Computational and Mathematical Methods in Medicine

Volume 2015, Article ID 710326, 14 pages

http://dx.doi.org/10.1155/2015/710326

## Segmentation of Regions of Interest Using Active Contours with SPF Function

^{1}Department of Computer Engineering and Mathematics, Rovira i Virgili University, 43007 Tarragona, Spain^{2}Department of Computer Science & Engineering, Chung-Ang University, Seoul 156-756, Republic of Korea^{3}Korea Institute of Science & Technology Information, Daejeon 305-806, Republic of Korea

Received 16 October 2014; Revised 10 January 2015; Accepted 31 January 2015

Academic Editor: Tianye Niu

Copyright © 2015 Farhan Akram et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Segmentation of regions of interest is a well-known problem in image segmentation. This paper presents a region-based image segmentation technique using active contours with signed pressure force (SPF) function. The proposed algorithm contemporaneously traces high intensity or dense regions in an image by evolving the contour inwards. In medical image modalities these high intensity or dense regions refer to tumor, masses, or dense tissues. The proposed method partitions an image into an arbitrary number of subregions and tracks down salient regions step by step. It is implemented by enforcing a new region-based SPF function in a traditional edge-based level set model. It partitions an image into subregions and then discards outer subregion and partitions inner region into two more subregions; this continues iteratively until a stopping condition is fulfilled. A Gaussian kernel is used to regularize the level set function, which not only regularizes it but also removes the need of computationally expensive reinitialization. The proposed segmentation algorithm has been applied to different images in order to demonstrate the accuracy, effectiveness, and robustness of the algorithm.

#### 1. Introduction

The advanced imaging technologies have improved significantly the quality of medical care for patients. These technologies allowed a radiologist to make increasingly accurate diagnoses of suspicious regions like tumors, polyps, and blood rupture areas and helped physicians to render precise and measured modes of treatment [1]. It is usually a difficult task to identify significant information in a medical image because of intensity inhomogeneity and blurred object boundaries. Expert radiologists are needed to analyze the region of interest (ROI) in a particular image modality, which is costly and time consuming job. There we need an automated ROI system, which can prompt a particular region of interest and can help untrained personnel, saving both time and money. A region of interest analysis is a fundamental step in a computer-aided diagnosis (CAD) system for medical imaging, which helps early detection of cancer [2]. It prompts suspicious regions in different medical images such as magnetic resonance imaging (MRI), X-ray imaging, and computerized tomography (CT) imaging. The necessity of thoroughly examining a large number of image modalities in order to detect small number of cancers can cause high false positive, which can lead to unnecessary biopsies. Moreover, some of the salient regions can be missed due to radiologist’s tiredness or distraction [3, 4]. A system which segments regions of interest can help radiologists by tapering their search only to the desired objects in an image. Use of this type of CAD system can increase the efficiency of correct detection of tumors and decrease number of false positives found by the radiologists [5, 6]. Numerous approaches have been developed to solve this tedious but necessary problem of ROI identification and segmentation in the postprocessing of cancer research and treatment. In late 1980s, Kass et al. introduced an active contour method, which is one of well-known techniques used to segment ROI in the computer vision and image processing applications [7]. In this method, a curve is evolved under a force by minimizing the energy until it stops at the object boundary. The energy functional is normally dependent on different characteristics like curvature, image gradient, and image statistical information. The existing active contour models can be classified into two categories: edge-based models [7–10] and region-based models [11–19]. These two types of models have their own advantages and disadvantages, and the choice between them in applications depends on the different characteristics of images. The edge-based model builds an edge stopping function using image edge information, which enforces the evolution of contour towards the object boundary. A balloon force term is used in the contour evolution process, which helps the contour to shrink or expand. The selection of an accurate balloon force is main problem in this method [18]. Furthermore, for the images with intense noise or weak edges, the edge stopping function based on the image gradient can hardly stop at correct boundaries.

