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1. 同济大学 计算机科学与技术系，上海 201804;
2. 同济大学 嵌入式系统与服务计算教育部重点实验室，上海 201804

Image segmentation algorithm based on the decision-theoretic rough set model
LI Feng1,2, MIAO Duoqian1,2, LIU Caihui1,2, YANG Wei1,2
1. Department of Computer Science and Technology, Tongji University, Shanghai 201804, China ;
2. Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University, Shanghai 201804, China
Abstract: Image segmentation is one of the important topics in image processing and analysis. The recent studies focus mainly on handling the ideal images without noise, which often go against the reality. What’s more, the grey value of the boundaries between objects in the image is often fuzzy. For images with noise, within the framework of granular computing and decision-theoretic rough sets, a novel algorithm for image segmentation is proposed. The algorithm deals with image segmentation by simulating the target and background regions with the decision-theoretic rough set model, and tolerates some noise points when calculating the approximate sets. It determines the threshold of partitioning through minimization of roughness in both object and background regions. The experimental results show that the proposed method can solve the problem of noise and improve the effects of image segmentation.
Key words: decision-theoretic rough sets     image segmentation     image noise     granule computing

Sezgin等[1]总结了2003年以前的40种经典的阈值分割方法，这些方法按照分割时考虑的图像信息分为6类：直方图形状、测试空间聚集度、熵、目标属性、空间相关性和局部灰度图。Sankar等[2]将粒计算和粗糙集思想运用于阈值分割，提出了一种基于粒计算和粗糙熵的目标提取方法。该方法主要解决灰度图像中物体之间的边界灰度值常常模糊的问题，图像信息具有较强的空间复杂性、相关性，处理过程中会遇到不完整和不确定性问题。Sankar等[3]还做了进一步的工作，将这种处理方式运用于运动目标检测。Sankar的方法是单阈值的分割，只是把图像分割成背景和感兴趣的目标区域，但有时感兴趣的目标是多个，所以为了能分割出多目标区域，Dariusz等[4]提出了自适应多阈值粗糙熵优化算法，这样可以比较灵活地处理一些特殊需求。这2种方法都是在灰度图像上进行处理，只是一维的，Dariusz等[5]又把处理的维度提升到两维。Dariusz等[6-7]针对粗糙集与图像分割的结合，还做了其他一系列工作。

1 基础知识

 (1)

1.1 Pawlak粗糙集

 图 1 集合X的上近似、下近似示意图 Fig. 1 The upper and lower approximations of set X

1.2 决策粗糙集

 (2)

2 基于决策粗糙集的图像分割 2.1 图像的粗糙集描述

 (3)

 (4)

 (5)

2.2 阈值最优选择算法

1)for i=1 to total_num

\*对所有的图像粒Gi进行如下操作*\

for j=1 to mn

\*计算该粒中大于阈值T的像素点个数Ni*\

if the gray of j > T

Ni=Ni+1

end

end

if Ni/mnα

\*粒中大于阈值T的点个数比率大于或等于α，则确定粒Gi属于目标区域，否则可能属于背景区域*\

OT=OTGi

else

BT=BTGi

end

if Ni/mn≤1－α

\*粒中大于阈值T的点个数比率小于或等于1－α，则确定粒Gi属于背景区域，否则可能属于目标区域*\

BT=BTGi

else

OT=OTOT

end

end

2)for L=min_gray to max_gray

\*对所有图像灰度级进行如下操作*\

end

3)当粗糙熵值取得最大时图像分割阈值取得最优值，即：

3 实验分析

3.1 粒尺寸的大小选择

3.2 实验结果

 图 2 灰度直方图 Fig. 2 Histogram of the image

 图 3 实验结果 Fig. 3 Experimental results
3.3 结果分析

4 结束语

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DOI: 10.3969/j.issn.1673-4785.201307022

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#### 文章信息

LI Feng, MIAO Duoqian, LIU Caihui, YANG Wei

Image segmentation algorithm based on the decision-theoretic rough set model

CAAI Transactions on Intelligent Systems, 2014, 9(2): 143-147
http://dx.doi.org/10.3969/j.issn.1673-4785.201307022