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International Journal of Innovative Research in Advanced Engineering (IJIRAE) ISSN: 2349-2763 Issue 02, Volume 4 (February 2017) www.ijirae.com

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Segmentation of MR Images using Active Contours:

Methods, Challenges and Applications

K V Mahesan* S. Bhargavi D. Jayadevappa Associate Professor Professor, Dept. of ECE Professor, Dept. of E& IE Dept. of Telecommunication SJCIT, Chikkaballapur, India JSSATE, Bengaluru,

Dr. AIT & Research Scholar VTU, Belagavi, India. Jain University, Bengaluru, India Abstract — In recent years, Active contours have been widely studied and applied in medical image analysis. Active contours combine underlying information with high-level prior knowledge to achieve automatic segmentation for complex objects. Their applications include edge detection, segmentation of objects, shape modelling and object boundary tracking. This paper presents the development process of active contour models and describes the classical parametric active contour models, geometric active contour models, and new hybrid active contour models based on curve evolution and energy minimization techniques. It also discusses challenges and applications of active contour models in medical image segmentation.

Keywords — Active Contours, Image Segmentation, Medical Image Analysis.

I. INTRODUCTION

Manual tracing of object boundaries generally suffers from poor reproducibility of results and it is also tedious and time consuming. Further, manual segmentations are often restricted to 2D slice-wise processing, often suffer from inconsistency across segmented slices. Quantitative analysis of medical images requires reproducible, accurate and efficient segmentation methods. In this paper, various approaches of medical image segmentation using active contours and available algorithms are reviewed and their advantages, disadvantages and limitations are discussed.

This paper reviews various types of active contour models used for the segmentation of medical images. Active contour models can be implemented on the continuum and achieve sub pixel accuracy, a highly desirable property for medical imaging applications. Current research on active contour models for medical image segmentation is extensive. Many variations, extension, and alternative formulations appeared since the introduction of traditional snake model [1]. Survey and review articles on active contour models in medical image segmentation are available in the literature [2], [3], [4], [5]. This review is on their basis for comparison of some more medical image segmentation techniques. Active contour models (ACM) are less sensitive to noise, as well as the location of the initial contour, and have better performance with weak boundaries. Hence these models can efficiently detect the exterior and interior tumour boundaries simultaneously.

II. ACTIVE CONTOUR MODELS

Medical image analysis has played a more and more important role in many clinical procedures due to the advancements in medical imaging modalities such as computed tomography (CT), magnetic resonance imaging (MRI), and ultrasound. Active contour models are capable of providing closed and smooth contours or surfaces of target objects with sub-pixel accuracy and have been extensively applied to 2D and 3D image segmentations. These models can be formulated under an energy minimization framework based on the theory of surface evolution and geometric flows. The first model of active contour (Snake model) was proposed in [6] and named snakes due to the appearance of contour evolution and is successfully applied to deal with a wide variety of computer vision applications.

The snake model is described as a controlled continuity model under the influence of image forces. Internal forces control the bending characteristics of the while image forces, such as the gradient, serve to push the snake toward image features.

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The total energy of the snake is defined as

1 1 1*

int0 0 0

( ( )) ( ( )) ( ( ))snake snake imageE E s ds E s ds E s ds v v v (1)

The spline’s internal bending energy has been defined by this paper as follows

2 2

int ( ) ( ) ( ) ( )E s s s s s ssv v (2)

The coefficients, and can be used to control the continuity characteristics of the snake by changing its elasticity and rigidity. Application of this basic model is limited because of contour initialization. Berger [7] has proposed the first and primary uses of parametric models in medical image analysis to segment objects in 2D images. However, this classic snake provide an accurate location of the edges only if the initial contour is given sufficiently near the edges, because they make use of only the local information along the contour. This limitation indicates that, basic snake model alone cannot serve the purpose of accurate segmentation and they need further modifications and extensions. Cohen [8] has incorporated an inflation force in the original snake model and the contour curve is treated as a balloon that is inflated in order to avoid local minima solutions i.e., the curve passes over edges and is stopped only if the edge is strong. However, it does not work image with weak edges. Cohen and Cohen [9] used an internal inflation force to expand a snake’s model past spurious edges towards the real edges of the structure, making the snake less sensitive to initial conditions. But it suffers with poor capture range. Poon et al. [10] have proposed an algorithm to minimize the energy of active contour models using simulated annealing. This method improves the capture range but noise and other image artefacts can cause incorrect regions or boundary discontinuities in objects recovered by this method.

A. Gradient Vector Flow and Geodesic Active Contour Models

In order to overcome the limitations posed by traditional snake, Xu and Prince [11] have made an effort by introducing gradient vector flow as an external force (region based features), that significantly increases the capture range. In this method they replaced the potential force in the traditional equation with a novel external force field called Gradient Vector Flow (GVF). The energy equation is as follows

2 22 2 2 2

x y x yE C u u v v f V f dxdy (3)

This technique makes the model free from the initial conditions and also they can handle concave objects. But still it poses the following drawbacks. Paragios et al. [12] have introduced a set of diffusion equations applied to image gradient vectors yielding a vector field over the image domain.

1 ,C g k Vk x k x u v N N

t

(4)

This method has the bidirectional flow and can extract concave object extraction problem, however, it suffers from high computational requirements. To overcome this drawback, Cvancarova et al. [13] proposed several improvements to the original GVF algorithm.

12 2

0

1 ' ''2 extE C s C s E C s ds (5)

Traditional snake often converges to local minimum and they do not perform well on noisy images, and their capture range is small. This problem is overcome by Osher and Sethian [14] and suggested some external force model to enhance capture range. By introducing several parameters to the GVF algorithm [15], the capture range is shown to be satisfactory. In order to improve both segmentation quality and computational efficiency, Liu et al. [16] suggested the combination of GVF algorithm and mean shift technique. The improved GVF using mean shift is formulated as,

1

1 2 3'' ''' 0g d C s g d C s g d V (6)

This algorithm reduces the interferences from other edges, but it suffers with parameter optimization. Caselles et al. [17, 18] and Malladi et al. [19] have introduced a new method called Geometric Active Contour (GAC) model. These models can handle topology changes without any additional task. This method is based on the level set frame work, where the curve C represented by the zero level set of a Lipschitz function : which is usually defined as a signed distance function such that





: 0

( ) : 0

: 0

C x x

inside C x x

outside C x x

(7)

GACg k v

t

(8)

Yezzi et al. [20] have proposed another geometric snake using energy to search for a curve of minimal weighted length, and then the energy minimization functional for geodesic active contour is given by

12

0

1 '2GeodesicE C C s I C s ds

(9)

This can be generalized by replacing the edge detector I with a decreasing function 2g I then the evolution equation for geodesic active contour is

Geodesicg k v g

t

(10)

Sapiro et al. [21] have also proposed the modified geometric active contour model by introducing the curvature term in the original snake model as,

1

0

, sE C s f N N KfN c ds

t t (11)

The above review on traditional snake, GAC, and GVF conclude that, in edge-based segmentation methods [22], the high similarity that exists (especially MR images) in the intensities of adjacent regions may not provide prominent edge information. Similarly, with region-based techniques with high similarity in intensities between adjacent structures may cause under-segmentation problem. In order to formulate this, level set based active contour models (belongs to geometric approach) are proposed. These models incorporate both edge and region information to provide an accurate segmentation of regions that has highly similar intensities with their backgrounds.

Fig. 1. Results of GVF and GAC to brain MR image segmentation

Malladi et al. [23] and Siddiqui et al. [24], have attempted the first application of level sets in medical image segmentation. Limitation of this method is that, one needs to ensure that a Zero Level Set (ZLS) lies embeded over the object to be modeled. Tsai et al. [25] have also proposed a shape based approch to curve evolution for the segmentation of medical images containing known objects. Goldenberg et al. [26] have explored a shape based level set approach. This method is based on the coupled surfaces model that was derived as a minimization problem in a variational geometric framework. Shi and Karl [27] have addressed the problem of segmenting heterogeneous features in the image by reformulating region based segmentation energy in a local way. Jayadevappa et al. [28] have addressed the advantages and disadvantages of various active contour models used in medical image segmentation.

