A Shape Prior-Based Active Contour Model for Automatic Images Segmentation

Due to the variable shapes of objects, high noise intensity and complex environments, the field of image segmentation still has great challenges. To address these issues, we present a new image segmentation strategy based on active contour model and shape priori information, which can accurately and efficiently segment various images. The data fitting term, inspired by Chan-Vese (C-V) model, is used to guide the curve evolving to desired target boundary. Meanwhile, the contour is utilized to reconstruct a prior shape so that can help to deal with images in the presence of complex target. After that, the length regularity term of energy functional is incorporated to ensure the stable calculation of the evolution curve. The quantitative and qualitative experiments on various real and medical images indicate that our method is more efficient and accurate than the existing unified models.


I. INTRODUCTION
Segmentation of medical images can provide doctors with a variety of valuable information, so it plays an important role in many medical applications, such as treatment planning, surgery and prognosis assessment. However, due to the complexity of body anatomy and the diversity of images, it is more difficult to segment medical images than natural images. In traditional medical image diagnosis, the lesions and edges of target are marked manually by radiologists, which is a time-consuming tasks and easily affected by human factors. Therefore, designing an efficient algorithm that can locate, segment, and quantify diseased tissue is of great significance for many clinical treatments.
Considering the characteristics of medical images, many traditional algorithms (such as thresholding, region growing, clustering) cannot meet the requirements of segmentation. As an important branch, active contour model presented by Kass et al. [1], also known as snake, has been proved to be efficient approach since the contour can give a closed and stably boundary. Thus, many researchers have done great effort and many methods have been presented to improve The associate editor coordinating the review of this manuscript and approving it for publication was Naveed Akhtar .
it [2]- [5]. Among them, one of the most famous active contour models is the C-V model [6], which utilizes the statistical information to guide the contour. In the C-V model, image intensities in each region are assumed to be statistically homogeneous, thus it cannot provide accurately segment the images with intensity inhomogeneity. To solve the problem of the C-V model, Li et al. presented the region scalable fitting (RSF) model [7] based on the local information of the image, which has achieved promising results. However, when an unreasonable initial contour is set, RSF model may fall into local minimum. In [8], Yang et al. integrated the local information term and the distance constraint into the variational framework for auroral oval segmentation, thus it can achieve a significantly improvement and obtain more accurate boundaries. Ding et al. [9] presented an image segmentation strategy by combining the Laplacian of Gaussian term and the RSF term, which is used to realize an accurate segmentation result. Based on the gravitational search technology, Çataloluk et al. [10] implemented an improved C-V model to solve the local minimum problem. Zhang et al. [11] presented a modified improved level set algorithm which draws upon the optimized area energy term. With an adaptive edge stopping function, this method can implement a correct segmentation and become more stable. In [5], saliency map and color intensity are taken into the active contour model as the region external energy to identify a more accurate boundary positioning.
Recently, shape-based active contour models have been constructed to regularize the smoothness of the contour for image segmentation [12]- [16]. Qin et al. [17] developed a level set framework for bladder MR image segmentation, which used an adaptive shape priors constrained to obtain the desired boundaries. In another study, based on the intensity information, Pham et al. [18] introduced the nonlinear shape priors into the energy functional, which is designed for cardiac MRI images. Yang et al. [19] presented an unsupervised prostate segmentation method for hierarchical prostate MRI segmentation. In this approach, the statistics information and shape prior was used in the segmentation task. Research by Meng et al. [20] utilized the prior knowledge and the local information term to obtain the outer boundary of the aurora, thus it can provide an accurate segmentation result. Ge et.al [21] improve the imperfection of C-V model based on fuzzy C-means clustering with shape priors, which has better performance and powerful anti-noise capacity. Han et.al [22] used the output of the fully convolutional networks as a probability map, and the improved level set method was employed to segment various images. Finally, both images can obtain accurate segmentation results. Niu et.al [23] created a new active contour model for computed tomography angiography images processing. In the algorithm, shape prior and local region fitting terms are employed. This work achieves the precise segmentation of the epicardial and endocardial parts of the myocardium.
Inspired by the works above-mentioned, we present an adaptive shape prior constrained segmentation algorithm in this paper. The new method can be summarized as follows: Firstly, using the improved C-V model as the data fitting term, we propose a region-based evolution equation. Secondly, the shape prior-based active contour model is built to deal with images in the presence of complex target. Finally, the length regularity term of energy functional is incorporated into the level set framework and the contour is evolved within the narrowed range. The numerical experiments on various real and medical images show that our method is more accurate and efficient than other state-of-the-art methods.
The remainder of the paper is organized as follows: Section 2 briefly introduces the related work. In next Section, the proposed method is discussed. Experiments and results are provided in Section 4, and finally concluding statements are given in Section 5.