On the other hand, a region-based model uses statistical information to construct a region stopping function, which stops the contour evolution between different regions. Compared to an edge-based model, a region-based model performs better on images with weak or blurred edges. A region-based model is not sensitive to initialization of the level set function and can recognize object’s boundaries efficiently. Therefore, region-based models, especially Chan and Vese (CV) model [11], have been widely applied for image segmentation. Although, a region-based model is better than an edge-based model in some aspects but it still has limitations. The traditional region-based models [11, 13] were proposed in the context of binary images with an assumption that input image has homogenous patterns throughout whole image domain. Therefore, such models cannot segment intensity inhomogeneous objects in an image. To solve this problem Zhang et al. proposed a new region-based active contour method [12], which uses the advantages of both CV and geodesic active contour (GAC) models.

Reinitialization, a technique used for occasionally reinitializing a level set function to a signed distance function (SDF) during the evolution, has been extensively used as a numerical remedy for maintaining stable curve evolution and ensuring desirable results. From a practical viewpoint, the reinitialization process can be quite convoluted and expensive and can have subtle side effects [20]. Zhang et al. proposed the active contours with selective local or global (ACSLG) segmentation method, which uses a Gaussian kernel to regularize the level function after each iteration step. It not only regularizes the level set but also removes the need of computationally expensive reinitialization. An edge-based active contour model gives very poor results for the images with intense noise and weak edges, while on the other hand a region-based model gives no satisfactory result for the images with the intensity inhomogeneity. In this paper, a new region-based model is proposed for image segmentation and contour maps computation by incorporating the advantages of algorithms the level set evolution without reinitialization (LSEWR) [9], CV [11], and ACSLG [12] models. The proposed model uses statistical information inside and outside of the contour to construct a region-based signed pressure force (SPF) function, which controls the direction of contour evolution. In the formulated energy function this SPF function substitutes the edge indicator function in LSEWR model.

The proposed SPF function having opposite signs across the object boundary helps level set to shrink and expand. Contour shrinks if the initial contour is outside the boundary of the object and it expands if initial contour is inside the object boundary. In the proposed SPF function a mask term is used to restrict the contour movement inwards. That mask term helps to select the inner region and discard the outer region during the contour evolution process. The proposed algorithm partitions an image into two subregions and then inner part of the subregions is partitioned further into two subregions iteratively and so on until a stopping condition is fulfilled. Subregions are detected through the minimization of a new energy model restricted to a characteristics function of a subregion. If is the number of iterations in order to attain final segmentation result, then would be total numbers of regions from initial to final contour.

The introduced model embeds an SPF function based on a traditional region-based model [11] to target images with intensity inhomogeneity. The traditional region-based model [11] cannot properly segment image with intensity inhomogeneity because it cannot differentiate small intensity differences between two consecutive regions and cannot detect weak object boundaries. In the proposed algorithm, the proposed SPF function by using a mask term can control the contour direction and contour stopping algorithm can control the stopping point between two consecutive contours. The proposed algorithm replaced an edge indicator function in LSEWR model with an SPF function to introduce a new region-based model to trace down high intensity ambiguous regions in medical images.

The proposed algorithm contemporaneously traces high intensity or dense regions, which are tumors, masses, or salient dense tissues in medical image modalities. The resulting representation establishes an analysis of the global structure of region of interest. The contour shrinkage depends on the intensity of the region. If intensity difference between background and desired object is high then contour will evolve quickly; otherwise, the contour evolution will take time. The proposed method is good at finding high intensity and dense regions in an image. Therefore, it can properly segment salient dense regions, tumors, polyps, and blood rupture veins. Segmentation of cancer tissues in mammograms, brain tumors in brain magnetic resonance (MR) images, and ruptured blood vessels analysis in the angiography are some of the applications in which proposed method can be used. The formulated algorithm has been applied to different real images in order to demonstrate the accuracy, effectiveness, and robustness of the algorithm. Furthermore, the proposed segmentation algorithm can also be used to produce an adaptive contour map for the topographic analysis of objects in medical images.

#### 2. Related Work

In [13] Mumford and Shah formulated the image segmentation problems as follows: find an optimal piecewise smooth approximation function of of image , which varies smoothly within each subregion of the image domain and rapidly or discontinuously goes across the boundaries of . They proposed the following energy functional: where is the length of the contour and and are fixed parameters. The unknown set and the nonconvexity of the above energy functional make it difficult to be minimized. Some alternative methods have been proposed to simplify or modify the above functional, introduced as follows.

