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1. 鲁东大学 信息与电气工程学院, 山东 烟台 264025;
2. 哈尔滨工程大学 自动化学院，黑龙江 哈尔滨 150001

Medical image segmentation based on FCM with peak detection
TANG Wenjing1, XU Zhaoxin2, ZHANG Xiaofeng1
1. College of Information and Electrical Engineering, Ludong University, Yantai 264025, China ;
2. College of Automation, Harbin Engineering University, Harbin 150001, China
Abstract: In order to balance the segmentation results and efficiency of traditional FCM and related improved algorithms, a fast FCM segmentation scheme based on peak detection is proposed in this paper. First the cluster centroids are initialized based on peak detection strategy, and then the medical image segmentation is performed based on the initial cluster centroids. The nature of the proposed scheme is to guide the initialization of cluster centroids with peak detection, which can make the initial centroids close to the final centroids and further improve the efficiency of the algorithm. Experiments on the medical images showed that the proposed scheme can improve the segmentation efficiency greatly and obtain good segmentation results.
Key words: FCM     FCMs     EnFCM     image segmentation     medical image processing     peak detection     clustering centers     histogram

1 峰值检测的FCM算法 1.1 经典的FCM算法

 (1)

 (2)

 (3)

 (4)
1.2 峰值检测的快速FCM算法

 图 1 几种算法对某医学图像的分割结果 Fig. 1 A medical image segmentation results of several algorithms

 图 2 图 1(a)的直方图 Fig. 2 Histogram of Fig.1(a)

1)计算给定图像的直方图H

2)计算直方图H上所有峰值的集合P，即

3)如果|P|≤C，转6)，否则转4)；

4)根据像素灰度值与峰值的距离，计算每个峰值i关联的像素数目，即

 (5)

5)删除关联像素数目最少的峰值，并将与其关联的像素与相邻的两个峰值重新关联，转3)；

6)根据获取的峰值初始化聚类中心；

7)根据式(4)初始化像素的隶属度uij

8)根据式(1)计算目标函数的值F

9)根据式(2)计算聚类中心；

10)根据式(4)更新像素的隶属度；

11)根据式(1)计算目标函数的值F′

12)如果FF′＜threshold，算法结束；否则，令F=F′，转9)。

1.3 聚类中心的初始化

1)基于获取的C个峰值将直方图分割为C个区间，具体如下：

(1)第一个区间下界l1=0，上界

(2)最后一个区间上界hC=255，下界

(3)其他区间下界，上界

2)在所获取的C个区间上，初始化算法的聚类中心，如式(6)：

 (6)
1.4 与其他算法的比较

2 实验分析

 图 3 实验选取的医学图像 Fig. 3 Experimental images
2.1 视觉效果比较

 图 4 不同算法的分割结果 Fig. 4 The results of different image segmentation algorithms
2.2 分割质量比较

1)第1个量化评价标准称为Bezdek划分系数[15]，其定义如下：

 (7)

VPC的定义来看，一个好的聚类应使图像中像素属于某一类的隶属度尽可能大，而属于其他类的隶属度尽可能小。因此，一个好的聚类的VPC值应尽可能大。

2)本文选用的第2个量化标准是VXB，具体定义如下[16]

 (8)

VXB的描述可以看出，VXB的值反映的是聚类内部的一种距离度量。由于在图像分割时希望聚类内部更紧致一些，因此，对一个好的聚类而言，其VXB值应稍小一些。

3)Liu在进行多分辨率彩色图像分割时，提出了一种Liu系数，用以描述分割后图像与原图像的差别[17]，本文对其中的距离进行了修正，使其可以运用在灰度图像的分割效果评价上，定义如下：

 (9)

4)重构错误率(reconstruct error)是由Pedrycz提出的，指的是利用分割后的图像对原图像进行重构后，与原图像之间的差别[18-20]，具体定义如下：

 (10)

 (11)

 标准 算法 breast head1 tumor head2 VPC FCM 0.908256 0.937925 0.920705 0.943104 FCMs 0.890121 0.910757 0.891943 0.923302 EnFCM 0.780815 0.880399 0.856142 0.875697 IntFCM 0.887940 0.937925 0.920705 0.943104 VXB FCM 1.708753 1.528459 3.980954 1.269151 FCMs 1.721053 1.529560 1.575088 6.249228 EnFCM 1.705063 3.370459 1.704269 1.702875 IntFCM 2.086202 1.528461 1.574369 1.269151 F(I) FCM 0.375072 1.785398 1.611865 1.164947 FCMs 0.383582 2.034325 1.77718 1.298093 EnFCM 3.054808 4.162635 4.45105 4.353452 IntFCM 0.373781 1.785398 1.611865 1.164947 VRE FCM 39.986882 96.725345 106.032120 61.193914 FCMs 40.237596 105.220373 114.231665 67.188700 EnFCM 288.00562 630.001101 542.438503 686.889253 IntFCM 37.937884 96.725322 106.032094 61.193855

2.3 运行时间比较

 算法 breast head1 tumor head2 FCM 197.921 875 163.937 5 212.390 625 177.875 000 FCMs 427.046 875 365.687 5 561.609 375 304.640 625 EnFCM 0.453 125 0.453 125 0.484 375 0.453 125 IntFCM 102.687 5 114.718 75 119.578 125 151.312 500

3 结束语

FCM算法用于医学图像分割时存在低效率问题，其相关改进算法在效率与分割效果方面又很难取得平衡，针对这个问题，本文提出了基于峰值检测的FCM算法，其本质是在FCM算法进行初始化时使初始化的聚类中心逼近最终的聚类中心，以提高算法的效率。在医学图像上的实验表明，本文算法在视觉效果、图像分割质量方面，要优于FCM及其相关改进算法；相比于FCM和FCMs算法，其运行效率有所提高，但与EnFCM算法仍有较大的差距。在接下来的工作里，将继续研究如何保证分割效果的前提下进一步提高算法的运行效率，使其与EnFCM在运行效率上可以相媲美。

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DOI: 10.3969/j.issn.1673-4785.201408007

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#### 文章信息

TANG Wenjing, XU Zhaoxin, ZHANG Xiaofeng

Medical image segmentation based on FCM with peak detection

CAAI Transactions on Intelligent Systems, 2014, 9(5): 584-589
http://dx.doi.org/10.3969/j.issn.1673-4785.201408007