II. RELATED WORK A. C-V MODEL
Chan and Vese presented a simplified Mumford-Shah model [24], which is named C-V model [6]. By assumption that objects of segmenting images have constant brightness, C-V model can accurately segment the images with intensity homogeneity. Let I : → R 2 be a given image, C represents the current or initial contour curve. In its most general form, the energy function of C-V is constructed as: where λ 1 , λ 2 , ν, µ are the fitting parameters of each energy items. The values of c 1 and c 2 represent the average intensity values of original image, based on the objects (inside(C)) and the background (outside(C)). By replacing C with level set functionφ(x), and introducing the Heaviside function H ε (x) and the Dirac function δ ε (x), the Eq. (1) can be modified as: where ε is a suitably chosen constant. Subsequently, by applying the gradient descent method, we can get the following equation: with c 1 and c 2 equal to Duo to the intensity inside and outside of the curve is assumed to homogeneous, so C-V model will leads to poor segmentation performance with intensity inhomogeneity.

B. LIF MODEL
To segment inhomogeneous images, Zhang et al. [25] combined the active contour model with local image fitting (LIF) energy to extract local image information. The energy functional of LIF is expressed as: where I LFI (x) is called a local fitted image, defined by where m 1 and m 2 are formulated as: 200542 VOLUME 8, 2020 where W k (x) is a local window function, with size (4k + 1) × (4k + 1) and standard deviation σ . According to the steepest descent method, the energy functional in Eq. (7) can be minimized by: Since the LIF model achieves image segmentation by minimizing the difference between the local fitted image and original image, thus, is more efficient and less sensitive to the initial contour. However, this method may produce less accurate when image with heavy noise.

III. PROPOSED METHOD
In this section, we present an active contour model for various real and medical images segmentation. The proposed method consists of three parts: the data fitting term, the shape priori term and the length regularity term. The detailed description is given in detail.

A. DATA FITTING TERM
Inspired by the works of Zhang [25] and Han [26], taking into account the intra-class variances of the pixel inside and outside the contour, a novel active contour model is presented and its objective functional is defined by: where d 1 and d 2 the intra-class variances of pixel grayscale values inside and outside the curve contour, which are calculated as: where N 1 and N 2 represent the number of pixels in the corresponding region.

B. SHAPE PRIOR TERM
The data fitting term E data (φ) proposed in Eq. (11) is sensitive to initial contour, it will result in the wrong segmentation. To solve the above problem, shape constraint information is introduced. Let φ be the current evolving shape and φ r is the reference shape, then the shape constraint term can be calculated as: In the process of energy function minimization, when the contour curve of the target deviates from the prior shape constraint, it will be punished. The greater the offset distance is, the greater the penalty is.

C. LEVEL SET FORMULATION
To keep the evolution curve smoothly, the length regularizing term are incorporated into the level set framework, which is defined by: Combining the data fitting term, the shape priori term and the length regularity term, then the final energy function of our method is expressed as: where λ, η, µ are three parameters. According to the variational rule and gradient descent method, and the corresponding partial differential equation of Eq. (15) is written as:

D. IMPLEMENTATION
To improve computational efficiency of the level set method, narrow band technology is used around the closed contour in this paper. Simply, narrow band is defined as: where r is the width of narrow band. In details, we summarize the main procedures of our algorithm as follows: Step 1: Give an initialized contour inside the object and initialize it to be a binary function φ = φ 0 (x): x is outside C Step 2: Build the narrow band according to Eq. (17).
Step 3: Compute the points in the narrow band via the evolution Eq. (16).
Step 4: Re-initialize φ(x) into the binary level set function.
Step 5: Check whether the evolution is stationary. If not, return to step 2.

A. SYNTHETIC IMAGES SEGMENTATION
The first testing experiment is the comparative results of ACM_LoG, ACM_LPF, C-V, CVXB, RSF, LRAC, Sun's, ACLEPF, HLFRA and the proposed model to verify the robustness of the initial contour, where the corresponding VOLUME 8, 2020  image is a synthetic plane image (pixel size: 135 * 125) with distinct shadow, as shown in Fig. 1. According to the experimental results, LRAC, Sun's, and ACLEPF models can segment the image correctly only under some initial contours. However, for the other evaluated methods, each initial contour leads to a desired segmentation result. This shows that the size and location of the initial contour curve has no effect on final results in these models, which establish that our model is robust to the initial contour curve.
As a further comparison, the segmentation results are tested to the above models to show the effectiveness of our method with various noise levels using the plane images. To make a fair experiment, we use the same initializations of the images for all the methods. Firstly, we use speckle noises to evaluate the performance of these different methods.   We can see that the RSF, LRAC, HLFRA and our method nearly have the best overall performance, which demonstrates that these methods are very robust against speckle noises. For the ACM_LoG, ACM_LPF, C-V, CVXB, Sun's and ACLEPF, when the strength of noises is weak, both of them can get the satisfactory segmentation results. However, when the noise intensity increases, they exhibit poor performance. In order to further validate the robustness of our method, Fig. 3 gives the comparison results of the eight models for images with different levels Gaussian noise (mean 0, variances 0.001, 0.005, 0.01, 0.05, 0.1). In contrast, our model obtained satisfactory segmentation results for the challenging noisy images. For a quantitative comparison, the Jaccard similarity (JS) [33], [34] index is employed to evaluate the images on Figs. 2 and 3. If S 1 and S 2 denote the segmented results obtained by the models and the ground truth respectively, then the metric is defined: where N (·) is the pixels number of the enclosed region. The value of JS ranges from 0 to 1, with a higher value VOLUME 8, 2020  representing a better segmentation result. The corresponding JS values are shown in Figs. 4 and 5. From the JS values we can see that, except for individual noise images, the proposed model has the highest JS values among these methods. Therefore, our model could have high and stable segmentation accuracies than other reference methods, qualitatively and quantitatively.

B. MEDICAL IMAGES SEGMENTATION
In the next experiment, these eight models are applied to a computed tomography scans of liver tumor, which has low contrast and weak boundary. As shown in Fig. 6, with different initial contours, C-V cannot segment out the objects, such as the weak boundaries. The ACM_LoG, ACM_LPF, CVXB, RSF, Sun's and ACLEPF are not only sensitive to the initial contours, but also have poor ability to exclude fake objects. Even when the initial contours are set on the correct liver target, it still captures the wrong outline in the background as pseudo object. As shown in the seventh and ninth columns, LRAC and HLFRA are sensitive to initializations and can get promising results to some extent. In contrast, our method is less sensitive to the initial contour and it captures the 200546 VOLUME 8, 2020 In this subsection, experiments on nine representative ultrasound medical images [35], [36] are presented to evaluate the proposed method. The images including intensity inhomogeneities, noise, and blurry boundaries are breast cyst, renal cyst, hydatid cysts with intramural nodules, liquified hematoma, intramural nodule, bronchus, and so on. The contours are manually initialized to irregular areas, as shown the red curve in the first column of Fig. 7. The second to last columns are results of ACM_LoG, ACM_LPF, C-V, CVXB, RSF, LRAC, Sun's, ACLEPF, HLFRA and the proposed model, while the iterations and computational time are list in Table 1. One can get that ACM_LPF, C-V, CVXB, ACLEPF and HLFRA produce severe over-segmentation in most images. The segmentation results of ACM_LoG, RSF, LRAC, and Sun's are subjectively close to the ground truth and most targets can be extracted correctly. Compared with the above models, our method perfectly extracts the desired objects from these images while avoiding boundary leakage and excessive contraction. In addition, from Table 1, we can find that the proposed method arrives at the minimum at a faster speed. This proves that our method is much more feasible.
In order to further verify the superiority of the proposed method, the brain pituitary adenoma images are used in this subsection obtained from Quzhou People's Hospital, Quzhou, China. All images are in the file format of bmp, which are 384 * 384 pixels in size. In this data set, the ground truths of lesions are constructed by an expert radiologist that listed in the last column of Fig. 8. Similarly, the JS values are used to quantify the outputs of the proposed method and other state-of-art segmentation methods, as shown in Fig. 9. As can    there are a lot of interference in the segmentation results. Nevertheless, LRAC and our method can accurately capture the lesion region, which are close to the ground truth. However, from Fig. 9, we can find that our method is slightly superior to the LRAC model in terms of JS values, and has a great advantage in computing efficiency.

C. NATURAL IMAGES SEGMENTATION
To demonstrate the effectiveness of our method for segmenting complicated nature images, a comparative experiment is tested on seven real images from the MSRA's database and the Berkeley database, and the segmentation results are shown in Fig. 10. It can be seen only the proposed model can exactly extract the objects in every images. The ACM_LPF model is still exists unexpected results to some extent with false detection and gains the worst segmentation effect. Based on the segmentation accuracy, we will employ the JS index to evaluate the performance of each model. From the Fig. 11, it shows that our model is the most stable than these traditional active contour models.

V. CONCLUSION
In this study, we proposed a novel shape prior constrained based approach to for image segmentation. Using the improved C-V model as the data fitting term, the proposed model can guide the curve evolving to desired target boundary quickly. In addition, we introduced the prior shape information to our proposed energy functional. Therefore, the proposed model can well handle images in the presence of complex target. Experimental results on real and natural images demonstrated that our approach achieves satisfactory results and has more robust against the complex background when compared with other seven representative methods.