Phan Truc et al. [29] presented a novel active contour model for medical image segmentation that is based on a convex combination of two energy functional to both minimize the in-homogeneity within an object and maximize the distance between the object and the background. This regularize the solution by constraining the length of the curve and the area of the region inside it, yielding the total energy functional as

( ) ( ) ( ( ) ( ) (1 ) ( )E c Length C Area inside C F C B C (12) One of the advantages of the Active Contour (AC) over other geometric AC models is that it can be initialized outside, inside, or even across the objects. Compared with the conventional model [30], this performs better and is less sensitive to noise and contrast.





An improved region-based model with local statistical features for medical image segmentation was proposed in [31]. This model utilizes an improved region fitting term to partition the regions of interests in images depending on the local statistics regarding the intensity and the magnitude of gradient in the neighbourhood of a contour. Since it uses gradient descent method, energy function will minimize by an efficient dual algorithm, which avoids the instability and the non-differentiability of traditional numerical solutions. The energy functional of the proposed model is as follows.

2

121

( ( ) ( ))( ) (log exp( )x y C

l x C yE X

(13)

2 2

2 12 22 1

( ( ) ( ) ( ( ) ( ))logexp log expI x C y I x v y

(14)

where, 1( )C y , 2 ( )C y and Y C denote the mean intensity inside and outside the contour in the local region. This model is different from other general region-based models in two ways. First, the new regularization term proposed in the proposed model is capable of extracting the complete local structural information from an image. B. Gradient Vector Flow and Geodesic Active Contour Models

A new region-based active contour model, namely local region-based Chan–Vese (LRCV) model [32] is proposed for image segmentation. By considering the image local characteristics, the proposed model can effectively and efficiently segment images with intensity in-homogeneity and also to reduce the dependency on manual initialization in many active contour models. In this technique, 1( )C x and 2 ( )C x degrade to constants,

1 21 2

( )( , ) 2 ( ) ( ) ( )2

c cx t c c I xt

(15)

Compared with the well-known local binary fitting (LBF) model and the LCV model, the LRCV is not only much more computationally efficient and but also much less sensitive to the initial contour. Graph cuts based active contour models [33] have been widely used in image segmentation for global minimization and efficient calculation. For local segmentation with surrounding nearby clutter and intensity in-homogeneity the general formulation of active contour model is used.

2 2( ) ( ( ( )) ( ( ) ) ( ( ) )in out

b in outC C CE c g I C S ds I x f dx I x f dx

(16)

where, I corresponds to pixel intensities, C is the closed curve, and fin and outf are local versions of mean intensities inside and outside curve C respectively. Based on the analysis of the initialized contour and the narrow band above, we initialize the contour around the true boundary in experiments, and the narrow band is built.

(a) (b) (c)

Fig. 2. Analysis of the Graph cuts based active contour models [33]. (a) Red curve is the initialized contour, and the narrow band RNB is constructed between the green curves, Result using only region term and (c) Result using only the edge term.

Qi Ge et al. [34] proposes a novel region-based active contour model (ACM) for image segmentation, which is robust to noise and intensity non-uniformity. The energy functional of the proposed model consists of three terms, i.e., the patch-statistical region fitting term, the improved regularization term, and the intensity variation penalization term. The patch-statistical region fitting term computes the local statistical information in each patch as the basis for driving the curve accurately with resist to intensity non uniformity and weak boundaries. The regularization term coupling with the gradient information improves the ability of capturing the boundaries with cusps and narrow topology structures. The image gradient describes intensity variation on two perpendicular orientations. So it is necessary to improve the total variation regularization term by gradient information of intensity. For simplicity, the images are considered as the 2-dimensional matrices and the level set function is defined in the continuous setting. Then an improved regularization term as





1 .( )

IR

I

(17)

Recently, ACM and Geodesic Contours (GC) have become the most popular and important methods in image segmentation. Considering the advantages of global minimization and efficient calculation over level set method, ACMs are often optimized via GC. However, most GC-ACMs are global segmentation models [35], i.e., no matter where the initial contours locate in the image, all of the objects in the image will be segmented globally. For local segmentation, the localized GC-ACMs [36].

Fig. 3. The effects of the improved regularization term, the patch-statistical region fitting term and the intensity-variation penalized term during the curve evolution [34].

The proposed model is different from other general region-based models in three ways. Firstly, a new region fitting energy extracts the statistical information in the local patch to classify the pixels; secondly, an intensity variation penalization term is proposed to make the evolution be robust to the noise and intensity non-uniformity; in addition, the new regularization term coupling with the gradient information enhances the curve’s ability of capturing the complex topological structures like cusps and corners. Region based segmentation in medical images considers the two facts; (i) Medical images have typical feature of intensity in-homogeneity. (ii) Object segmentation in medical images has typical feature of surrounding nearby clutter.

A nonparametric local region-based active contour driven by a local histogram fitting energy is presented by Weiping Liu et al. [37]. In this algorithm, the energy is defined in terms of an evolving curve and two fitting histograms that approximate the distribution of object and background locally through a truncated Gaussian kernel. In this method, a nonparametric region-driven ACM using local histogram fitting energy is proposed. For a given point, the region is localized by a Gaussian kernel. The local histogram fitting energy is defined as,

1 0( , , ) ( ) ( , ) ( ) ( , )x x x y x yx t LE C P P K X Y D P P dy K X Y D P P dy

(18)

where, xiP and 0

xP are the fitting histograms that approximate the distribution inside and outside the evolving curve.

Fig. 4. Segmentation results using local histogram based active contour model [35].

The experiment in figure 3 shows the evolution process from the initial curve (first column) to the final curve (fourth column) using local histogram fitting energy with varying kernel width. This technique applies the nonparametric statistic and does not predefine any kind of distribution of each region. It is not appropriate to use a fixed kernel width when compute the local fitting histograms and evolve the curve. This method can also be able to segment texture images and low contrast image.

A new radial active contour technique, called pSnakes [38] using the 1D Hilbert transforms as external energy. The pSnakes method is based on the fact that the beams in ultrasound equipment diverge from a single point of the probe, thus enabling the use of polar coordinates in the segmentation. The control points or nodes of the active contour are obtained in pairs and are called twin nodes. The internal energies as well as the external one, Hilbertian energy, are redefined. The active contours, pSnakes, is a radial active contour method which can be used to segment objects from digital images, and is defined by

2[0,1] R 1 2( ) ( ( ). ( ));( ( ). ( ))S C S r s s r s S (19)





where 1( , )r and 1( , )r are polar coordinates of the control points of the polar active contour (pSnake). The main applications of this work are; the use of the pSnakes method in the image segmentation of the LV and the use of Hilbert energy to calculate the external force of the radial pSnakes method though Hilbert transform. First the 1D Hilbert transform must be applied along the radial beams, which are the image rays represented in polar coordinates, after which it should be normalized and its absolute value can then be used as the external energy. The external Hilbertian energy of pSnakes is defined as the absolute value of the normalized Hilbert transform applied along the signal beam. Figure 4 shows the main geometric differences among snakes, radial snakes and pSnakes respectively.

(a) (b) (c)

Fig. 5. Different types of snakes: (a) Snakes, (b) Radial snakes, (c) pSnakes [36]

In order to segment the image accurately, many energy functionals integrated an edge-based method and a region-based technique in the literature. The external energy functional incorporates an edge-based information fitting term [39], which is an adaptive diffusion flow (ADF), and responsible for extracting object boundaries, especially segmenting the weak and missing borders, and a localizing region intensity fitting, which localizes the Chan–Vese external energy gain intensity. This challenging task is accomplished by establishing an active contour model in a variational level set formulation.

Fig. 6. The segmentation result of the adaptive diffusion flow (ADF) snake [39]. This method combines the advantages of the LACM and the ADF model by taking the localizing region and edge-based intensity information into account. The following general expression as the evolution equation

( ) ( ) ( )( ) (1 )region edge Lx x xx

dt dt dt dt

(20)

In this technique, the contour is initialized automatically and the division of contours [40], [41] takes place depends on the number of objects present in the image.

C. Active Contour Model Based on Local and Global Intensity Information

An energy functional with a local intensity fitting term, which is dominant near object boundaries and responsible for attracting the contour toward object boundaries, and an auxiliary global intensity fitting term which incorporates global image information [42], [43], [44] to improve the robustness of the system. When the contour is close to object boundaries, the local intensity fitting force becomes dominant, which attracts the contour toward and finally stops the contour at object boundaries. This force plays a key role in accurately locating object boundaries, especially for images with intensity in-homogeneity. The global intensity fitting force is dominant when the contour is far away from object boundaries, and it allows more flexible initialization of contours by using global image information.

Another technique of active contour model driven by local and global probability distributions [45]. In this method, a new local signed pressure force (SPF) function, which is defined based on the local probability distributions, was proposed. According to different methods of probability density estimation, the SPF function is categorized into two classes: parametric and non-parametric SPF function. By incorporating the SPF function into a generalized geodesic active contour model [46], [47], [48], a novel local segmentation model can be obtained. This model is capable of extracting the desired target, whose intensity possesses non-uniform property and boundaries suffer from fuzzyness. Considering that when the evolving curve is located far away from the target’s boundary, we might obtain similar local interior and exterior regions, and then the curve will be trapped in the current position.





Therefore, a global based term is introduced to help the curve evolve in this case. In this approach, composed of two SPF terms, including a local based SPF function and a global based SPF functions are introduced.

1( ( )) . ( ( )) (1 ). ( ( ))h gSpf I x Spf I x Spf i x (21) With the assistance of the global force, the robustness to the initialization is improved. The global force is dominant if the evolution curve is away from the object. Meanwhile, the local force is significant to determine the final contours, if the contour is near object boundaries. For the better results, the parameter can alter referring to the intensity distribution in different regions in a given image. A smaller parameter may be set in the smooth region, while a larger one will be set within a region with abundant edge information.

Fig. 6. Active contour model based on local and global intensity information for brain MRI segmentation [45]. Sanping Zhou et al. [49], defined an unified fitting energy frame work based on Gaussian probability distributions to obtain the maximum a posteriori probability (MAP) estimation. The energy term consists of a global energy term to characterize the fitting of global Gaussian distribution [50], according to the intensities inside and outside the evolving curve, as well as a local energy term to characterize the fitting of local Gaussian distribution based on the local intensity information. In the resulting contour evolution that minimizes the associated energy, the global energy term accelerates the evolution of the evolving curve far away from the objects, while the local energy term guides the evolving curve near the objects to stop on the boundaries. However, for the medical images with intensity in-homogeneity, the final obtained curve can hardly divide the image into object region and background region even after along iteration time. There is a global energy term assumes that both the intensity mean and the intensity variance are piecewise constant. As a result, the constant intensity mean and variance cannot represent the in-homogeneous intensities in both the object region and the background region. In order to achieve good performance in segmenting medical images with intensity in-homogeneity, the local information has to be taken into account.

Fig. 7. Results obtained from active contour model based on local and global intensity information for the segmentation of brain MR image [49].

Recently, local intensity information has been incorporated into the active contour models to deal with images with intensity in-homogeneity. This model not only can segment medical images with intensity in-homogeneity, but also allows flexible initializations.

III. CONCLUSIONS

This paper presents the basic principle of active contour models, different types, recent advancements in active contour models applications and challenges. This also has discussed a variety of approaches developed over the last decades for the task of medical image segmentation. Although some of the techniques have found applications within the medical image segmentation area, active contour models such as snakes, GVF, GAC, level sets, variational level sets have opened up a very interesting research directions because of their strong mathematical foundation. These methods can be applied based on how the contour is represented, leading to the parametric and geometric types or how the flow is derived leading to the energy-based or the curve evolution-based types. Moreover, the fact is that active contour models play a more and more important role as a modern technique in medical image segmentation.





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