3.1.

Boundary-Driven Techniques

3.1.1.

Active contours (or snakes)

Boundary-driven segmentation techniques are based on the concept of evolving contours, deforming from the initial to the final position. One of the most widely used methods is the “active contour” model, which is also referred to as “snakes.”²¹ The active contour model allows a curve defined in the image domain to evolve under the influence of internal and external forces. The internal force is imposed on the contour in order to control the smoothness while the external force is usually derived from the image itself. An edge detector function is utilized as the external force in the classical active contour model. Most active contour models only detect objects with edges defined by the gradients. Kass et al.^21,22 were the first to formulate the classical active contour model using an energy minimization approach. The active contour model seeks the lowest energy of an objective function, where the total energy of the active contour model is defined as

Eq. (3)

$$E_{\text{total}}=E_{\mathrm{in}}+E_{\mathrm{ex}},$$

where $E_{\mathrm{in}}$ denotes the internal energy incorporating prior knowledge such as smoothness or a particular shape and $E_{\mathrm{ex}}$ represents the external energy describing how well the curve matches the image data locally. A curve $v(s)$ can be represented as

Eq. (4)

$$v(s)=[x(s),y(s)],0\le s\le 1.$$

With such a representation, the internal and external energies can be formulated as

Eq. (5)

$$E_{\mathrm{in}}={\int }_0^1{E}_{\mathrm{in}}[v(s)]\mathrm{d}s\text{and}{E}_{\mathrm{ex}}={\int }_0^1{E}_{\mathrm{ex}}[v(s)]\mathrm{d}s,$$

where $E_{\mathrm{in}}(v(s))$ can be given by

Eq. (6)

$$E_{\mathrm{in}}(v(s))=\alpha (s){\left|\frac{dv}{ds}\right|}^2(\text{Elasticity})+\beta (s){\left|\frac{d^{2}v}{d{s}^2}\right|}^2(\text{Stiffness}),$$

and one example of external energy is

Eq. (7)

$$E_{\mathrm{ex}}[v(s)]=-\{{|G_x[v(s)]|}^2+{|G_y[v(s)]|}^2\}.$$

A simple edge detector is used in Eq. (7) to formulate the external energy term $E_{\mathrm{ex}}$, where $G_x$ and $G_y$ denote the gradient images along $x$ and $y$ axes, respectively.

An example of the evolving 2-D contours obtained by applying the active contour model to a sequence of US of the LV is shown in Fig. 2. These contours deform gradually to the exact object boundaries by minimizing the energy of the active contour model. Although the active contour model has been a seminal work, it has some limitations. For instance, it is sensitive to the initialization as the contour may get stuck to a local minimum near the initial contour. The curve may pass through the boundary of the field of view of the image when the image has high amounts of noise. In addition, the accuracy of the active contour model depends on the convergence criteria employed in the minimization technique. A few attempts have been made to improve the original model by adopting new types of external field, including gradient vector flow²³ and the balloon model.²⁴

Fig. 2

Short axis ultrasound images illustrating the tracking of the endocardial border by the active contour technique.²⁵ An initial contour evolves to the final contour as indicated by the white dotted line in each image. (Reproduced from I. Mikic et al. with permission of ©1998 IEEE.)

3.2.

Region-Based Techniques

In the region-based segmentation techniques, regions of interest, including chambers from extracardiac structures, are partitioned by a selected global model that provides approximations of the region of interest. In other words, the global information defined within the region of interest is used to differentiate the region of interest from others by global homogeneity regional properties.^34,35 Hybrid techniques that combine the region-based and boundary-based information have also been proposed to enhance the segmentation performance.

3.2.2.