Chan and Vese [11] proposed an active contour method (ACM) based on the Mumford and Shah model [13]. Let be an input image and let be a closed curve; the energy functional is defined by where , , , and are fixed parameters. The Euclidean length term is used to regularize the contour. and are two constants that approximate the image intensities inside and outside of the contour , respectively. Minimizing the above energy functional by using the steepest gradient descent method [21] and representing the contour with zero level set, that is, , we obtain the following variational formulation:

The data fitting term plays a key role in curve evolution, and and govern the trade-off between the first and second term. In most cases, we set and . is a scaling parameter. If it is small enough, then small objects are likely to be extracted; if it is large, big objects can be detected [11]. Obviously, in 4, and are related to the global properties of the image contents inside and outside the contour, respectively. However, such global image segmentation is not accurate if the image intensity inside or outside the contour is inhomogeneous.

In [12] proposed a region-based active contour method. First a new region-based signed pressure force function is proposed, which efficiently stop the contours at weak or blurred edges. Second the exterior and interior boundaries are automatically detected with the initial contour being elsewhere in the image. Third the proposed ACM with selective binary and Gaussian filtering regularized level set has the property of selective local or global segmentation. It can segment not only the desired object but also the other objects. The computational cost for the traditional reinitialization is reduced. Finally, the proposed algorithm is efficiently implemented by the simple finite difference scheme.

Let be a bounded open subset of and let be a given image. Let be a parameterized planar curve in image domain. The GAC is formulated by minimizing the following energy functional:

Using calculus of variation, we get the following Euler Lagrange equation: where is the curvature of the contour computed across the boundary of the system and is the normal computed inwards to the computed contour. Normally a velocity term is added in order to accelerate the evolution process of the contour. Then the above equation can be rewritten as

The corresponding level set formulation will be as follows:

The SPF function defined in [22] is in the range . It modulates the sign of pressure force inside and outside of the region of interest and it is used to shrink the contour when outside the object and expands it when inside the object. The mathematical formulation of the proposed SPF function is as follows:

By replacing the edge indicator function with the sign pressure force function we get the following formulation:

In [12] a new regularization method is introduced for the level set regularization; therefore, curvature term can be removed.

In addition, the term in above equation can also be removed, because their model utilizes the statistical information of regions, which has a larger capture range and capacity of antiedge leakage. Finally, the level set formulation of the proposed model can be written as follows:

In [19] a region-based active contour method is proposed, which utilizes an SPF function based on a traditional active contour method [11]. The proposed method uses both region and edge-based information in the implementation of the energy formulation. It is formulated by using edge-based model [9] as a base and by replacing the edge indicator function with a region-based SPF function, which was formulated using traditional active contour method [11].

Let be an input image and let be a closed curve; the energy functional is defined by where is length term of the level set curve, is the area term which deals with the area across the object of interest, and is the penalizing term used to remove the penalizing energy during the level set curve evolution process:

By replacing the edge indicator function with an SPF function based on a traditional region-based active contour method we get the following formulation:

By the calculus of variations [21] the steepest descent process for minimization of the energy functional is the following gradient flow: where is the Laplacian operator used in the energy penalization step during the evolution of level set curve.

#### 3. The Proposed Region-Based Active Contour Method for Segmentation of Region of Interest and Contour Mapping

A curve in is represented by a level set function , which is zero at object boundary in image . Curve partitions a subregion into two subregions , with , such that

In the proposed algorithm, the evolution of the level set starts from the initial level set function and goes on by moving the contour inwards. In order to compute the contour map of the image the initial contour is defined at the boundary of the image. To move the level set inwards, we calculate the inner subregion of zero level curve using .

Figure 1 shows an isocontour map image in which the inner regions , , and are calculated using , whereas the outer regions are calculated by subtracting the energy component of the current calculated inner subregion from the previous calculated inner region, as shown in the equations below: