.Segmentation over the whole cardiac cycle is then obtained by minimizing an energy that couples the volumetric model deformations and the image data (Fig.8).The dynamic laws of motion expressed in PDE can be solved using?nite element method(Pham et al.,2001; Papademetris et al.,2002;Sermesant et al.,2003).Note that these approaches generally include further investigations regarding car-diac motion estimation,tissue deformation analysis and strain computation from3D image sequences.In particular,the introduc-tion of functional information regarding the heart can help recover tangential motion of the ventricle,which cannot be obtained from standard tracking approaches because of the aperture problem (Billet et al.,2009).

anatomical constraints for the segmentation of the left ventricle.Black contours:initial conditions

Science+Business Media).

volumetric mesh and associated segmentation result.(a)Mid-diastole image.(b)Segmented mesh with synthetic?ber directions.

the cardiac cycle(from(Billet et al.,2008),licensed under the Creative Commons3.0Unported License).

2The authors have made their software freely available for research purposes at

http://segment.heiberg.se/(Heiberg et al.,2010).

4.2.4.Conclusion

A wide variety of image-driven approaches using weak or no prior have been proposed to tackle the ventricle segmentation in cardiac MRI.Almost all of these methods require either minimal or great user intervention.If image-based and pixel classi?ca-tion-based approaches offer a limited framework for incorporating strong prior,extensions of deformable models in this sense have been extensively studied.In the next section are presented meth-ods relying on strong prior for heart segmentation.4.3.Segmentation with strong prior

As shown by the growing literature on this matter,automatic organ segmentation can bene?t from the use of a statistical model regarding shape and/or gray levels,to increase its robustness and accuracy.This especially applies if the nature of the shape does not change much from an individual to another,which is typically the case for the heart.Statistical-model based segmentation tech-niques comprise three steps:

1.Spatial (and temporal if required)alignment of manually seg-mented contours or images is of utmost importance to compen-sate for differences in ventricle position and size,and can be very dif?cult,especially in 3D (Frangi et al.,2002).One subject in the database is arbitrarily chosen as reference.Every other subject is af?nely registered on the reference,and an average shape is com-puted.This procedure can be performed iteratively by replacing the reference subject with the mean model.When segmentation is computed over the complete cardiac cycle,temporal aligne-ment is needed as well:the number of phases of each individual must be aligned on the number of phases of the reference and thus requires resampling and interpolation (Fig.9).

2.Model construction generally implies the computation of an average shape or image and the modeling of variability present in the training images and contours.This latter can be made via the widely used principal component analysis (PCA),when point correspondences between contour points are available,or else via variance computation or probability density model-ing.The PCA provides the eigenvalue decomposition of the shape set covariance matrix,yielding principal eigenvectors (or components),that account for as much of the variability in the data as possible.Each instance of a new shape can thus be described by the mean shape and a weighted linear combina-tion of eigenvectors.

3.The use of the model for segmentation speci?es how the aver-age model is applied to ?t the contours in a new image,while taking into account the variability present in the training set.Methods based on a statistical model mainly fall into three cat-egories:shape prior segmentation (Cremers et al.,2007),active

shape and appearance models (Heimann and Meinzer,2009)and atlas-based segmentation techniques (Rohl?ng et al.,2005).Whereas steps 1and 2are globally common to these methods,they mostly differ by step 3,i.e.the application of the model for segmentation.

4.3.1.Deformable models based segmentation using strong prior

The principle of deformable models with strong prior takes up the variational framework de?ned in Section 4.2.3.The principle is to modify the energy functional to be minimized by introducing a new term,that embeds an anatomical constraint on the deform-ing contour,such as a distance to a reference shape model.To con-struct the reference model,an original variational technique to compute the mean signed distance map is proposed in (Paragios et al.,2002).Then an aligment transformation to this reference is incorporated into the criterion to be minimized.A probability den-sity function (PDF)or probabilistic map can be computed from the data by adding the binary segmented images of both contours,after scaling and alignment.This PDF is embedded as a multiplica-tive term in the evolution equation (Lynch et al.,2006b )or inte-grated into the energy function of a graphcut (Lin et al.,2005).An alternative to the use of a PDE is proposed in (Tsai et al.,2003;Kaus et al.,2004),with the advantage of being fast and di-rect,based on a preliminary PCA on the training data.For a new contour to be segmented,eigenvector weights as well as pose parameters are iteratively updated with a gradient descent,by minimizing the region-based energy terms.Note that these ap-proaches include the coupled propagation of both contours,as al-ready seen in Section 4.2.3,that maintains the relative positions of the endocardium and the epicardium according to a distance model (Kaus et al.,2004;Lynch et al.,2006b;Paragios et al.,2002).To address the temporal aspect of segmentation,approaches relying on bayesian formulation are proposed (Sénégas et al.,2004;Sun et al.,2005).Under the statistical modeling of the image,the segmentation process becomes a MAP (Maximum A Posteriori)estimation.Here,the regularity term is based on the prior,that contains a shape model and a motion model,thus allowing to track ventricle contour over time.The shape model is obtained from an PCA (Sun et al.,2005)or based on a Fourier representation,whose parameters are learned on a database of segmented images (Sénégas et al.,2004).Segmentation is performed with Monte-Carlo techniques or particle ?ltering.

4.3.2.Active shape and appearance models

The ASM consist of a statistical shape model,called Point Distri-bution Model (PDM),obtained by a PCA on the set of aligned shapes,and a method for searching the model in an image (Cootes et al.,1995).Segmentation is performed by placing the model on the image,and iteratively estimating rotation,translation and scal-ing parameters using least square estimation,while

constraining

resampling:linear interpolation is used to generate time frames from image sequence B which correspond kind permission from Elsevier).

the weights of the instance shape to stay within suitable limits for similar shapes.ASM have been extended to gray level modeling,yielding Active appearance models (AAM)(Cootes et al.,1998),that represent both the shape and texture variability seen in a training set.This technique ensures to have a realistic solution,since only shapes similar to the training set are allowed.

AAM applied to LV segmentation are ?rst presented indepen-dently in (Mitchell et al.,2000)and in (Stegmann and Nilsson,2001),demonstrating the clinical potential of the approach for the segmentation of both the endocardium and epicardium.Strengths of AAM and ASM can be combined in a hybrid model (Mitchell et al.,2001;Zambal et al.,2006;Zhang et al.,2010).In (Mitchell et al.,2001),the authors introduce a multistage hybrid model,arguing that AAM are optimized on global appearance but provide imprecise border locations,whereas ASM have a great abil-ity to ?nd local structures.They thus propose to concatenate sev-eral independant matching phases,starting with an AAM early stage,that positions the model onto the heart,followed by a hybrid ASM/AAM stage,that allows for position re?nement.A ?nal stage of AAM aids in escaping a possible local minimum found during the ASM/AAM stage.Although this method provides accurate re-sults,and,for the ?rst time with AAM,results on the RV,the current model training has been limited to mid-ventricular,end-diastolic images.3The idea of combining AAM and ASM has also been used in (Zambal et al.,2006),where the global model con-struction consists in interconnecting a set of 2D AAM by a 3D shape model.The goal of the AAM is to match contours on each image individually,while the 3D shape model provides an overall consis-tency to the instance of the model.The obtained segmentation re-sult is improved on apical slices:if the local matching of 2D AAM fails,is it corrected by the 3D model,through iterative global and local matching.

Several modi?cations of the original framework have been pro-posed to increase segmentation accuracy such as the use of an Independent Component Analysis instead of a PCA (üzümcüet al.,2003),the introduction of ASM with Invariant Optimal Fea-tures (IOF)(Ordas et al.,2003),a technique that replaces the Maha-lanobis distance with feature selection from a set of optimal local features.The current model training for these studies has also been limited to mid-ventricular,end-diastolic images.The local search of corresponding points during ASM segmentation can be made

more reliable by the use of a robust estimator,such as Robust Point Matching,a technique that allows to match two sets of features using thin-plate splines (Abi-Nahed et al.,2006).This method has been speci?cally applied to the RV segmentation.

Extension of the model to the temporal dimension is proposed in (Lelieveldt et al.,2001),with the introduction of 2D+time Active Appearance Motion Model (AAMM).Authors propose to extend the 2D AAM framework by considering the whole sequence of images over one cardiac cycle and by modeling not only shape and gray levels of the heart,but also its motion.Because of the variation of the image number per cardiac cycle from one patient to another (from 16to 25in their study),a temporal normalization is re-quired,here set to 16phases.The model allows to obtain in a fast manner segmentation over the whole cardiac cycle,still limited to mid-ventricular slices.The extension to 3D AAM and ASM is pre-sented in (Mitchell et al.,2002;Stegmann and Pedersen,2005;van Assen et al.,2006),although not straightforward,especially be-cause the model requires point correspondences between shapes (a result is provided in Fig.10).The great amount of data to be pro-cessed in 3D models leads to an increase of the computational load,that can be lowered thanks to the use of techniques such as grid computing (Ordas et al.,2005).

