segmentation of left ventricle in cardiac mri using ...

R. Sreemathy et al. / International Journal of Engineering Science and Technology (IJEST)

SEGMENTATION OF LEFT VENTRICLE IN CARDIAC MRI USING SNAKE AND GVF SNAKE R. Sreemathy Pune Institute of Computer Technology, Pune, India

Rekha. S. Patil Dr.D.Y.Patil College of Engineering & Technology,Kolhapur,India Abstract: This study carries out the segmentation of left ventricle with the help of active contour model or Snakes algorithm and the same is also carried out with the help of GVF Snake. The segmentation is carried on multi slice magnetic resonance images (MRI) of the heart, transversing the short axis length from base to apex. The algorithm is carried out on the inner boundary known as endocardium. The boundaries tracked by both the algorithms are compared with computational complexity and accuracy.GVF Snakes provide a better accurate segmentation as it can penetrate into concavities and the boundaries are tracked properly. Keywords: Left ventricle, Segmentation, Snakes, GVF Snakes. 1. Introduction The alarming increase in the statistics of death due to cardiovascular diseases (CVD’s) has spurred the increase in research into the diagnosis and prevention of the same. The size and structure of the left ventricle is a primary indicator for the diagnosis and treatment monitoring of many CVD’s. Segmentation and calculation of LV volumes will provide useful information for diagnosis Critical MRI data can be prepared in order to supply medical doctors with important meaningful high-level information. Such prepared information cannot directly be extracted from the MRI data. It can only be derived from a well-done automated segmentation of this data. The cardiac volumetric analysis consists of covering the base to apex images in approximately 8 to 10 levels of MRI .Each of the level consists of approximately 20 frames Hence the whole cycle consists of approximately segmenting 200 frames. Hence manual segmentation of MRI data takes medical doctors quite a lot of time. Highly automated segmentation methods can help to save a lot of time in every-day medical work. There are two general types of active contour models: parametric active contours [Kass et al(1987),Cohen(1991)] and Geometric active contours[Caselles et al(1993)(1995)] .Snakes or active contours, are curves defined within an image domain that can move under the influence of internal forces coming from within the curve itself and external forces computed from the image data. The internal and external forces are defined so that the snake will conform to an object boundary or other desired features within an image. Snakes are widely used in many applications, including edge detection, shape modeling and segmentation and motion tracking [Surendra Ranganath (1995)]. There are two key difficulties with active contour algorithms. First, the initial contour must, in general, be close to the true boundary or else it will likely converge to the wrong result. The second problem is that active contours have difficulties progressing into concave boundary regions .A new class of external forces proposed by Jerry & Prince for active contour models that addresses the problems listed above. These fields, known as gradient vector (GVF) fields, are dense vector fields derived from images by minimizing the energy functional in a variational framework. The minimization is achieved by solving a pair of decoupled linear partial differential equations which diffuses the gradient vectors of a gray-level or binary edge map computed from the image. The active contour that uses the GVF field as its external force which is called a GVF snake. Particular advantages of the GVF snake over a traditional snake are its insensitivity to initialization and ability to move into concave boundary regions [Chenyang and Prince (1996)(1997)(1998)].Gradient vector flow (GVF) snake begins with the calculation of a field of forces, called the GVF forces, over the image domain. The GVF forces are used to derive the snake, modeled as a physical object having a resistance to both stretching and bending, towards the boundaries of the object. A fundamental difference between this formulation and the traditional formulation is that GVF forces are not purely irrotational (curl-free) forces. In fact, they typically comprise both irrotational and solenoidal (divergence-free) fields [Chenyang and Prince (1996) (1997) (1998)].

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Model based segmentation [Cootes et al(1994)(1995)(1998)(1999), Alexander and John(2008) ] exploits apriori-knowledge about the properties of an object which is to be segmented. The considered data is acquired in the form of multiple slices from the lower part of the heart. Exploiting this knowledge helps in the design of robust automatic segmentation algorithms. The position and shape of the model reflect the position and shape of the depicted object. Geometric deformable models proposed provide an elegant solution to address the primary limitations of parametric deformable models. These models are based on curve evolution theory and level set method [Malladi et al(1995), Osher and Sethian (1988)].The level set method is used for automatic topology adaptation[Chunming et al(2005),(2007), 2008)]. It also provides the basis for a numerical scheme that is used by geometric deformable models.

2. Method and Theory In this section we describe active contour MRI segmentation method which is based on active contour or snake model. The simple active contour is applied to the preprocessed cardiac MR images. The preprocessing included the smoothing and threshold operation. The initial contour is drawn automatically by using circular Hough transform and the locking of the left ventricle boundary is obtained using energy minimization technique. The traced boundary of the first frame is used as the initialization of the next frame and the subsequent boundaries are tracked. Thus all the 20 frames of the first level is tracked using Snakes .The segmentation is carried out on all levels and the area of end diastole and end systole is carried out. The cardiac volumes are calculated using snake and GVF snake. 2.1 Active Contour Model or snake model The ‘Snake’ [Kass et al (1987)] is a dynamically evolving curve, which in its efforts to minimize its energy, gets attracted towards the object edges. The user must initialize the contour somewhere close to the object of interest. The contour then evolves under the influence of internal and external forces and is drawn towards the object boundaries. Thus, Snakes promises a segmentation technique that does not have any bias towards a specific shape. It is thus applicable in a variety of circumstances, which is one of its significant advantages. Snakes can also be used for object tracking in moving images and is therefore preferred for initial processing.. The problem of locating object boundary is reduced to one of energy minimization. The energy functional is the addition of a function of the contour’s internal energy, its constraint energy, and the image energy. These are functions of the set of points which make up a snake, v(s), which is the set of x and y co-ordinates of the points in the snake. The energy functional Esnake is then: (1) . The internal energy, Eint controls the natural behavior of the snake and hence the arrangement of the snake points; the image energy, Eimage attracts the snake to chosen low level features; and the constraint energy, Econ, allows higher level information to control the snake’s evolution. The internal energy is further given by: (2) It is defined as the weighted summation of first- and second-order derivatives around the contour since the elastic energy, Eelastic,

E elastic =

2 1 α ( s ) vs ds  2

(3)

And the bending energy, Ebending,

Ebending =

2 1 β s v ds ( ) ss 2 

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(4)

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dv ( s ) d 2v(s) where, v s = and v ss = ds ds 2 Thus, Eint can be written as, (5)

The first-order differential is weighted by α(s) which controls the contribution of the elastic energy due to point spacing; the second order differential is weighted by β(s) which controls the contribution of the curvature energy due to point variation. The solution of this snake can be found by iteratively solving where Eext refers to the image energy. 3. GVF Snake model The overall approach is to define a new non-irrotational external force field, called the gradient vector flow (GVF) field. Using a force balance condition as a starting point, the GVF field replaces the potential force field in (6), defining a new snake, called the GVF snake. The GVF field points toward the object boundary when it is very near to the boundary, but varies smoothly over homogeneous image regions, extending to the image border. The main advantages of the GVF field are that it can capture a snake from a long range, from either side of the object boundary and can force it into concave regions. [Chenyang. and Prince (1996)(1997)(1998)]. 3.1 Edge Map The edge map f(x, y) derived from the image I (x, y) having the property that it is larger near the image Edges. Hence

Where i =1, 2, 3, or 4. The field f has vectors pointing toward the edges, but it has a narrow capture range. Furthermore, in homogeneous regions, I(x, y) is constant, f is zero, and therefore no information about nearby or distant edges is available. 3.2 Gradient Vector Flow (GVF) The gradient vector flow (GVF) field is the vector field V(x, y) = (u(x, y) v(x, y)) that minimizes the energy functional

This Variation formulation follows a standard principle that of making the result smooth when there is no data. In particular, when f is small, the energy is dominated by partial derivatives of the vector field, yielding a smooth field. On the other hand, when f is large, the second term dominates the integrand, and is minimized by setting α .The parameter α is a regularization parameter governing the tradeoff between the first term and the second term. This parameter should be set according to the amount of noise present in the image (more noise, increase α).. The GVF can be found by solving the following Euler equation

where is the Laplacian operator. In homogeneous regions, the second term of both equations (9) and (10) is zero (because the gradient of f(x, y) is zero). Therefore, within these regions, u and v are each determined by Laplace's equation. This results in a type of “filling-in” of information taken from the boundaries of the region. Equations (9) and (10) can be solved by treating v as functions of time and solving

GVF snake is obtained by replacing the external or image energy by V(x, y) in (6) The solution to GVF snake can be obtained by iteratively solving the above equation as in the case of traditional snake.

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4. Results: The snake algorithm and GVF snake is applied to the single frame of cardiac MR images. The original test image is shown in figure(1) The edge map is shown in figure(2).The edge map gradient is shown in figure(3). Snakes algorithm: The initialization is done by using approximation of circle and the initialization is done closer to the boundary as shown in figure (4).The value of elasticity and bending parameters are adjusted so that Segmentation is done properly. The results of snake algorithm with final locked left ventricle is shown in figure(5).

Fig.1.Original image

Fig.4.Initial Contour

Fig.2.Edge Map

Fig.3.Edge Map gradient

Fig.5.Final Snake Contour

GVF snake algorithm: The GVF field of the original image is shown in figure(6).The initialization is done by using approximation of circles but far away from the boundary of the image and is shown in figure(7)..The value of elasticity and bending parameters are adjusted so that Segmentation is done properly. The final tracked left ventricle is shown in figure(8)

Fig.6.GVF Field

Fig.7.Initial Contour

Fig.8.Final GVF contour

The snake algorithm and GVF snake algorithm is applied to the entire cardiac cycle provided by database[Alexander and John(2008)].The result of the entire cardiac cycle using snake is shown in figure(9) and GVF snake is shown in figure(10).

