Level set formulation for automatic medical image segmentation based on fuzzy clustering
Introduction
Image segmentation is a fundamental and forward-looking research in the field of medical image processing in recent years. It can detect the location of target tissues and divide boundaries, which makes it possible to connect modern medical imaging equipment such as ultrasound or positron emission tomography with accurate and fast lesion detection. In conventional medical image diagnose, doctors find object lesions and margins manually, which is very time consuming. Therefore, automatical analysis of medical images with the computer is very helpful for doctors to diagnose diseases.
The level set method was originally proposed by Osher and Sethian [1]. This method can track moving boundaries easily and overcome the interference of topological deformation. However, the higher requirement for initialization is its biggest disadvantage. In recent years, several level set algorithms have been proposed for image segmentation based on image intensity and most of the research work is deliberated along with edge-based active contour models [2], [3], [4], [5] and region-based models [6], [7], [8], [9]. The gradient vector flow is a classic concept in edge-based active contour models, in which a decoupled linear partial differential equation is solved by the gradient vector of the diffused edge image, thereby minimizing an energy functional [10]. The Chan–Vese (CV) model is the first improvement of the region-based model [11], in which boundaries are not necessarily defined by gradient and the level set formulation is utilized to control the curve evolution. The biggest drawback of this model is that it is hard to deal with image intensity inhomogeneity which is a common phenomenon in medical image processing. In the active contour model, the key is to minimize an energy function subject to certain constraints. Li et al. proposed the region-scalable fitting (RSF) model [12], where the image intensity is regarded as two fitting functions that locally approximate the image intensities on the two sides of the contour. However, there are certain shortcomings such as high computation cost, noise sensitivity and parameter sensitivity. Sometimes, totally different results are obtained on the same images due to the improper initialization of contours or different choices of parameters. Fuzzy c-means (FCM) is one of the most powerful algorithms in fuzzy clustering and has been widely used in medical images processing fields. Fuzzy segmentation of magnetic resonance images was proposed early in the 1990s [13], [14], [15]. However, for conventional fuzzy clustering methods, they neglect the neighboring information compared with general boundary detection techniques which limits their application a lot. Therefore, Chuang et al. [16] present a FCM algorithm that incorporates spatial information into the membership function for clustering which has been proved satisfactory.
There have been many integrated approaches with fuzzy clustering to facilitate level set segmentation proposed in recent years. Li et al. proposed a new algorithm integrating fuzzy clustering with level set methods, in which the initialization of the level set function is directly evolved from the fuzzy clustering [17]. And the parameters of level set evolution are also estimated from the result of fuzzy clustering, which reduced a lot of manual operations. Xuan et al. described a new clustering method called kernelized fuzzy entropy clustering with local spatial information and bias correction, which achieves satisfactory performance on brain MR images [18].
Considering the prior knowledge such as ground truth and plenty of datasets nowadays, models based on deep learning have been widely used [19], [20], [21], which can solve many challenging segmentation problems. Ronneberger et al. [22]proposed the U-Net model, which is a useful network to carry on the biomedical image segmentation. Liu et al. [23] proposed a method called GIU-Net, which combines an improved U-Net neural network model with graph cutting to improve the liver CT sequence image segmentation algorithm. The split Bregman method is a technique to minimize energy functional, which can greatly improve computation efficiency. Goldstein and Osher proposed the split Bregman method for L1-regularized problems and applied it to a compressed sensing problem that arises in magnetic resonance imaging [24]. Yang et al. utilized the split Bregman method for minimization of the region-scalable fitting energy [25], [26] and also used this method to accelerate the minimization process of the level set evolution (LSE) model [27], which has proved the great improvement on computation efficiency.
In this paper, a novel algorithm is proposed which integrates fuzzy clustering with level set method through a dynamic constrained term in our new energy functional. The proposed method is improved a lot mainly in the following aspects. Firstly, the results given by FCM are automatic, which eliminates the manual operations. Secondly, the results of FCM are only regarded as the first constrained information to the level set function. During the curve evolution, the constrained term will update continuously until the stop condition we set to replace the previous result, which is helpful to better regularize the level set evolution. Thirdly, the proposed algorithm is robust to the noise and parameters. Finally, we verified the proposed algorithm on medical images such as magnetic resonance imaging (MRI), computed tomography (CT) and other images in Joint Photographic Expert Group (JPEG) format.
The remainder of this paper is organized as follows. In Section 2, we introduce the theoretical background such as the RSF model and fuzzy clustering segmentation. Section 3 presents the proposed new method and its corresponding minimization algorithm. The experimental results and discussion are in Section 4. Finally, Section 5 concludes the paper.
Section snippets
The region-scalable fitting (RSF) model
Consider a given image . In particular, for gray level images and for color images. The energy formulation of the RSF model can be written as: Let be a closed contour in the image domain that separates into two regions: and , which represent the outside and inside the contour respectively. In the energy function (1), where , , and are positive parameters, is a
The novel energy formulation
This section elaborates our proposed method in this study. Both the FCM algorithm and the RSF model have many advantages and some disadvantages. If we concentrate on medical image problems, it is possible to integrate the two methods for a better performance. The proposed method begins with spatial fuzzy clustering, whose result is used to be the first constraint in the dynamic constrained term. The novel dynamic constrained term plays a significant role during the curve evolution, which
Experimental results and quantitative evaluation
In this section, the performance of the proposed algorithm is evaluated through some medical images and the corresponding performance measures. The images used in this study are from https://competitions.codalab.org and https://warwick.ac.uk/fac/sci/dcs/research/tia/glascontest, whose sizes were converted into 256*256 in experiments. In this part, we also show the comparisons with other models in Fig. 6, Fig. 7. The quantitative evaluation of our experiments is shown in Tables 1, 2 and Fig. 5.
Conclusion
In this paper, a novel algorithm is proposed which integrates fuzzy c-means clustering with the level set method through an additional dynamic constrained term in our energy functional. Firstly, we introduce an additional term to connect fuzzy clustering and level set method, then we give the new energy formulation and its minimization process using the split Bregman method. Experimental results show that our model can segment medical images successfully and also show a good performance on
CRediT authorship contribution statement
Yunyun Yang: Conceptualization, Methodology. Ruofan Wang: Writing - original draft, Writing - review & editing. Chong Feng: Software, Data curation.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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