Level-set based technique

Unlike the parametric representation, the level-set framework represents curves implicitly as the zero level set of a scalar function proposed by Osher and Sethian.⁴³ Following the introduction of the level-set framework, Sethian,^30,44 Osher and Fedkiw,⁴⁵ and Osher and Paragios⁴⁶ built a solid foundation of the level-set representation applied to a variety of problems. An example of LV segmentation using the level-set method is depicted in Fig. 3. The representation for contour evolution in the level-set framework is implicit, parameter-free, and intrinsic. Let $\mathrm{\Omega }\subset {\mathbb{R}}^n$, where $n$ is 2 or 3, denote the image domain. A contour $C\subset \mathrm{\Omega }$ can be represented by the zero level set of a higher-dimensional embedding function $\varphi (x):\mathrm{\Omega }\to \mathbb{R}$ as given by

Eq. (11)

$$\{\begin{array}{l}C=\{x\in \mathrm{\Omega }|\varphi (x)=0\}\\ \text{interior}(C)=\{x\in \mathrm{\Omega }|\mathit{\varphi }(x)>0\}\\ \text{exterior}(C)=\{x\in \mathrm{\Omega }|\mathit{\varphi }(x)<0\}\end{array},$$

where $\varphi (x)$ is a signed distance function that imposes $|\nabla \varphi |=1$ almost everywhere. The contour evolution equation is then given by

Eq. (12)

$$\frac{dC}{dt}=F\overrightarrow{n},$$

where $\overrightarrow{n}$ denotes the outward unit vector normal of $C$ and $F$ denotes a speed function.

Fig. 3

The LV segmentation results for MR images by the level-set function with the visual information and anatomical constraints, where the sequence of images corresponds to the same slice but in different moments of a cardiac cycle.³⁵ (Reproduced from N. Paragios with permission of ©2002 Springer Science and Business Media.)

The interface is the zero level of $\varphi$ (i.e., $\varphi (C(t),t)=0$ for all $t$). An evolution equation for $\varphi$ then can be derived using $\overrightarrow{n}=\frac{\nabla \varphi }{|\nabla \varphi |}$ as

Eq. (13)

$$\frac{\partial \varphi }{\partial t}=-F|\nabla \varphi |.$$

The contour evolution $\frac{dC}{dt}=F\overrightarrow{n}$ corresponds to an evolution of $\varphi$ given by $\frac{\partial \varphi }{\partial t}=-F|\nabla \varphi |$. The level-set based segmentation method has been extensively utilized in the image segmentation problems due to a variety of advantages: it is parameter free, implicit, can change the topology, and provides a direct way to estimate the geometric properties. In addition, a large amount of effort has been made for its performance improvement.^{27,29,31,47–50}

In boundary-driven techniques, the gradient is used as a criterion to stop the curve. However, there are objects whose boundaries cannot be defined, such as smeared boundaries. Chan and Vese³² proposed a different model incorporating an implicit energy functional in boundaries $C$ with active contours and the level-set representation by modifying the Mumford-Shah functional, i.e.,

Eq. (14)

$$E(f,C)=\sum _{i=1}^N{\lambda }^2{\iint }_{R_i}{[c_i(x,y)-I(x,y)]}^2\mathrm{d}x\mathrm{d}y+\mu |C|,$$

where a set of disjoint regions $R_i$ cover $R$ and $f(x,y)=\text{constant}$ $c_i$ on $(x,y)\in R_i$. $N$ is the number of image partitioning. Equation (14) is minimized in $c_i$ by setting $c_i$ to the mean of $I(·,·)$ in $R_i$. In the case of the two partitioning regions $c_1$ and $c_2$, the Euler-Lagrange derivation of Eq. (14) is demonstrated by

Eq. (15)

$$\frac{\partial \varphi }{\partial t}=\delta (\varphi )\left[\mu \mathrm{div}\right(\frac{\nabla \mathit{\varphi }}{|\nabla \mathit{\varphi }|})-{|c_1-I|}^2+{|c_2-I|}^2],$$

where $\delta$ is a Dirac delta function. Therefore, this energy minimization process depends on regional constants $c_i$ and the level-set function $\varphi$. $\mu \in {\mathbb{R}}^{+}$ is a balancing parameter between data fidelity and regularization.

3.3.