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Fig.9.Cascaded Cardiac Cycle with Snake

Fig.10.Cascaded Cardiac Cycle with GVF Snake

The value of alpha, beta, gamma and Kappa are respectively 0.05, 0.8, 0.4 and 2 for snake algorithm and the time required for segmenting the entire cardiac cycle is found to be 20.1 Seconds. The value of the above parameter are kept same for GVF snake and the time required is found to be 28.4 Seconds, The initial contour has to be closer to the object boundary for traditional snakes and the initial contour drawn is also far away from the boundary for GVF snakes and it can easily penetrate into the concavities. Table 1 provides the volumetric analysis using snake and GVF snake. The GVF provides better results due to better penetration into the concavities.

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Table1.Volumetric analysis of left ventricle

S.No 1 2 3 4 5

Parameters End Diastolic Volume(EDV) End Systolic Volume(ESV) Stroke Volume(SV) Ejection Fraction Time

Traditional snake 55 ml 108ml 53.5 46.6 20.1Seconds

GVF snake 67.17ml 125.78ml 58.61ml 49.19 28.4Seconds

Conclusion: The following are the advantages of GVF snake over conventional snake: In the GVF snake the initialization can be far away from the boundary. In traditional snake the initial contour must be close to the true boundary or it is likely to converge to the wrong result. Second active contours have problem of penetrating to the boundary cavities .In contrast GVF has a large capture range, enabling initialization of the active contour far from the decision boundary. Hence GVF is a useful and powerful tool for segmentation and quantification of left ventricle in cardiac MRI References: [1] Alexander A, John K T (2008): Efficient and generalizable statistical models of shape and appearance for analysis of cardiac MRI,Medical Image Analysis 12 ,pp 335–357. [2] Caselles V, Catte F, Coll T, Dibos F (1993): A geometric model for active contours,Numer. Math, vol. 66, pp. 1–31, 1. [3] Caselles V, Kimmel R, Sapiro G(1995):Geodesic active contours, in Proc. 5th Int. Conf. Computer Vision, pp. 694–699. [4] Chenyang X, Prince J L (1998): Snakes, Shapes, and Gradient Vector Flow, IEEE Transactions on Image Processing, 7(3), pp. 359- 369. [5] Chenyang X, Prince J L (1997): Gradient vector flow: A new external force for snakes, IEEE Proc. Conf. on Computer Vision and Pattern Recognition, pp 66–71. [6] Chenyang X, Prince J L (1996): A new external force model for snakes, in Proc. of Image and Multidimensional Signal Processing Workshop, pp 30–31. [7] Chunming L ,Chiu-Yen K, John C G, Zhaohua D (2008): Minimization of region-scalable fitting energy for image segmentation,IEEE Transactions on Image Processing, vol. 17, NO. 10, pp 1941-1949. [8] Chunming L, Chiu-Yen K, John C G, Zhaohua D (2007): Implicit active contours driven by local binary fitting energy, Proceedings of the 2007 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’07). [9] Chunming L, Chenyang X, Changfeng G, and Martin D F (2005): Level set evolution without re-initialization: a new variational formulation Proceedings of the 2007 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05). [10] Cootes T F, Edwards G J, and Taylor C J (1998): Active appearance models, In Proc. European Conf. on Computer Vision,volume 2, pages 484–498. Springer. [11] Cootes T F, Edwards G J, and Taylor (2001): Active appearance models. IEEE Trans. On Pattern Recognition and Machine Intelligence, 23(6):681–685. [12] Cootes T F, Edwards G J, and Taylor (1992): Active shape models – ’smart snakes’. In Proc. British. Machine Vision Conf., BMVC92, pages 266–275. [13] Cootes T F and Taylor C J(2001): Statistical Models of Appearance for Computer Vision, Tech.Report, University of Manchester. [14] Cohen L D (1991): On active contour models and balloons, CVGIP Image Understand, vol. 53, pp. 211–218. [15] Kass M, Witkin A, Terzopoulos D (1987): Snakes: Active contour models, Int. J. Comput. Vis, vol. 1, pp. 321–331. [16] Malladi R, Sethian J A, and Vemuri B C (1995): Shape modeling with front propagation: a level set approach, IEEE Trans. Patt. Anal. Mach. Intell., vol. 17, no. 2, pp. 158–175. [17] Osher S and Sethian J A (1988): Fronts propagating with curvature-dependent speed algorithms based on Hamilton-Jacobi formulations, J Computational Physics, vol. 79,pp. 12–49. [18] Surendra Ranganath(1995), “Contour Extraction from Cardiac MRI studies using Snakes,” IEEE Trans .on Medical Imaging,vol. 14, no. 2. [19] Sethian J A (1985), Curvature and evolution of fronts, Commun. Math. Phys., vol. 101, pp. 488-499

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