Anti-noise FCM image segmentation method based on quadratic polynomial

doi:10.1016/j.sigpro.2020.107767

Signal Processing

Volume 178, January 2021, 107767

https://doi.org/10.1016/j.sigpro.2020.107767 Get rights and content

Abstract

Image segmentation is an important and challenging task in computer vision and image understanding, in which the segmentation model is the key to improve the quality of image segmentation. In this paper, a new fuzzy c-means clustering(FCM) algorithm based on quadratic polynomials is proposed, which can better distinguish the weak edge region in the image and has certain noise resistance. Firstly, the algorithm proposes to define the segmentation center using a quadratic polynomial surface,and divide the set of data points according to the algebraic distance between data points and the segmentation surfaces. The existing model with constant as the segmentation center is a special case with quadratic polynomial surface as the segmentation center, so the new model has higher segmentation accuracy. Secondly, based on the quadratic polynomial surface as the segmentation center, a new fuzzy factor is designed, and the deviation value is used to represent the difference between the mean algebraic distance of neighborhood points and the algebraic distance of center pixel. By calculating the deviation value, the influence of neighborhood points on the center point can be better measured and the segmentation accuracy can be improved. Experimental results show that the new algorithm has better anti-noise ability as well. Thirdly, select a local window on the edge of the global segmentation result for local window segmentation, which is equivalent to using a clustering center that is more in line with local information to do segmentation in a local small window, optimize misclassified pixels, and obtain the final segmentation result. The experimental results show that in the final segmentation results of medical images with 5% noise, segmentation accuracy can reach above 96%, partition coefficient V_pc has been increased by 0.14. So the algorithm can get the membership matrix with less ambiguity, which means more reliable segmentation results, and can effectively eliminate noise effects, retain the image details.

Introduction

Image is an important tool for humans to know and perceive the world. Image segmentation is a good processing method [1] for computers to interact with humans. Image segmentation is a very important link in the process of computer vision and image understanding, which has been widely used in medical image processing, pattern recognition, video detection, industrial automation and other fields [2]. Image segmentation refers to the segmentation of an image into non-intersecting sub-regions according to a certain standard. These regions are not identical to each other and do not intersect with each other, while elements within the same region have the same or similar characteristics, which refers to the partition standard [3]. Accurate image segmentation results will bring a more reliable basis for subsequent image processing. However, the image is complex and diverse, so there is no perfect image segmentation algorithm that can solve all the image segmentation problems. For irregular images, such as those affected by noise, intensity, or uneven brightness [4], how to accurately segment and determine objects has always been one of the difficult and hot issues in image segmentation. The gray value of a pixel in an image will be affected by different objects in the image. Therefore, traditional segmentation algorithms are not suitable for the segmentation of complex images. They fix pixels in a certain category. For example, the k-means algorithm [5] is a typical hard classification and clustering algorithm. It is considered that pixels belong to only one cluster in the process of classification, and it is an either/or relationship, which will lead to the loss of a lot of information in the classification process. Therefore, the fuzzy clustering algorithm is more widely used. In the fuzzy clustering algorithm, pixels no longer belong to a certain category in the division process, but an index is adopted to measure what extent they belong to which category. There is no either/or relationship between pixels and classes, but an either-or relationship, and this index is membership degree. After updating the membership degree and clustering center, the principle of maximum membership degree is generally adopted to divide pixels into the classes to which they belong to the greatest extent and complete the segmentation. The fuzzy c-mean algorithm (FCM) is a typical fuzzy segmentation method [6]. FCM algorithm is simple, efficient, easy to recognize and implement, and other advantages [7], [8], [9]. The traditional FCM algorithm performs well in noiseless images, but when there is noise or artifact in the image, the effect is not very significant [10]. Therefore, many papers have proposed various improved algorithms of FCM to fully consider neighborhood information to obtain a better segmentation effect [11], [12], [13], [14]. For example, Ahmed et al. [15] proposed FCM_S algorithm. By correcting the objective function of the FCM algorithm, spatial neighborhood information was introduced to make up for the unbalanced gray distribution and adjacent elements were brought into the calculation, which improved the noise resistance of the algorithm. However,FCM_S algorithm needs to calculate the neighborhood information every time during its operation, so its efficiency is low [16]. Tasdizen [17] proposed FCM_S1 and FCM_S2 algorithms, which can improve the running speed of FCM_S algorithm. When running these two algorithms, the image will be filtered first, with mean filtering and median filtering respectively, and then the iterative process of the algorithm will be carried out. Bezdek [18] proposed a fast FCM algorithm based on the fact that the number of pixels in the image is much larger than the number of image gray level, and recalculated the image to improve the segmentation speed. Cai et al. [19] proposed a fast general FCM clustering algorithm, which combines spatial distance and gray difference for calculation, and has certain noise resistance. Krinidis and Chatzis [20] proposed a FLICM algorithm combining local information, redefining the fuzzy factor with gray level information and local information, and adjusting parameters adaptively. Machine learning algorithms have become very popular in recent years. Therefore, many researchers have proposed image segmentation methods using machine learning, Jie Wei et al. proposes M³Net segmentation algorithm. However, through analysis, it can be found that the frameworks of segmentation algorithms using machine learning are relatively complex and difficult to understand. And they also need to rely on a large number of training resources and long training time, which means higher requirements for space and running speed of the computer. Besides, Ning et al. [21] proposed a novel segmentation method based on generative adversarial networks. Although such method has achieved satisfactory segmentation performance, it usually relies on strong computational ability.