Graph-Cuts Techniques

The graph-cuts technique^64,65 was originated from Greig's maximum a posteriori (MAP) estimation⁶⁶ in order to find the maximum flow for binary images. An interactive graph-cuts technique can find a globally optimal segmentation of an image. The user selects some pixels called “seed points” as hard constraints inside the object to be segmented as well as some pixels belonging to the background. The objective function is typically defined by boundary and regional properties of the segments. Therefore the obtained segmentation provides the best balance of boundary and region properties satisfying the constraints.⁶⁵

In the graph-cuts theory,⁶⁵ an image is interpreted as a graph, where all pixels are connected to its neighbors. Graph node set $P$ and edge set $Q$ connect nodes $v\in P$ to form a graph $G=\{P,Q\}$. Terminals are two special nodes, known as the source (s) and sink (t), which are the start and end nodes of the flow in the graph, respectively. Also, there are two types of edges: n-links that connect neighboring pixels and t-links that connect pixels in image to terminal nodes. The cost or weight $w_e$ is assigned to each edge, $e\in Q$. The costs of n-links are the penalties for discontinuities between the pixels, and the costs of t-links are the penalties for assigning the corresponding terminal to the pixel. Thus, the total cost of the n-links represents the cost of the boundary while the total cost of the t-links indicates the regional properties. A cut $\mathrm{X}\subset Q$ is a set of edges that separates the graph into regions connected to terminal nodes. The cost of a cut is defined by the sum of the costs of edges that belong to the cut, which is denoted by

Then optimal segmentation results using the graph-cuts technique amount to finding the optimal solution for the cost of a cut, i.e., a minimal cost cut. An example of medical image segmentation using the graph-cuts techniques is illustrated in Fig. 4.

Fig. 4

LV segmentation examples for contrast cardiac CT images using the graph-cuts technique.⁶⁷ The segmentation algorithm used here combines the EM-based region segmentation, the Dijkstra active contours using graph-cuts, and the shape information through a pattern matching strategy. The graph-cuts algorithm is used to cut the edges in the graph to form a closed-boundary contour between two different regions. (Reproduced from M. P. Jolly with permission of ©2006 Springer Science and Business Media.)

Several methods to find an optimal cost cut have been proposed such as minimizing the maximum cut between the segments⁶⁸ and normalizing the cost of a cut.⁶⁹ Boykov and Kolmogorov⁷⁰ proposed a max-flow/min-cut algorithm and compared its efficiency with Goldberg-Tarjan's push-relabel⁷¹ and Ford-Fulkerson's augmenting paths.⁷² Based on the cut cost described above, the energy function can be formulated, consisting of the boundary term and the regional term. Let $l_p$ be the label for a given pixel $p$, which can be either an object or the background. Let $S$ be a set of pixels and $N$ be a set of all pairs of neighboring elements. The energy function⁷³ for graph-cuts can then be given by:

One limitation of the graph-cuts technique is that it is not fully automated, as it demands the initialization of seed points in the object and the background regions.

3.4.

Model-Fitting Techniques

The model-fitting segmentation attempts to match a predefined geometric shape to the locations of the extracted image features of an image. A two-step procedure is usually needed in the model-fitting segmentation: (1) generating the shape model from a training set and (2) performing the fitting of the model to a new image. The models contain the information about the shape and its variations. The main tasks in the model-fitting are the extraction of the features and generation of the best fitting model from the features. Given an accurate and appropriate model, the segmentation procedure becomes an optimization problem of finding the best model parameters for a given patient image. Human heart anatomy exhibits specific features and therefore the similar shape or intensity information about hearts can be utilized by means of a shape-prior knowledge. Prior knowledge can be used to compensate for common difficulties such as poor image contrast, noise, and missing boundaries.

