Medical Image Segmentation by Active Contour Improvement

Transcription

1 American Journal of Software Engineering and Applications 7; 6(): doi:.648/.asea.76. ISSN: (Print); ISSN: 37-49X (Online) Medical Image Segmentation b Active Contour Improvement Abdelaziz Essadike, Elhoussaine Ouabida, Abdenbi Bouzid Optronic and Information Treatment Team, Atomic, Mechanical, Photonic and Energ Laborator, Facult of Science, Moula Ismail Universit, Zitoune, Meknès, Morocco address: essadikeab@gmail.com (A. Essadike), contact.ouabida@gmail.com (E. Ouabida), ab.bouzid@gmail.com (A. Bouzid) To cite this article: Abdelaziz Essadike, Elhoussaine Ouabida, Abdenbi Bouzid. Medical Image Segmentation b Active Contour Improvement. American Journal of Software Engineering and Applications. Vol. 6, No., 7, pp doi:.648/.asea.76. Received: March 3, 7; Accepted: March, 7; Published: April 3, 7 Abstract: This paper introduces a new medical image segmentation approach based on active contour improvement. The boundaries in brain images are detected using an original technique of active contour improved b a Region of Interest (ROI) extraction. We compare the results of the proposed model to Chane-Vese active contour model and Caselles s et al. Geodesic active contour model. Experimental results of brain boundar localization on a national center of Oncolog s database demonstrate the promising performance of this method. Kewords: Medical Image Segmentation, Active Contours, Energ Minimization, ROI, Level Sets. Introduction Medical images including CT (Computed Tomograph) contain several anatomical structures. Accurate segmentation of one obect is quite important for diagnosis and therapeutic interventional planning. Brain image segmentation methods must incorporate models that describe prior knowledge about the expected geometr and intensit characteristics of the anatomical obects of interest in the images. The simplest image segmentation methods, such as region growing and edge detection, rel entirel on local image operators and a heuristic grouping of neighboring pixels with similar local photometric characteristics. Active contour models have widel been used for image segmentation after the were formall introduced b Kass and Witkin [] in 987 as the first model. The use of level set theor has enriched the implementation of active contours with more flexibilit and simplicit. The past models of active contours rel on a gradient based stopping function to stop the curve evolution. An active contour is a curve that evolves from an initial shape to the borders of an obect of interest, under the action of a force. Active contour models can be categorized into parameterized ([] - [5]) and non-parameterized models ([6] - [7]). This classification is based on how obect boundar is detected. The active contour can be defined as a parametric curve b: [ α β ] [ T ] C :,, C x = The evolution of the contour is governed b a general form of equation: Where C C τ = F = C ( ρ) C ρ is the initial contour. The contour is deformed b following a force F whose direction is a priori arbitrar. In this article we propose to use a non-parameterized active contour model to segment a skull image in order to build a 3D reconstruction of human brain. The active contour model proposed use the theor of ROI (Region of Interest) to detect the initial contour in the skull image. This initial contour minimizes the number of iterations and thus minimize the computation time but with great accurac. () ()

2 4 Abdelaziz Essadike et al.: Medical Image Segmentation b Active Contour Improvement This article is organized as follows. The previous work is reviewed in section. Then the proposed model and algorithm are described in section 3. Section 4 shows the results of our experiments. Finall a brief conclusion comes in section 5.. Previous Works The active contours takes their origin from elastic models, but the communit agrees to attribute them to the team Kass,Witkin and Terzopoulos [], who introduced the snakes or theminimizing curves. SNAKES models take their name from their abilit to deform like snakes. Let be a bounded open subset ofr, with itsboundar. Let U : R be a given image, and C ( s) :, R be a parameterized curve. This classicalmodel is inf ( C ) where: ' '' C C s ds C s ds u C s ds = α + β λ ( ) Here α, β and λ are positive parameters. Active contours approaches can be linked to the famil ofgeodesic optimization problems in spaces whose geometr isdetermined b the dnamics of the image. These techniques,called geodesic active models have been proposed b Caselleset al. [4] as: Φ = g( u )..,in, div + υ t + R Φ (, x, ) =Φ (, ),in x R Where υ is a constant, Φ is a Lipschitz function, represent a curvec b C = {( x, ) / Φ ( x, ) = }, Φ initiallevel set function, (3) (4) g ( u ( x, ) ) = G ( x, ) u ( x, p (5) + σ ) For, p = wheregσ u, a smoother version of u, is the convolution of the image u with the Gaussian G ( x, ) σ σ =. x + e 4σ The function g ( u ) is positive in homogeneous regions, and zero at the edges. Caselles et al. [3] proposed an new model called Geodesic Active Contour model (GAC), which is equivalent to the weighted total variation as shown b Bresson et al. [5], and it is given as: (), where: (6) inf ( C) = '. C s g u ( C ( s) ) ds (7) C When the term g u C(s)disappears, a minimizer will be obtained. The formulation of the geodesic model b using level set method can be written as: Φ. div g ( u ). υ. g( u ),, = + t + R Φ (, x, ) = Φ ( x, ), R While man segmentation methods rel heavil, in some wa, on edge detection, the Active Contours without Edges method b Chan and Vese [6] ignores edges completel. This method is inspired b the Mumford-Shah model [8]. Chan and Vese approximate the image u b two regions of approximativel piecewise-constant intensities, of distinct values, obect region with u, rest of the image with u, and C obect boundar. This obect boundar is a minimizer of the following fitting term: F C + F C = u x c (, ) inside( C ) (8) + u ( x, ) c (9) outside( C ) Where is an other variable curve, and the constants,, depending on, are the averages of inside C and respectivel outside C. Chane and Vese in their model introduce the energ functional( ; ;), defined b: = µ + υ,,c..area F c c length C insidec + λ u ( x, ) c () inside C + λ u ( x, ) c outside C Where µ, υ, λ λ are fixed parameters. In almost all their numerical calculations, Chane and Vese fix these parameters as: λ = λ = and υ =. 3. Description of the Model 3.. Active Contour Improvement b ROI In our model we use the parameterυ different from zero, and we use the ROI extraction to calculate the area of the obect. Visual attention is not equal to all regions in the visual field but focus on a few conspicuous visual targets which are called ROI (region of interest). It exactl the same case in image processing speciall in brain image database that we have.