A little gray value is usually used as the cluster center in FCM and its improved algorithms. But in general, the gray level of pixels in an image is much larger than the number of cluster centers. Using a simple point as the cluster center and only using the pixel gray value to measure a pixel in the image will result in that pixels in the same class are very different from each other, and the segmentation results will be biased. When the segmented data points are taken from different curved patches, this deviation will become more obvious, and the ideal result is often not obtained with the constant as the center of segmentation. So the proposed method uses a clustering surface instead of the previous cluster center, introducing a quadratic polynomial, and fitting the image to eventually make more pixels fall on the surface.

In the improved algorithm, use a quadratic polynomial to replace the previous point clustering center, establish a new division standard, divide the set of data points by the algebraic distance between the data point and the division center, reduce the pixel difference in the same class and correct the classification of image pixels. Experiments show that the improved algorithm is particularly effective for pixel classification in weak edge regions. Substituting a quadratic polynomial surface for the cluster center point can take into account both the position information of the image and the gray value information, so that more data points fall on the surface, thereby achieving better segmentation results.

Based on the previous research work, aiming at the existing problems of FCM segmentation algorithm, this paper proposes a new FCM segmentation algorithm, which has the following three contributions:

1)
A new image segmentation model is defined, and a segmentation center defined by the quadratic polynomial surface is proposed to divide the set of data points according to the algebraic distance between data points and the segmentation center. The existing model with constant as the segmentation center is a special case of the model with the quadratic polynomial surface as the segmentation center. Therefore, the new model has a higher segmentation accuracy.
2)
A new fuzzy factor is designed based on the quadratic polynomial surface as the segmentation center. The deviation value is used to represent the difference between the mean algebraic distance of the neighborhood points and the algebraic distance of the central pixel. The influence of neighborhood points on the center point can be better measured by calculating the deviation value, and the segmentation accuracy can be improved.
3)
Add local post-segmentation processing based on global segmentation. In the process of global segmentation, the gray level of pixels is much higher than the number of clusters, which will lead to the pixel at the edge is not correctly classified. However, re-selecting the window at the edge for segmentation is equivalent to using the clustering center which is more in line with local information in the local small window for segmentation. Therefore, local Windows can correct the misclassified pixels and improve segmentation accuracy.

The improved algorithm in this paper is suitable for image processing of small samples. Compared with the algorithms using neural network, it can be found that the algorithm in this paper does not require sample learning, runs fast, and is higher in time efficiency than the neural network algorithm, and can guarantee a certain accuracy as well.

The improved algorithm can achieve more accurate segmentation results. It can be seen from Fig. 1 that the segmentation result obtained by the improved algorithm is much more closer to the groundtruth. This shows that the improved algorithm can make better use of the location information and spatial information of pixels and obtain more accurate fitting results.

The algorithm flow chart is showed in Fig. 2.

Section snippets

Related work

Generally, the FCM algorithm achieves the minimum objective function by iteratively updating the membership degree of each pixel relative to each class and each clustering center, so that the pixel similarity divided into the same cluster can be as high as possible, and the pixel similarity between different clusters can be as small as possible to realize image segmentation.

The objective function of traditional FCM is defined as: $E = \sum_{i = 1}^{N} \sum_{k = 1}^{C} μ_{k i}^{m} {∥ x_{i} - v_{k} ∥}^{2}$

In this formulation, C is for the number

New segmentation model

In FCM and its improved algorithm, the gray value of a point is used as the clustering center. However, generally speaking, the pixel gray level in an image is much more than the number of clustering centers. If a constant is used as the clustering center and only the pixel gray value is used to measure a pixel in the image, the pixel in the same class will be very different, so the segmentation results will be biased. In particular, when the segmented data points are taken from different

Experiments

In order to verify the effectiveness of the proposed algorithm, compare the algorithm in this paper with nine algorithms: FCM_S [15], EnFCM [18], FGFCM [19], FLICM [20], GLFCM [26], KWFLICM [27], NLFCM [28], FRFCM [29], DSFCM [30]. These ten algorithms are used to process composite images, natural images and medical images, and then compared the segmentation results. It includes visual effect comparison, noise resistance analysis, edge analysis of segmentation results and quantitative

Conclusion

This paper designs and proposes a new segmentation model. The new model uses the quadratic polynomial surface to define the new segmentation center, combines the fuzzy factor with the local segmentation, and can distinguish the weak edge region of the image well, and has certain noise resistance, which greatly improves the accuracy of the algorithm. Firstly, quadratic polynomial is introduced to establish a new segmentation model. The algebraic distance between the data points and the

CRediT authorship contribution statement

Xijing Zhang: Writing - original draft, Writing - review & editing, Software, Visualization, Data curation. Yang Ning: Conceptualization, Writing - review & editing, Methodology. Xuemei Li: Supervision. Caiming Zhang: Supervision, Funding acquisition.

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.

Acknowledge

The work was supported partly by the NSFC Joint Fund with Zhejiang Integration of Informatization and Industrialization under Key Project under Grant No. U1609218; the Natural Science Foundation of Shandong Province under Grant Nos. ZR2017MF033ZR2018BF009; the NSFC under Grant Nos. 61772312, 61873117. We would like to thank the support of the fund and the authors who share their source codes, and also like to thank every teachers and the anonymous reviewers for their helpful suggestions to

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Anti-noise FCM image segmentation method based on quadratic polynomial☆

Abstract

Introduction

Section snippets

Related work

New segmentation model

Experiments

Conclusion

CRediT authorship contribution statement

Declaration of Competing Interest

Acknowledge

IEEE Trans. Image Process.

Appl. Math A J. Chin.Univ.

A convergence theorem for the fuzzy ISODATA clustering algorithm

IEEE Trans. Pattern Anal. Mach.Intell.

Research on a pulmonary nodule segmentation method combining fast self-adaptive FCM and classification

Comput. Math. Methods. Med.

Image segmentation algorithm research and improvement[c]

2010 3rd International Conference on Advanced Computer Theory and Engineering (ICACTE)

Random walks for image segmentation

IEEE Trans. Pattern Anal. Mach.Intell.

Improved Canopy-Kmeans algorithm based on mapreduce

Comput. Eng. Appl.

Pattern recognition with fuzzy objective function algorithms

Adv. Appl. Pattern Recognit.

Topography image segmentation based on improved Chan-Vese model

Comput. Aided Drafting Des. Manuf.

Segmentation of MRI brain images by incorporating intensity inhomogeneity and spatial information using probabilistic fuzzy c-means clustering algorithm

2012 International Conference on Communications, Devices and Intelligent Systems (CODIS)

Brain MRI segmentation and bias correction model based on improved FCM with non-local information

J. Comput. Aided Des. Comput.Graph.

Object class recognition by unsupervised scale-invariant learning

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