4.3.3.Atlas-guided segmentation and registration

An atlas describes the different structures present in a given type of image.It can be generated by manually segmenting an im-age or by integrating information from multiple segmented images from different individuals.Given an atlas,an image can be seg-mented by mapping its coordinate space to that of the atlas,using a registration process (Rohl?ng et al.,2005).Widely applied to brain segmentation (Collins et al.,1995),this technique has also been used for heart segmentation.As shown in Fig.11,the princi-ple is to register the labeled atlas onto the image to be segmented,and then apply the obtained transformation to the atlas,so as to obtain the ?nal segmentation.Segmentation can thus easily be propagated throughout the cardiac cycle using the same principle.In the literature,the construction of an anatomical heart atlas is based either on a single segmented image (Lorenzo-Valdés et al.,2002),an average segmentation result obtained over a population of healthy volunteers (14Lorenzo-Valdés et al.,2004or 25L?tj?-nen et al.,2004),or a cadaver atlas (Zhuang et al.,2008).The atlas or model can be matched on a new individual using non-rigid reg-istration (NRR),a transformation that accounts for elastic deforma-tions.NRR consists in maximizing a similarity measure between a source image S (the atlas)and a target or reference image R

(the

3D AAM.(a)Manually identi?ed contours.(b)3D AAM determined segmentation of the left ventricle (from 3

In this work the segmentation is performed in full-size image volumes.The location of the approximate center of the LV cavity is found with a Hough transform and is used to place the AAM model on the target image.

unsegmented image).Since the atlas and the MR image can have non corresponding gray levels,the similarity criterion must only account for statistical dependencies between them.The most widely used criterion for NRR is the normalized mutual informa-tion measure E NMI(Studholme et al.,1999).Based on individual and joint gray level distributions,E NMI is de?ned as:

E NMIeS;RT?HeSTtHeRTHeS;RT

where H(á)denotes marginal entropy and H(á,á)joint entropy of cor-responding pixel or voxel pairs.Maximizing only the similarity cri-terion provides under-constrained equations,that makes image registration an ill-posed problem and thus requires the use of addi-tional constraints.One way is to restrict the transformation space to parametric transformations,such as cubic splines(Lorenzo-Valdés et al.,2002)or the basis of eigenshapes,obtained with a PCA on the database of shapes(L?tj?nen et al.,2004).Another way is to add a regularization term to the similarity criterion,such as a clas-sical viscous?uid model(Zhuang et al.,2008),or a statistical model (L?tj?nen et al.,2004).In this latter work,the variability of the shape in the database of subjects is used as a regularizer.This var-iability is modeled with probabilistic shape models,including a probabilistic atlas,that provides the probability that a structure ap-pears at each pixel.It is constructed by af?nely registering all sub-jects to the reference,blurring the registered segmentation image with a Gaussian kernel and averaging all blurred segmentation.It has the advantage not to require point correspondence.Note also the use of a probabilistic atlas in(Lorenzo-Valdés et al.,2004),to initialize the parameters of an EM algorithm.The segmentation ob-tained after convergence of the EM algorithm is re?ned thanks to contextual spatial information modeled through MRF.

4.3.4.Conclusion

By imposing constraints on the?nal contour through the use of a statistical model,strong prior based methods can overcome the previously de?ned segmentation problems(ill-de?ned cavity bor-ders,presence of papillary muscles and gray level variations around the myocardium),without the need of user interaction, but at the expense of manually building a training set.The compo-sition of the training set is questionable,as variability depend upon initial data.ASM cannot approximate data that are not in the train-ing set and have to be representative enough of all possible heart shapes to achieve high accuracy.In(Zhang et al.,2010),the authors compensate the limited size of their training set by introducing an-other source of information,namely a manual segmentation of the ?rst frame.The method is proved to be more robust but loses the bene?t of being user-independant.Note that incorporation of time dimension and the third dimension into the model is not straight-forward.For AAM,its high dimension increases the risk of over?t-ting.The non-rigid registration framework is more?exible,allowing for shapes not present in the training set,but does not im-pose anatomical constraint on the transformation.As a result,the composition of the atlas has little in?uence on the segmentation results,since it is only used as a starting point for registration (Zhuang et al.,2008).