3 American Journal of Software Engineering and Applications 7; 6(): To define an initial contour for the active contour we use this theor of ROI b calculating the average of colons and lines to define a mask used as the initial contour: Let H L be the size of the CT image u ( i, ) of a brain. We calculate the average on the lines to create a horizontal mask (Fig.-b): H m = u ( i, ) () i = We calculate the average on the columns to create a vertical mask (Fig.-c): L m i = u ( i, ) () = We calculate the product of these two masks: M = m m i (3) Which makes the total mask of the image which is the region of interest (Fig..-d). This total mask is used as an initial contour to segment the image. This initial contour minimizes the number of iterations and the computation time. And the one-dimensional Dirac measure δ H' δε = ε we ε express the terms in the energ, and constants,, in the following wa: Fε ( c, c, C ) = µ δε ( Φ( x, ) ) ( x, ) + υ Hε ( Φ ( x, ) ) + λ u c H ( ( x, ε Φ )) + λ ( ( (, u c Hε Φ x) )) (, ). ( Φ (, )) u x H ε x c ( Φ ) = Hε ( Φ ( x, ) ) (, ).( ( Φ(, ))) u x H ε x c ( Φ ) = ( Hε ( Φ( x, ) )) 3.3. Numerical Approximation of the Model (5) (6) (7) For the numerical approximation of this model, we use a finite difference implicit scheme similar to Chane and Vese approximation b following Rudin et al. [9] for the discretization of the divergence operator in Lipschitz function expression, b taking: the space step,δ the time step, ( xi, ) = ( ih, h) the grid points, λ = λ = and υ = n Φ = Φ(n t,x, ) x i i, i, i, x + i, i+, i, i, i, i, + i, i, + i, (8) to get the following linear sstem solved b an iterative method: Figure. a) Original image, b) horizontal mask, c) vertical mask, d) total mask. 3.. Level Set Formulation of the Model For the level set formulation of this improved active contour model, we follow steps made b Chane and Vese. B using the Heaviside function Hε ( ε ) :. H z artan z ε = + (4) π ε x n+ µ x +. h x n+ n n ( + ) ( + ) + h h n+ n n+ n µ + n n = δh( Φ i, ) +. + ( Φi+, Φi, ) t h n+ ( + ) h υ λ, Φ + λ, Φ n n ( ui c ) ( ui c ) (9) Therefore, as it was also pointed out b Chane and Vese, their model is a particular case of the minimal partition

4 6 Abdelaziz Essadike et al.: Medical Image Segmentation b Active Contour Improvement problem, for which the existence of minimizers of the energ F c, c, C has been proved in [8], for that, and in order to compute the associated Euler-Lagrange equation, we use the regularized functional ( ; ;: Φ = δ ε( Φ) µ div( ν λ( u c) + λ( u c) = t Φ (, x, ) = Φ ( x, ) 4. Experiments 4.. Images Database Used in Experiments () iterations number, the elapsed time b seconds and segmented image percentages performed on a,4 GHz AMD E- with 4Go of RAM. For each iteration from to, and for each brain images, we calculate the elapsed time and the segmented image percentage with our model, and then we compare it with the Chane-Vese [6] and the Caselles et al. [3] models where we use the same initial contour used in Chane and Vese experiments. All of the experiments were performed in Matlab version 5a (Mathworks, Natick, CA). This database used in our experiment is from Meknes Oncolog Centre contains a total of 4 brain images. All the brain images are 8 bit color PNG files (Fig. ). Figure 3. Segmentation of the brain image database. Figure. Examples of brain images from the database used in experiments. 4.. Experimental Results In this section, we present experiments to evaluate the performance of our proposed model. We will present the a) are the original image and initial contour, b)-c)-d)-e) are segmentation results of Chane-Vese model for,, 5 and iterations respectivel. f) are the original image and initial contour, g)-h)-i)-) are segmentation results of Caselleset al. model for,, 5 and iterations respectivel. k) are the original image and initial contour detected b the ROI extraction, L)-m)-n)-o) are segmentation results of our model for, 5 and iterations respectivel. Figure 4. Comparisons of segmented image percentage (accurac ) along with iterations. Figure 5. Comparisons of the elapsed time along with iterations.