Integrating the prior knowledge using explicit shape representation into segmentation process has been a topic of interest for decades. For instance, global shape information with closed curves represented by Fourier descriptors was proposed where the Gaussian prior was assumed for Fourier coefficients.^74,75 The shape model was built by learning the distribution of Fourier coefficients. In addition, active shape models (ASM) were used in a variety of segmentation tasks.^18,76–78 In brief, key landmark points on each training image generate a statistical model of shape variation, and a statistical model of intensity is built by warping each example image to match the mean shape. Principal component analysis (PCA) is applied on the key landmark points where the sample distribution is assumed as a Gaussian distribution. Any sample within the distribution can be expressed as a mean shape with a linear combination of eigenvectors.⁷⁹ Cootes et al.^76,80,81 built statistical models by positioning control points across training images and developed the active appearance model (AAM).⁸² An example of image segmentation based on the AAM is illustrated in Fig. 5. The landmark points should be placed in a consistent way over a large database of training shapes in order to avoid incorrect parameterization.⁷⁷ Also, if the size of a training set is small, the model cannot capture its variability and is unable to approximate data that are not included in the training set.⁷⁸ Furthermore, a statistical model is incorporated in order to describe intersubject shape variabilities. For example, the dimension of the parametric contours was reduced by the use of PCA. By projecting the shape onto the shape parameters and enforcing limits, global shape constraints have been applied to ensure that the current shape remains similar to that in the training set.⁷⁶ Wang and Staib⁸⁴ extended the work of Cootes et al.⁷⁶ using a Bayesian framework to adjust the weights between the statistical prior knowledge and the image information based on image quality and reliability of the training set. The B-splines based curve representation was applied to the classical active contours model.^85–87

Fig. 5

Segmentation results obtained by applying the AAM technique to an ultrasound image sequence over one heart beat period:⁸³ (a) the initial 1-phase AAM model positioned, (b) the match after 5 AMM iterations, (c) the final match after 20 AAM iterations, and (d) the manual contours for comparison. The first row shows phase images 1, the second row shows phase images 2, and the third row shows phase images 3 from 16 image phases. (Reproduced from J. Bosch et al. with permission of ©2002 IEEE.)

There have been several attempts to incorporate the prior knowledge of shape in the implicit shape representation. Leventon et al.⁸⁸ incorporated the shape-prior information in the level-set framework with a set of previously segmented data using the signed distance function. A shape-prior model was also proposed to restrict the flow of the geodesic active contour, where the prior shape was derived by performing the PCA on a collection of the signed distance function of the training shape. A similar approach was proposed in Ref. 89 with an energy functional, including the information of the image gradient and the shape of interest in geometric active contours using the distance function to represent training distances. Another objective function for segmentation was proposed in Ref. 90 by applying the PCA to a collection of signed distance representations of the training data. Rousson and Paragios⁹¹ applied a shape constraint to the implicit representation using the level-set to formulate an energy functional, where an initial segmentation result can be corrected by the level-set shape prior model through PCA. They also considered a stochastic framework in constructing the shape model with two unknown variables: the shape image and the local degrees of shape deformations.

In specific applications, 3-D heart modeling was explored in Ref. 19 and the four-chamber heart modeling was proposed in Refs. 1 and 92. Geometric constraint was also incorporated in the LV segmentation problem. The model-based approach in Ref. 93 has gained a lot of attention as a solution to the image segmentation problem with incomplete image information.^94,95

Several other model-fitting methods have been investigated to date. The atlas-based segmentation was carried out based on the registration, where multiple atlases were registered to a target image by propagation of the atlas image labels with spatially varying decision fusion weight in CT scans.⁹⁶ In addition, a deformable surface represented by a simplex mesh in the 3-D space used the time constraints in segmenting the SPECT cardiac image sequence in Ref. 2. Modeling the four-chamber heart was performed for 3-D cardiac CT segmentation,⁹⁷ where the simplex meshes were used to provide a stable computation of curvature-based internal forces. Heart modeling was accomplished with a statistical shape model⁷⁶ and labeling is performed on mesh points that correspond to special anatomical structures such as control points that integrate mesh models.¹ The whole heart segmentation method, including four chambers, myocardium, and great vessels in CT images, was proposed in Ref. 98, where ASM and the generalized Hough transform for automatic model initialization were exploited.

4.1.

Ultrasound Imaging

US imaging is the most widely used technique in cardiology for evaluation of contractile cardiac function. It has several advantages, including good temporal resolution and relatively low cost. It can be used to assess tissue perfusion by myocardial contrast echocardiography.¹⁰⁰ Additionally, it is well-suited for image-guided interventions due to its recent advances, allowing visualization of instruments as well as cardiac structures through the blood pool.¹⁰¹ However, US imaging suffers from low SNR (signal-to-noise ratio) and speckle noise,¹⁰² making the LV segmentation task challenging. Moreover, the acquisition is usually performed in 2-D¹⁰² and therefore depends on the orientation, leading to missing boundaries and low contrast between regions of interest.¹⁰³ US imaging of the heart involves 2-D, 2-$\mathrm{D}+t$, 3-D, 3-$\mathrm{D}+t$, and Doppler echocardiography, each of which poses different challenges. In this review, we focus primarily on the segmentation of the 3-D and 3-$\mathrm{D}+t$ data.

A recent advance in this field of cardiac imaging is three-dimensional echocardiography (3-DE). This tool has been used only for research purposes in the past, but due to recent improvements in software algorithms and transducer technology, it is now used in clinical practice.^104,105 2-D and 3-D echocardiography use different transducers. 3-DE is well-suited for LV mass, volumes, and EF^104,105 because 2-D imaging can potentially provide biased measurements of EF.¹⁰⁶

Numerous segmentation techniques have been proposed for US imaging. 3-D AAM was proposed,^79,107 where its model was learned from the manual segmentation results and the information of the shape and image appearance of cardiac structures was included in a single model. The level-set or the active contour segmentation methods were also applied to the US segmentation.^108–111 Level-set based method with specialized processing was adopted to extract highly curved volumes while ensuring smoothness of signals.¹⁰⁸ Additionally, an algorithm based on deep neural networks and optimization was employed¹¹² and a discriminative classifier, random forest, was used to delineate myocardium.¹¹³ For an in-depth review on the segmentation of US images, we refer the reader to Ref. 102.

4.2.

Nuclear Imaging (SPECT and PET)

Nuclear imaging has been an accepted clinical gold standard for the quantification of relative myocardial perfusion at stress and rest.¹¹⁴ It is also the mainstream imaging technique to estimate myocardial hypo-perfusion due to coronary stenosis. Gated myocardial perfusion SPECT¹¹⁵ is also widely used for the quantitative assessment of the LV function. LV regional wall motion and thickening by SPECT play an integral part to assess coronary artery disease and determine the extent and severity of functional abnormalities.¹¹⁶ Accurate segmentation of LV and quantification of the volume offer an objective means to determine the risk stratification and therapeutic strategy.¹¹⁷ However, delineation of the endocardial surface with nuclear imaging is challenging due to relatively low image resolution, extracardiac background activities, partial volume effect, count statistics, and reconstruction parameters.¹¹⁸

A few techniques have been developed for nuclear imaging segmentation. Germano et al.¹¹⁹ proposed LV segmentation method for SPECT, which is widely used in nuclear cardiology practice as illustrated in Fig. 6. In addition, wall motion and thickening were further investigated with the same technique.¹¹⁶ In brief, an asymmetric Gaussian was exploited to fit to each profile in each interval of a gated MPS volume, where a maximal count myocardial surface was determined. Other well-established methods for the quantitative analysis of nuclear myocardial perfusion imaging exist such as the Corridor4DM,¹²⁰ the Emory Cardiac Toolbox,¹²¹ the University of Virginia quantification program,¹²² and the Yale quantification software.¹²³ These automated software tools allow highly automatic definition of the LV contours and measure perfusion defect size, EF, EDV, and LV mass.

Fig. 6

The gated SPECT segmentation in Ref. 119, where the first row shows original myocardial perfusion SPECT (MPS) and the second row shows the segmented image of the first row.

In other developments, the level-set technique was employed for the segmentation of cardiac gated SPECT images¹²⁴ and a geometric active contour-based SPECT segmentation technique was proposed.¹²⁵ Slomka et al.¹²⁶ and Declerck et al.¹²⁷ proposed a template-based segmentation method using the registration-based approach. Additionally, the 4-D (3-$\mathrm{D}+t$) shape prior was adopted in Ref. 128 using implicit shape representation of the left myocardium in SPECT image segmentation. This study extended the shape modeling to the spatiotemporal domain by treating time as the fourth dimension and applied the 4-D PCA. Faber et al.¹²⁹ employed an explicit edge detection method to estimate endocardial and epicardial boundaries using the structural information in gated SPECT perfusion images. The 3-D ASM segmentation algorithm was adopted in Refs. 118 and 130 for cardiac perfusion gated SPECT studies and the construction of geometrical shape and appearance models. Reutter et al.¹³¹ used a 3-D edge detection technique for the segmentation of respiratory-gated PET transmission images and Markov random fields were adopted for 3-D segmentation of cardiac PET images.¹³²

4.3.

Computer Tomography (CT)

In cardiac CT, there are two imaging procedures: (1) coronary calcium scoring with noncontrast CT and (2) noninvasive imaging of coronary arteries with contrast-enhanced CT. Typically, noncontrast CT imaging exploits the natural density of tissues. As a result, various densities using different attenuation values such as air, calcium, fat, and soft tissues can be easily distinguished.¹⁴⁶ Noncontrast CT imaging is a low-radiation exposure method within a single breath hold, determining the presence of coronary artery calcium.¹⁴⁶ In comparison, contrast-enhanced CT is used for imaging of coronary arteries with contrast material such as a bolus or continuous infusion of a high concentration of iodinated contrast material.¹⁴⁷ Furthermore, coronary CT angiography has been shown to be highly effective in detecting coronary stenosis.¹⁴⁸ Especially in the recent rapid advances in CT technology, CT can provide detailed anatomical information of chambers, vessels, coronary arteries, and coronary calcium scoring. Coronary CT angiography can visualize not only the vessel lumen but also the vessel wall, allowing noninvasive assessment of the presence and the size of the noncalcified coronary plaque.¹⁴⁹ Additionally, CT imaging provides functional as well as anatomical information, which can be used for quantitative assessment for systolic WT and regional wall motion.^150,151

Various segmentation techniques have been proposed for cardiac CT applications. Funka-Lea et al.¹⁵² proposed a method to segment the entire heart using graph-cuts. Segmenting the entire heart was performed for clearer visualization of coronary vessels on the surface of the heart. They attempted to set up an initialization process to find seed regions automatically using a blowing balloon that measures the maximum heart volume and added an extra constraint with a blob energy term to the original graph-cuts formulation. Extracting the myocardium in 4-D cardiac MR and CT images was proposed in Ref. 67 using the graph-cuts as well as EM-based segmentation. Zheng et al.¹ presented a segmentation method based on the marginal space learning by searching for the optimal smooth surface. Model-based techniques were also adopted for cardiac CT image segmentation using ASM with PCA.¹⁵³ Methods for region growing^154,155 and thresholding^156,157 were also employed. An entirely different topic is the segmentation of coronary arteries from the CT angiography data, which is well covered by other reviews.^158,159

4.4.

MRI

Cardiac MRI allows comprehensive cardiac assessment by several types of acquisitions that can be performed during one scanning session.⁹ It provides high-resolution visualization of cardiac chamber volumes, functions, and myocardial mass.¹⁶⁰ Cardiac MRI has been established as the research gold standard for these measurements, with more and more clinical impact. Moreover, recently developed delayed enhancement imaging with gadolinium contrast has emerged as a highly sensitive and specific method for detecting myocardial necrosis. This allows improved evaluation of the myocardial infarction.^161,162 Perfusion MRI imaging can also be performed for the diagnosis of ischemic heart disease. However, the perfusion MR imaging depends on a first-pass technique, which limits the conspicuity of perfusion defects.^163,164 The advantages of MRI include exquisite soft-tissue contrast, high spatial resolution, low SNR, ability to characterize tissue with a variety of pulse sequences, and no ionizing radiation. Compared to PET or SPECT, the dependence of MR signal on regional hypoperfusion is minimal and does not prevent segmentation tasks. Some of the disadvantages are that cardiac MRI typically employs one breath-hold per slice with 5 to 15 slices per patient study, therefore necessitating multiple breath-holds for each patient dataset. Additionally, the images are of high-resolution in-plane but the resolution between slices is low (typically 8 to 10 mm). Also, multiple breath-hold acquisitions can cause errors in spatial alignment and result in artifacts of the 3-D heart image. These misalignments can be corrected by software registration techniques.¹⁶⁵ Recently, full volume 3-D MRI acquisitions have been proposed.⁹