5.Results and discussion

5.1.Methodological issues

Now let us examine how issues presented in Section3.2have been dealt with,according to the type of methods,by commenting Table2.Among the70papers that have been reviewed in this pa-per,only three studies are entirely devoted to the RV,while a quar-ter of the rest of the papers show segmentation results on both ventricles.As mentioned above,physical characteristics of the RV as well as its lesser vital function has restrained research efforts on its segmentation.Nonetheless there is a growing interest for the segmentation and volume computation of the RV,since MRI is increasingly used as a standard tool in the evaluation of RV func-tion,being the most accurate tool for assessing RV volume(Haddad et al.,2008).Furthermore,in some pathologies(RV out?ow tract obstruction,pulmonary stenosis,transposition of great vessels, tetralogy of Fallot,pulmonary hypertension),the RV is generally hypertrophied,which could help the segmentation process.Be-cause of the RV’s greatly varying shape,strong prior-based meth-ods and in particular,atlas-based methods,thanks to their ?exibility,seem of particular interest for RV segmentation.Regard-ing the endocardium and epicardium,they are of different nature, and thus present different segmentation challenges,as described in Section2.2.For some categories of methods,namely image-driven methods and pixel-classi?cation based approaches,speci?c solu-tions for each contour have been developed.On the contrary,mod-el-based approaches do not require the design of two different algorithms.One of the segmentation challenges is the handling of papillary muscles.Currently,the common segmentation stan-dards recommend to consider them as part as the ventricle cavity and to contour only the walls,because manual segmentation is more reproductible in this case,than when papillary muscles are segmented as well.But the exact cavity volume computation should exclude the volume occupied by the papillary muscles.In-deed,in some methods,pillars are segmented as well,authors arguing that the radiologist should decide whether to incorporate them or not(Pednekar et al.,2006;Lynch et al.,2006a).

Regarding the use of external information,this review high-lights the fact that knowledge is necessarily integrated into the segmentation process,be it during the initialization phase (through user interaction)or during the process itself,with differ-ent prior levels.The tradeoff between user interaction levels and levels of external information is illustrated in Fig.12.

5.2.Tracking the ventricle borders and motion information

Tracking the ventricle boundaries over time allows for full cycle segmentation and for further investigation of the cardiac deforma-tions and strain.Only a few methods really exploit the information provided by cardiac motion,partly because of the complexity and the variability of the motion model,but also because ED and ES im-age segmentations are suf?cient for estimating the cardiac con-tractile function in a clinical context.Making use of the temporal dimension can help the segmentation process and yields tempo-rally consistent solutions.Temporal continuity is also of interest for the clinician during manual segmentation,as he often examines images that follow or precede the image to be segmented in the se-quence,as well as corresponding images in slices below or above.

11.Anatomical atlas-based segmentation principle:(i)computation of

transformation T between the atlas and the image and(ii)deformation of the atlas

T(from(Lorenzo-Valdés et al.,2002),with kind permission from Springer

Science+Business Media).

Image Analysis15(2011)169–184179

The expert behavior can thus be emulated by considering that the neighborhood of each voxel includes its six spatial nearest neighbors and the voxels in the neighboring time frames of the sequence,such as in MRF (Lorenzo-Valdés et al.,2004)or in (Cousty et al.,2010),where a 4D graph corresponding to the 3D+t sequence is considered.

Tracking the ventricle contours over time may be performed with or without external knowledge.In this latter case,tracking re-lies on intrinsic properties of the segmentation methods.The var-iational approach of deformable models has been shown to be a very powerful and versatile framework for tracking the ventricle borders,the temporal resolution of cardiac MR allowing for using the segmentation result of the previous frame and propagating it to the next one (Pham et al.,2001;Gotardo et al.,2006;Hautvast et al.,2006;Ben Ayed et al.,2009).In order to improve the robust-ness of the propagation results,solutions have been proposed,like tracking the contours both backwards and forwards in time (Gotardo et al.,2006)and constraining the contour to respect the user’s preference by maintaining it to a constant position,through the matching of gray level pro?les (Hautvast et al.,2006).Non-rigid registration may also be used to propagate manually initialized contours or a heart atlas (Lorenzo-Valdés et al.,2002;Noble et al.,2003;Zhuang et al.,2008).In this case,the segmenta-tion boils down to a registration problem:the matching of one (segmented)image to the other (unsegmented)is then applied to the contour of the segmented image,thus providing the new de-formed contour.Segmentation and registration can also be coupled together by jointly searching for the epicardial and encocardial contours,and for an aligment transformation to a shape reference (Paragios et al.,2002).

Deformable models also are ef?cient for introducing knowledge regarding heart motion.Prior knowledge about cardiac motion can be encoded in a weak manner,by temporally averaging the trajec-tories of the contour or surface points (Heiberg et al.,2005;Montagnat and Delingette,2005),or in a strong manner,by using external prior.In (Lynch et al.,2008),the authors observed that the change of the blood volume of the ventricle is intrinsically linked to the boundary motion and that the volume decreases and increases during one cardiac cycle.The movement of the con-tour points are then modeled by an inverted Gaussian function,used to constrain the deformation of the level set.The dynamics of the heart can be taken into account via a biomechanical model (see Section 4.2.3),used not to predict motion but to regularize the deformations of the volumetric model.Another possibility is to consider the moving boundaries as constituting a dynamic sys-tem,whose state must be estimated thanks to observations (the

images)and a model,learned from training date (Sénégas et al.,2004;Sun et al.,2005).This explicit combination of shape and mo-tion information,together with the appearance of the heart,can also be embedded in an ASM/AAM framework as a single shape and intensity sample (Lelieveldt et al.,2001).

Tracking the LV and RV borders over time is feasible,mainly in a deformable model framework.Thanks to full cycle image segmen-tation,the volume variation throughout the cardiac cycle can be assessed,along with other quantitative parameters (such as strain),that have proven useful for assessing the cardiac contractile func-tion (Papademetris et al.,2002).

5.3.Assessment of segmentation accuracy

The assessment of segmentation accuracy greatly varies among reported works and ranges from visual qualitative assessment to perpendicular distance between contours computation,via surface overlap,ventricle volume,mass and EF computation.Note that al-most all of the strong prior-based approaches are assessed via the mean P2C error.Test conditions change also a lot from one study to another:the number of test images,the number and nature of the patients (healthy and/or pathological),the phase of the cardiac cy-cle (only ED vs.all phases),the slice levels (only mid-ventricular le-vel vs.all slice levels),not to forget that these conditions are sometimes not or only partly speci?ed.Since these conditions have an in?uence on the segmentation complexity and thus on the ?nal result,they have been reported in the result table (Table 3).The last lines of this table include the participants to the MICCAI’09challenge.For this contest,two databases 4(one for training and the other for validation)have been provided to the participants,and results are provided either on one or both databases.Interest-ingly,the methods that have been assessed during this challenge are quite representative of existing methods.They range from simple image-based techniques,as proposed in (Huang et al.,2009;Lu et al.,2009),to ASM and AAM (O’Brien et al.,2009;Wijnhout et al.,2009),including deformable models (Constantinides et al.,2009)(an im-proved version of El Berbari et al.,2007;Casta et al.,2009),taking over works from Pham et al.(2001),a 4D watershed framework (Marak et al.,2009),based on (Cousty et al.,2007),and Jolly’s im-age-based method (Jolly,2009)based on (Jolly et al.,2009).

In order to limit the scope of our comparison,and also because we search for the best estimate of segmentation accuracy,the

fo-vs.levels of prior in cardiac MR segmentation methods in terms of paper numbers.Each circle is proportional interaction.U2:Advanced user interaction.

4

The database of the MICCAI’09contest is the Sunnybrook Cardiac MR Database,available at https://www.sodocs.net/doc/bc4080956.html,/projects/cardiac-mr/?les/.

cus is given in this review to the mean distance between contours. The choice of mean P2C error allows for comparison with intra and inter-observer variability of manual contouring,which is in the range1–2mm(Ordas et al.,2005;van Assen et al.,2006;L?tj?nen et al.,2004;Marak et al.,2009).On the whole,reported errors com-pare favorably to this value.As expected,error is higher on the epi-cardial wall than on the endocardial one,an observation that can be made in19out of28results.Results obtained on ED images are also better than results obtained on other phases.Note that a few segmentation results,especially on the RV endocardium,have been obtained on a reduced number of slices,highlighting the dif-?culty of segmenting apical and basal images.Indeed,the segmen-tation error computed on the RV endocardium is higher than on the LV.In a restricted number of papers,the spatial distribution of errors is reported(Lin et al.,2006;Jolly et al.,2009;Grosgeorge et al.,in press).These studies con?rm that segmentation is more dif?cult in apical than in basal or mid-ventricular slices.Because testing conditions differ from one study to another,it seems dif?-cult to draw more conclusions.Regarding the MICCAI Challenge studies,the ambiguity in the database choice does not allow for full comparison of the results.Nonetheless,one can note that among the eight involved methods,the ones obtaining the best results are image-based techniques(Lu et al.,2009;Huang et al.,2009). However these techniques require user interaction and cannot as-sess the ventricular surface in all phases,contrary to O’Brien et al. (2009),Casta et al.(2009),and Jolly(2009).In this sense,the work described in(Jolly,2009)offers a good compromise.Although results presented in(Lu et al.,2009;Huang et al.,2009;Constantinides et al.,2009)are interesting,their associated methodologies are LV speci?c and not applicable to the RV,whereas it would directly be possible with more generic methodologies such as in(O’Brien et al.,2009;Wijnhout et al.,2009).These trends illustrate the compromise between method performance and speci?city.

6.Conclusion and perspectives

This paper has been presenting segmentation methods in car-diac MRI.It seemed important to us to integrate the recent devel-opments of the last decade about prior knowledge based segmentation,almost10years after Frangi et al.’s comprehensive review(Frangi et al.,2001).We have proposed a categorization for these methods,highlighting the key role of the type of prior information used during segmentation,and have distinguished three levels of information:(i)no information is used,but our study shows that in this case user interaction is required,(ii)weak prior,that is,low level information such as anatomical assump-tions on the ventricle shape or biomechnical models,often com-bined to low-level user interaction,(iii)strong prior such as statistical models,constructed or learned from a large number of manually segmented images,usually not requiring user interac-tion.Our image segmentation categorization includes on the one hand image-driven and pixel classi?cation based approaches,and deformable models,making use of weak or no prior.On the other hand,strong prior approaches comprise shape prior deformable models,ASM and AAM,and atlas-based segmentation.We have tried to point out that segmentation results on cardiac images are obtained in diverse experimental conditions,on different,pri-vate image databases and using varying error measures,thus mak-ing it dif?cult to conclude on the ef?ciency or the superiority of

Table3

Reported segmentation errors.When multiple results were available,only best results were reported.H/P:number of healthy(H)and pathological(P)subjects.

Authors Nb H/P Slice Phases Mean errors(mm)

Subj.nb.LV epi LV endo RV endo

Mitchell et al.(2001)2011/93mid ED 1.75±0.83b 1.71±0.82b 2.46±1.39b Lelieveldt et al.(2001)25c–3mid all0.77±0.740.63±0.65–Mitchell et al.(2002)56c38/188–14ED 2.63±0.76 2.75±0.86–Ordas et al.(2003)7413/613mid5ph. 1.52±2.01d 1.80±1.74 1.20±1.47 Kaus et al.(2004)1210/1217–10ED 2.62±0.75 2.28±0.93–

ES 2.92±1.38 2.76±1.02–Sénégas et al.(2004)30–5ED 1.98a 1.34a–

ES 2.74a 2.62a–üzümcüet al.(2006)202/188–12All 1.77±0.57 1.86±0.59–Lynch et al.(2006a)25–5–12ED,ES 1.31±1.860.69±0.88–Lynch et al.(2006b)4––All 1.83±1.850.76±1.09–van Assen et al.(2006)1515/010–12ED 2.23±0.46 1.97±0.54–Abi-Nahed et al.(2006)13––ED–– 1.1a Lorenzo-Valdés et al.(2004)100/103mid All 2.99±2.65 2.21±2.22 2.89±2.56

ED 2.75±2.62 1.88±2.00 2.26±2.13 L?tj?nen et al.(2004)25c25/04–5ED 2.77±0.49d 2.01±0.31 2.37±0.5 Hautvast et al.(2006)69–9/14ES 1.84±1.04 2.23±1.10 2.02±1.21 El Berbari et al.(2007)13–3ED 1.3±0.70.6±0.3–Jolly et al.(2009)19–All ED,ES 2.91a,b 2.48a,b–Zhang et al.(2010)2525/0–All 1.67±0.3 1.81±0.4 2.13±0.39