5 American Journal of Software Engineering and Applications 7; 6(): iterations for a time of seconds (Fig. 5) and for a pixels segmented percentage of 5.68% from a 537x637 pixels image. Unlike our model, the curves of Fig.3 show that the other two models have problems in the accurac of brain segmentation with time of seconds and 7.33 seconds for the Chane-Vese model and Caselles et al. model respectivel after iterations (Fig. 3-e-). Comparing the results in Fig. 4, we notice that the Chance-Vese model is faster than Caselles et al. model and slower than our model, but it reaches its performance after iterations for seconds as elapsed time. Once the brain images are segmented, an edge detector filter is used to present sections of the brain volume (Fig. 6). [4] C. Xu and J. Prince, Snakes, shapes, and gradient vector flow, IEEE Trans. Image Process., vol., pp , 998. [5] C. Xu and J. Prince, Generalized gradient vector flow external forces for active contours, Signal Process., vol. 7, no., pp. 3-39, 998. [6] T. Chan and L. Vese, Active contours without edges, IEEE Trans. Image Process., vol., no., pp ,. [7] C. Li, C. Kao, J. Gore and Z. Ding, Minimization of region-scalable fitting energ for image segmentation, IEEE Trans. Image Process., vol. 7, pp , 8. [8] L. Wang, L. He, A. Mishra and C. Li, Active contours driven b local gaussian distribution fitting energ, Signal Process., vol. 89, no., pp , 9. [9] X. Bresson and T. Chan, Non-local Unsupervised Variational Image Segmentation Model, UCLA CAM Report, pp. 8-67, 8. [] K. Ni, X. Bresson, T. Chan and S. Esedoglu, Local histogram based segmentation using the Wasserstein distance, Int. J. Comput. Vis., pp. 97-, 9. [] K. Zhang, H. Song and L. Zhang, Active contours driven b local image fitting energ, Pattern Recognit., vol. 43, no. 4, pp. 99-6,. [] T. Brox and D. Cremers, On the statistical interpretation of the piecewise smooth Mumford-Shah functional, Scale Space Var. Methods Comput. Vis., pp. 3-3, 7. Figure 6. Sections show the segmented brain series. 5. Conclusion In this paper, we have proposed a new improved active contour model with a Region Of interest (ROI) extraction. ROI is extracted b calculating the average of colons and lines to define a mask used as the initial contour. This model has been applied to the Meknes Oncolog Centre databases. Based on the results presented above, we can conclude that the proposed method is encouraging and outperforms most of the existing active contours models in terms of segmentation accurac and iterations number and the elapsed time. References [] M. Kass, A. Witkin and D. Terzopoulos, Snake: active contours model, Int. J. Comput. Vis., vol., pp , 99. [] L. Cohen, On active contour models and balloons, Comput. Graph. Image Process., vol. 53, pp. -8, 99. [3] T. Chan, S. Esedoglu and M. Nikolova, Algorithms for finding global minimizers of image segmentation and denoising models, SIAM J. Appl. Math., vol. 66, pp , 6. [4] T. Goldstein, X. Bresson and S. Osher, Geometric applications of the split Bregman method: segmentation and surface reconstruction, J. Sci. Comput., vol. 45, no., pp. 7-93,. [5] X. Bresson, S. Esedoglu, P. Vanderghenst, J. Thiran and S. Osher, Fast global minimization of the active contour/snake model, J. Math. Imaging Vis., vol. 8, pp. 5-67, 7. [6] M. Jung, G. Per and L. Cohen, Non-local active contours, SIAM J. Imaging Sci., vol. 5, no. 3, pp. -54,. [7] P. Yan, W. Zhang, B. Turkbe, P. Choke and X. Li, Global structure constrained local shape prior estimation for medical image segmentation, Comput. Vis. Image Understand., vol. 7, pp. 7-6, 3. [8] D. Mumford and J. Shah, Optimal approximations of piecewise smooth functions and associated variational problems, Commun. Pure Appl. Math., vol. 4, pp , 989. [9] L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Phs. D, vol. 6, pp , 99. [3] V. Caselles, R. Kimmel and G. Sapiro, Geodesic active contours, Int. J. Comput. Vis., vol., no., pp. 6-79, 997.