Abstract— In the present work, a robust algorithm for

automatic identification and segmentation of heart portion from cardiac Magnetic Resonance video Image (MRI) is presented. At first, an outline has been generated to get the region of interest (ROI) by employing the moving object criterion, which eventually reduces the processing time significantly. In the next step, Expectation Maximization (EM) algorithm is used to segment the grey scale images into 5 distinct regions. This is done to make them more suitable for further processing and easy to use in the developed software. Finally Level set algorithm added with automatic contour generation module is used for tracking the exact heart boundary to segment it out from the rest of the image. This algorithm gives equally persistent result for both long axis and shot axis cardiac MRI data consisting of a movie (in AVI format) containing 32 separate frames of grayscale images.

Index Terms—Cardiac MRI, Image segmentation, Level set Algorithm, Expectation Maximization Approach.

I. INTRODUCTION AGNETIC resonance imaging (MRI) is an advanced medical imaging technique providing rich information

about the soft tissue anatomy including that of heart. Outline of heart and its computer-aided diagnosis is a growing application domain of medical image analysis. Automatic segmentation and tracking of cardiac structures can be employed to assist physicians in various states of treatment of cardiovascular diseases. [1].

Manual tracing of heart from cardiac MRI is a tedious process. Primary studies on automatic segmentation of cardiac images were based on thresholding or region growing. However, these methods could not provide appropriate results because of the presence of smooth boundaries in the cardiac images. Some more elaborate approaches are based on probability theory. A disadvantage of probabilistic models is that they require a learning database to adapt themselves with the pathology. Therefore, the image base should be relatively

This work is partly funded by Department of Biotechnology (DBT), Govt. of India. B.B. Chaudhuri and Sucharita Mitra are with Computer Vision and Pattern Recognition Unit, Indian Statistical Institute, Calcutta, India (e-mail: bbc@isical.ac.in, sucharita_r@isical.ac.in,).

Arindam Bhattacharya, Sutama Mitra, Saugata Dutta are with Department of Computer Science and Engineering, Heritage Institute of Technology, India (e-mail: arindambhattacharya1986@gmail.com, sutama.m@gmail.com, sauagata.dutta@gmail.com )

large. A recent segmentation model, which is useful in cardiac images, is the deformable model [9].

The maximum used representation of deformable model is the snake model. Specifically the ‘‘snakes’’ can be viewed as Lagrangian geometric formulations wherein the boundary of the model is represented in a parametric form [11].

Generally parametric deformable models and geometrical deformable models have been used widely for the segmentation problems; however, they both tend to fail in case of noise, poor image resolution, occluded shapes and or diffused boundaries, and they do not generally take advantage of a priori information. Yet, especially in the area of medical imaging, organs such as heart have well constrained forms within a family of shapes, and this information could be profitably used to get better results.

Our algorithm uses this feature to remove the time consuming and tedious process of drawing the boundaries manually. The proposed approach is also general in that the same approach can be used for both short axis and long axis image sequences. Different from the previous studies, in our approach, instead of directly using the average image itself, we employ Expectation Maximization approach (EM) to differentiate the original grey scale image into constituent parts and using the same as our external energy component of the deformable model framework. We also develop a knowledgebase of training shapes to use them as the initial contour, thus not only automating the entire process, but also make it robust against high noise or in images with missing edges.

Recently Chunming Li et al [2] proposed a variational formulation called level set without re-initialization for cardiac image analysis. Our algorithm is an application of the same with modification in the external energy component of the deformable model. The proposed external energy component does not directly depend on the grayscale image. Istead it is dependent on the output of the EM procedure (explained later) and also on the shape information which is obtained through a learning process.

In this way, we propose a cascaded set of steps leading to robust automatic segmentation of the inner cardiac wall in cardiac MRI images. This approach presents several advantages over the traditional parametric active contours. First, the contours represented by the level set function may break or merge naturally during the evolution, and the

A Modified Approach of Identification and Tracking of Heart Boundary from MRI Image

Sequences B.B. Chaudhuri, Fellow, IEEE , Sucharita Mitra, Arindam Bhattacharya, Sutama Mitra, Saugata Dutta

M

topological changes are thus automatically handled. Second, the level set function always remains a function on a fixed grid, which allows efficient numerical computation. Along with this we have incorporated the idea of Energy Minimization for segmentation of cardiac MRI images. Moreover, our approach is applicable for both the long axis and short axis images which is innovative because most related works are applicable only for short axis and very few for long axis. To the best of our knowledge, no significant related studies have been reported where both form of images are treated under single framework.