Cardiac MR tagging is an important reference technique to measure myocardial function, which allows quantification of local myocardial strain and strain rate.^166,167 Tagged MR produces signals that can be used to track motion. Several techniques have been developed, including magnetization, saturation, spatial modulation of magnetization (SPAMM), delay alternating with nutation for tailored excitation (DANTE), and complementary SPAMM (CSPAMM). These techniques produce a visible pattern of magnetization saturation on the magnitude reconstructed image without any post-processing. However, quantifying myocardial motion requires exhaustive post-processing. In contrast, more advanced techniques such as Harmonic phase (HARP), displacement encoding with simulated echoes (DENSE), and strain encoding (SENC)^167,168 compute motion directly from the signal and do not directly show tagging pattern. Simple post-processing is required for myocardial motion information. For more details, we refer readers to the recent review of cardiac tagged MRI.¹⁶⁷

Numerous image segmentation techniques have been applied to MRI and are summarized below. Petitjean et al.¹⁶⁹ presented a review of segmentation methods in short axis MR images. Paragios³⁵ used the level-set technique using a geometric flow to segment endo- and epicardium of the LV. Two evolving contours were employed for the endo- and epicardium and the method combined the visual information with anatomical constraints to segment both regions of interest simultaneously. Paragios et al.^35,170,171 applied the shape prior knowledge with the level-set representation to achieve robust and accurate results.

Moreover, several constraints and prior knowledge have been incorporated in the level-set framework for efficiently segmenting regions of interest. For example, the velocity-constrained front propagation method was proposed by using the magnitude and direction of the phase contrast velocity as the constraints.¹⁷² Woo et al.¹⁷³ proposed statistical distance between the shape of endo- and epicardium as a shape constraint using signed distance functions. Tsai et al.¹⁷⁴ proposed a shape-based approach to curve evolution and Ciofolo et al.¹⁷⁵ proposed a myocardium segmentation scheme for late-enhancement cardiac MR images by incorporating the shape prior with contour evolution. Zhu et al.¹⁷⁶ applied a dynamic statistical shape model with the Bayesian method.

Segmentation techniques using thresholding,^177,178 region growing,^179,180 and boundary detection^181,182 were applied to MRI data. For instance, a local assessment of boundary detection method was proposed to improve the capture range and accuracy.¹⁸³ Segmentation algorithm using optimal binary thresholding method and region growing was presented to delineate 3-$\mathrm{D}+t$ cine MR images.¹⁸⁴ In addition, learning frameworks were used to segment 2-D tagged cardiac MR images.^185,186

4.5.

Parameter Correlation between Imaging Modalities

Several attempts have been made to compare and correlate the quantitative parameters obtained by different imaging modalities and different image segmentation approaches. Various reports in the literature indicate that cardiac MRI can provide accurate estimates of EF, LV volumes.^187–191 and wall motion/thickening analysis.^187–189 In addition, gated SPECT has been extensively validated against various two-dimensional imaging techniques, such as echocardiography,¹⁹² but there are only a limited number of studies comparing gated SPECT with other three-dimensional techniques such as cardiac MRI, which is considered the reference standard for assessing LV volumes.^193–196 Visual interpretations of wall motion by observers on the two modalities have been compared along with LV volumes^193–196 but quantitative comparison for assessment of regional wall motion/thickening has not been reported previously. Using echocardiographic sequences, values of LV volumes, EF, and regional endocardial shortening also correlate with MR. Cardiac MRI was used as a reference method for comparison with unenhanced and contrast-enhanced echocardiography.^197,198 LV mass obtained by contrast enhanced color Doppler echocardiography has shown excellent agreement with those from MRI.¹⁹⁹ The left and right ventricular EDV, ESV, stroke volume, EF, and myocardial mass obtained by dual-source CT also correlated well with those from MRI.²⁰⁰