250/25–All 1.71±0.45 1.97±0.58 2.92±0.73 Cousty et al.(2010)180/189–14ED,ES 1.42±0.36 1.55±0.23–Casta et al.(2009)e153/126–12ED,ES 2.72a––Wijnhout et al.(2009)e153/126–12ED,ES 2.29a 2.28a–Lu et al.(2009)e153/126–12ED,ES 2.07±0.61 1.91±0.63–Marak et al.(2009)e––6–12ED,ES3±0.59 2.6±0.38–Constantinides et al.(2009)e306/246–12ED,ES 2.04±0.47 2.35±0.57–Jolly(2009)e306/246–12ED,ES 2.26±0.59 1.97±0.48–Huang et al.(2009)e306/246–12ED,ES 2.06±0.39 2.11±0.41–O’Brien et al.(2009)e306/246–12ED,ES 3.73a 3.16a–

a No standard deviation provided.

b RMS error.

c Leave-one-out protocol.

d RV epicardium is taken into account for error computation.

e Study part o

f the MICCAI contest.

C.Petitjean,J.-N.Dacher/Medical Image Analysis15(2011)169–184181

one method over the others.One result of our review is that seg-mentation results are generally satisfying for the LV,especially on mid-ventricular slices,since the precision is of the order of manual tracing variability.These results are suitable for clinical pratice and?nally show that room for improvement on the LV seg-mentation problem might be limited and restricted to basal and apical slices.Just as image segmentation can rely on anatomical modeling,tracking the ventricle borders over a complete cardiac cycle can rely on prior knowledge regarding the heart motion(such as a biomechanic model).Tracking allows to compute the varia-tions of the ventricle volumes and other quantitative parameters. It is thus a complementary way to characterize the heart contrac-tile function,that may be used in clinical routine in the future. Regarding the RV segmentation results,one can note that they have been reported in a limited number of papers.This task is still a critical issue,due to the varying and complex shape of this ven-tricle and to its thin and ill-de?ned borders,appearing fuzzy in api-cal slices.

Other challenging image processing and pattern recognition is-sues connected to short axis MR images include the automatic identi?cation of ED and ES frames,currently made by browsing through all the image sequence(Lalande et al.,2004),and the determination of imaging slices that can be taken into account for volume computation.Physicians are confronted to a hard choice for those situated around the base of the heart,since certain slices are above the ventricle and include atria.

Until now,the problem of LV segmentation was still open, partly because of the lack of publicly available image database and of common performance evaluation protocols.Today,image databases,such as the one made available during the MICCAI’09 contest,exist and should be used to assess and compare further proposed algorithms,along with the proposed validation tools, namely the mean perpendicular distance between contours,and the Dice metric(surface overlap).An equivalent database of seg-mented images would be of great help for RV segmentation,espe-cially because of the growing interest for this very challenging segmentation task.

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每当人们不尊重我们时,我们总被深深激怒。然而在内心深处,没有一个人十分尊重自己。———马克·吐温 忍辱偷生的人,绝不会受人尊重。———高乃依 敬人者,人恒敬之。———《孟子》 人必自敬,然后人敬之;人必自侮,然后人侮之。———扬雄 不知自爱反是自害。———郑善夫 仁者必敬人。———《荀子》 君子贵人而贱己,先人而后己。———《礼记》 尊严是人类灵魂中不可糟蹋的东西。———古斯曼 对一个人的尊重要达到他所希望的程度,那是困难的。———沃夫格纳 经典素材 1元和200元 (尊重劳动成果) 香港大富豪李嘉诚在下车时不慎将一元钱掉入车下,随即屈身去拾,旁边一服务生看到了,上前帮他拾起了一元钱。李嘉诚收起一元钱后,给了服务生200元酬金。 这里面其实包含了钱以外的价值观念。李嘉诚虽然巨富,但生活俭朴,从不挥霍浪费。他深知亿万资产,都是一元一元挣来的。钱币在他眼中已抽象为一种劳动,而劳动已成为他最重要的生存方式,他的所有财富,都是靠每天20小时以上的劳动堆积起来的。200元酬金,实际上是对劳动的尊重和报答,是不能用金钱衡量的。 富兰克林借书解怨 (尊重别人赢得朋友)

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