II. METHODOLOGY The data used for testing our procedure consisted of MR

image set of normal patient's heart acquired with the Siemens Avanto scanner [3] of the Auckland MRI research group. These images have been acquired in the standard image planes of axial, coronal and sagittal to the cardiac specific planes of long and short axes. Each data set consists of a movie (in AVI format) containing 32 separate frames of grayscale images. Each of these frames of images consists of 209x257 pixels. The software for extraction of heart boundary is developed in the MATLAB 7.01 platform running on a PIV 2.4 GHz Intel processor. The following steps are involved in the algorithm.

A. Extraction of Region of Interest Generally, in MRI images the heart and other viscera

surrounding it are visible. But our region of interest is mainly the boundary of heart. So a region of interest is extracted from the sequence of images. This process consists of comparing pixel to pixel of every alternate frame in the sequence such that

For i = 2...32.

1),( =yxROIi if tyxyx ff ii

≥−−

|),(),(|1

(1)

=0 Where ROI is a 209×257 array with all values initialised to

zero and ‘f’ represents a single image in the sequence. This algorithm takes into account an important feature that during the entire sequence of cardiac cycle, only the heart moves (i.e, individual pixels go through gradient changes), the other features remain relatively constant. Each time there is a movement in a pixel a weight is assigned to that pixel value in the ROI array. As movement of the pixels in heart is more than it’s surrounding (mentioned earlier) more weight is assigned to the pixels within the heart. A simple thresholding technique followed by selection of the largest blob separates the region of importance. A ROI image and its corresponding grey level histogram is shown in fig. 1 (a) and (b). Fig 1(c) shows the image after application of a threshold limit 0.7 and fig. 1(d) is after filling the image using flood fill algorithm. Then ROI can be obtained by selecting the largest object from that image.

(a) (b)

(c) (d) Fig 1. (a) A ROI image (b) the grey level histogram (c) thesholded image (d) image filled by flood fill algorithm

For the rest of our processing only those parts that are within the region of interest are considered. In medical applications speed is one of the most important criteria and the above algorithm ensures that the least possible amount of data is processed i.e. no extraneous region is processed by the later procedures. In the images given below (fig 2) the region of interest is enclosed by a blue boundary.

(i) Long axis (ii) Short axis Fig. 2 The out line for ROI is shown by blue boundary

B. Pre-processing by EM Algorithm After getting the region of interest a pre-processing has

been done to this region by Expectation Maximization (EM) algorithm. The cardiac images generally consist of a lot of variations and thus any procedure applied directly on the grayscale images is prone to frequent errors.

For this purpose we have used EM algorithm to segment the grey scale image into few distinct regions. Expectation Maximization consists of

Expectation Step (E-step): Given the current Bias Field estimation, the E-step computes the likelihood of each tissue class.

Maximization Step (M-step): Given the likelihood of each tissue class, the M-step estimates the image homogeneities.

The EM algorithm [12] attempts to classify data using a soft membership function as a weighted sum of a number of Gaussian distribution called Gaussian Mixture Model (GMM). The method aims to find the maximum likelihood estimate for an underlying distribution from a given dataset when the data

is incomplete. The basic idea of expectation-maximization is illustrated in figure 3 where a 5-class GMM is used to segment an input grey scale image into 5 distinct regions.

Fig 3 An illustration of the principle of signal intensity classification using a 5-class Gaussian Mixture Model. The advantage of EM over other clustering techniques like k-means is its capacity to offer a statistical model of the data and its potential to grip the related uncertainties. Consider the general case of a d-dimensional random variable x = [x1, x2, x3, ….. xd]T and suppose it follows a k-component finite mixture distribution. Its probability density function (PDF) could be written as:

∑=

=k

mmm xpxp

1

)|()|( θαθ (2)

where αm is the mixing parameter for each of the Gaussian distributions in the GMM and },{ σμθ mmm= are the parameters of

the Gaussian distributions. Where

,0≥mσ and ∑=

=k

m 11α

The algorithm is built on an iterative scheme of above-mentioned two steps. The E-step, calculates the expected log-likelihood function for the complete data, defined by using the

estimates for the parameters )(^

tθ .

)](,|)|,([log))(,(^^

tXYXpEtQ θθθθ ≡ (3) The M-step, uses the maximized values of this result to generate the next set of parameters.

))(,(maxarg)1(^^

tQt θθθθ

=+ (4)

The algorithm iterates between equations (3) and (4) until convergence is reached. The updates for the parameters for the GMM are the mixture values αm and the parameters of the Gaussian distributions },{ σμθ mmm= . These can be calculated

from equations (5), (6) and (7).

))(|(1 ^tmp

N xi

new

m θα = (5)

∑∑

=

==k

m i

h

m inew

m

xx

mp

mxip

1

^1

^

),|(

),|(

θ

θμ (6)

∑

∑ −

=

=−

=k

m i

k

m

Tnew

miinew

m

xxxx

mp

newmimp

1

^

1

^

),|(

))(,|( )(θ

θ μμσ

(7)

This pre processing of the image makes it more suitable for further processing and less susceptible to noise and other artifacts in the images. So, in the present method, the initial image is segmented into 5 classes based on intensity and maximum likelihood estimates. This processed image gives more accurate results during the contour tracking process.

The results obtained after processing of images using EM algorithm is given in fig 4.

(a) (b) (c)

(a) (b) (c) Fig. 4 Upper row Long axis, lower row Short Axis view before and after EM segmentation; (a) Initial image (b) After EM Segmentation (c) Graphical form

C. Tracking of heart boundary by Level set method Level set theory provides a framework for tracking the evolution of a closed curve of the plane given the velocity of the curve along its normal direction. The parametric representation of the curve C(t) used in some other methods is unsuitable for many applications since morphological changes of the moving contour, such as splitting and merging, are extremely difficult, if not impossible, to manipulate. In the pioneering work by Osher and Sethian [8] the various locations of the evolving contour are embedded as level sets of a function of higher dimensionality.

Its model has two components: External energy component and internal energy component.[2]

)()(

,,int φφμ ε υλgext PEEE +=+= (8)

Where )(φμP is the internal energy , θψ>ψ0�is a

parameter controlling the effect of penalizing the deviation of φ ψfrom a signed distance function, and P defined as

dxdyP ∫ −∇Ω

= )1|(| 2

21)( φφ (9)

)(,,

φε υλg is the external energy function described in

section ‘D’. Traditional external forces are based on lines or, edges, or

the gradient vector flow and they frequently fail to make the deformable model closely approach an intricate boundary with

concavities. In recent years, several approaches on geometric active

contours, i.e., active contours implemented via level set methods, has been proposed to address a wide range of image Segmentation problems [6,7] in the field of medical image processing. Active contours were introduced by Kass, Witkins, and Terzopoulos [9] for segmenting objects in images using dynamic curves. The active contour models are broadly classified as

• Parametric active contour models: The parametric active contours are represented explicitly as parameterized curves in a Lagrangian framework, and

• Geometric active contour models: the geometric active contours are represented implicitly as level sets of a two-dimensional function that evolves in an Eulerian framework.

The basic idea is to represent contours as the zero level set of an implicit function defined in a higher dimension, usually referred as the level set function, and to evolve the level set function according to a partial differential equation (PDE).

The major advantage of this approach is that the level set function can break and merge naturally during evolution, thus taking care of topological changes, which are frequent in medical images.

Early Lagrangian formulation that yielded a certain PDE were used for geometric active contour models [7]. This PDE was subsequently converted to an evolution PDE for a level set function using the related Eulerian formulation from level set methods. As an alternative, the evolution PDE of the level set function can be directly derived from the problem of minimizing certain energy functional, defined on the level set function. This type of variational methods are known as variational level set methods.

In level set formulation of moving fronts (or active contours), the fronts, denoted by C, are represented by the zero level set

}0),,(|),{()( == yxtyxtC φ (10)

of a level set function (t↪ψx↪ψy). The evolution equation of the level set function ψ can be written in the following general form:

0|| =∇+∂∂ φφ F

t (11)

which is called level set equation [8]. The function Fψis called the speed function. For image segmentation, the function Fψ

depends on the image data and the level set function . In traditional level set methods [7], the level set function ψcan develop shocks, very sharp and/or flat shape during the evolution, which makes further computation highly inaccurate. To avoid these problems, a common numerical scheme is to initialize the function ψas a signed distance function before the evolution, and then “reshape” (or “re-initialize”) the function ψ to be a signed distance function periodically during the evolution. Indeed, the re-initialization process is crucial and cannot be avoided in using traditional level set methods. But Chunming li’s[2] method does not need the

costly re-initialization and thus is a lot faster than contemporary level set methods. Our deformable model is thus based on their framework.

D. External energy in Level set In image segmentation, active contours are dynamic curves

that move toward the object boundaries. To achieve this goal, we explicitly define an external energy that can move the zero level curve toward the object boundaries. Let Iψbe an image, and gψbe the edge indicator function defined by

2||11

IGg

∗∇+=

σ

(12)

Where Gσψ is the Gaussian kernel with standard deviation .

The external energy function[2] defined as )()()(

,,φυφλφε υλ AL ggg

+= (13)

Where ψ>ψ0�and ψare constants, and the terms )(φLgand

)(φAg are defined by

∫Ω

∇= dxdygLg ||)()( φφδφ (14)

and

∫Ω

−= dxdygHAg )()( φφ (15)

respectively , where ψis the univariate Dirac function, and Hψis the Heaviside function.

Using the given image directly in the above formula gives the erroneous results in medical image processing applications, whereas our approach of defining the initial contour and using the output of pre-processing in “ I” gives more accurate results.

Fig: 5 Quiver plot of ‘g’ showing the external forces as arrows

E. Automatic generation of initial contour in Level set algorithm One of the major disadvantages of using level set is the

requirement of an initial contour, which should be quite close to the original boundary to avoid the tracking of unwanted features by the algorithm. Automation in initial contour generation is not an easy task. Considering this fact, the developed algorithm has two modes of operation. In the first mode, which is semi automatic, an expert must provide the initial contour for a single image in a sequence and that contour will be used for the rest of the images of that particular sequence. Else a predetermined model, which is developed from the contours given in the expert mode, is used.

The user is prompted to enter the particular picture set, namely short axis or long axis for selection of initial contour.

III. RESULT The developed software has been tested on several sets of

images. Each image of size 209×257 of both long and short axis and the results obtained are shown in figure 6 and 7 given below.

Initial image Image after segmentation

Fig. 6 Long axis view of initial cardiac MR image and segmented image

Initial image Image after segmentation

Fig. 7 Short axis view of initial cardiac MR image and segmented image

To find how well our tracking algorithm works, we have

used a set of data where the boundary was plotted manually. The area enclosed within the boundary was calculated in terms of number of pixels. The area enclosed by the boundary calculated by our automated approach for the same images were also calculated by the same way [table 1,2]. The results for the same are presented in the tables 3 and 4 shown below. Table1: Area estimation for Long axis:

Image name (Number of

image)

Manually detected area

(Number of pixel)

Our detected area (Number of pixel)

Long_1 6.7524e+003 6.5625e+003 Long_2 6.2418e+003 5.9238e+003

Long2_3 6.3846e+003 6.0362e+003 Long2_4 6.4727e+003 6.0674e+003 Long2_5 6.7948e+003 6.5491e+003 Long2_6 6.7167e+003 6.4656e+003

Table2: Area Estimation for Short axis: Image name (Number of

image)

Manually detected area

(Number of pixels)

Our detected area (Number of

pixels) Short_1 1.6418e+003 1.4793e+003 Short_2 1.1376e+003 1.0750e+003 Short_3 0.9273e+003 1.0453e+003 Short_4 0.9086e+003 1.0115e+003 Short_5 1.4597e+003 1.3304e+003 Short_6 1.5263e+003 1.4391e+003

The error is calculated as a deviation of the area enclosed by

the automated boundary against the area enclosed by the manual boundary following the below mentioned formulae

MAMError )( −= (16)

A= Area enclosed under automatically detected boundary M= Area enclosed under manual boundary Table 3: Error calculation for long axis:

Image name Error Long_1 0.0281 Long_2 0.0509 Long_3 0.0545 Long_4 0.0601 Long_5 0.0361 Long_6 0.0373

Table 4: Error calculation for short axis:

Image name Error Short_1 0.0989 Short_2 0.0550 Short_3 -0.1272 Short_4 -0.1132 Short_5 0.0885 Short_6 0.0571

The graphs have been constructed from the above tables,

the x axis shows the number of the image in the sequence and the Y axis shows deviation of area from that enclosed by the manually drawn boundary.

Error in long axis

0

0.05

0.1

1 8 10 16 24 32Number of image

Erro

r

Fig7 Graphical representation of error in long axis

Error in short axis

-0.2

-0.1

0

0.1

0.2

1 8 10 16 24 32

Number of frame

Erro

r

Fig 8 Graphical representation of error in short axis A positive error shows that the area under the manually

traced boundary was larger than that computed by our procedure; a negative error shows the opposite that the area

under our procedure is larger than that under the manually traced boundary. A zero error shows that both the area are same.

The above graphs show that the area never deviated more than 0.6 percent of total area in the case of long axis images and not more than 0.15 percent of the total area in short axis images. Thus the error is within limits.

IV. CONCLUSION This Paper represents an efficient and robust algorithm for

localization of heart in both long and short axis cardiac MRI data with the help of few image-processing techniques. The software has been developed in MATLAB 7.01 platform and tested with movie of MRI data containing 32 frames of gray scale images. The approach showed accurate and repeatable performance in tracking of cardiac boundaries.

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