外文翻译---一种新的模糊边缘检测算法

A new fuzzy edge detection algorithm
Sun Wei Xia Lianzheng
( Department of Automatic Control Engineering,SoutheastUniversity,Nanjing,210096,China) Abstract：Based upon the maximum entropy theorem of information theory, a novel fuzzy approach for edge detection is presented .Firstly, a definition of fuzzy partition entropy is proposed after introducing the concept of fuzzy probability and fuzzy partition, The relation of the probability partition and the fuzzy c-partition of the image gradient are used in the algorithm。

Secondly, based on the conditional probabilities and the fury partition, the optimal thresholdingis searchedadaptively through the maximum fuzzy entropy principle, and then the edge image is obtained。

Lastly, an edge-enhancing procedure is executed on the edge image .The experimental results show that the proposed approach performs well。

Key words:edge detection ;fuzzy entropy ;image segmentation ;fuzzy partition Image segmentation is an important topic for image analysis, computer vision and patternrecognition .Until now, many classical edge detection algorithms have been put forward .In recent years, fuzzy set theory has been successfully applied to many areas, such as automation control, image processing, pattern recognition and computer vision, etc .It is generally believed that image processing bears some fuzziness innature due to the following factors: ①Information loss while mapping 3-D objects into 2-D images; ②Ambiguity and vagueness in some definitions (such asedges, boundaries, regions, and textures, etc.)；③Ambiguity and vagueness in interpreting low-level image processing results .Therefore, fuzzy techniqueshave frequently been used in image segmentation.
Jin Lizuo .et a1. proposed a new definition of fuzzy partition entropy using the conditional probability and conditional entropy, and designed a new thresholding selection algorithm based on the maximum fuzzy entropy .This paper extends the application of the work to the problem of the edge detection and presents a new fuzzy edge detection algorithm .In the algorithm, a gradient image is considered as being composed of an edge region and a smooth region .Based on the conditional probability and the fuzzy partition entropy, the optimal thresholding is searched adaptively through maximum fuzzy entropy principle .There are two major differences between the problems of the edge detection and the image thresholding segmentation .First, theproblem is actually reduced to a two-level thresholding problem, where the purpose of thresholding is to
partition the image into two regions :an edge region anda smooth region .Second ，in order to find the best compact representation of the image edges and contours, the gradient image is processed.The experimental results show the effectiveness of the algorithm.
The rest of this paper is organized as follows .In section 1,we briefly outline the concept of fuzzy probability and fuzzy partition entropy .In section 2,we describe the fuzzy edge detection algorithm, In section 3,the experimental results and conclusions are presented.
2.4 Edge detection
Let the edge image be (,)e x y ,then calculate it as
200(,)(,)0(,)if g x y T e x y f g x y T ≥⎧=⎨<⎩ (1)
Spurious or weak edges(intensity discontinuities)may result in the image edge representation due tomany factorsamong them are noise and breaks in theboundary between two regions due to non —uniform illumination .In this section, e introduce a simple yeteffective procedure for removing spurious or weakedges .The procedure is as follows:
1)Run a 3×3 pixel window on the edge image .where the center of the window imposed on each location (x, y);
2)Sum the number of points which have beenclassified as edge in the window, if the number isgreater than four, leave these edge points, else theyrepresent weak or spurious edges.
3) Experimental Results and conclusions
In this section, the experiments on various kinds of images have been carried out with proposed method .The three original images areselected andshown in Figs.2—4.Fig.2 is an airplane image .The size of which is 212×200 pixe1.The membershipfunction parameters set(a,b)= (5,157)and theimage thresholding is 81.Fig.3 is a baboon image, thesize of which is 202×200 pixe1.The membershipfunctions parameter set(a, b) = (6,164)and theimage thresholding is
85.Fig.4 is a Lena image, thesize of which is 212×208 pixe1.The membershipfunction parameters set(a, b)= (3,147)and theimage thresholding is 75.
In this paper, we combine conditional probabilitywith fuzzy maximum entropy to introduce a new fuzzyedge detection algorithm. The experimental resu1tsshow that this algorithm performs well. It is verified that segmentationmethods, which combine fuzzystatistics. are suitable fortheoryfurther research.
作者：孙伟夏良正
国籍：中国
出处：东南大学学报(英文版).第二期.卷20.2003.
一种新的模糊边缘检测算法
孙伟夏良正
(东南大学自动控制系，南京210096)
摘要:基于信息论中最大熵原理，提出了一种新的模糊边缘检测算法。

首先介绍了模糊概率、用条件概率与条件熵定义模糊划分熵的概念以及模糊划分的原理。

算法利用了自然划分以及梯度图像模糊划分的关系，在条件概率与模糊划分熵的基础上，通过最大模糊熵原则实现图像分割中最优阈值的自动提取，从而实现图像的边缘检测。

对不同测试图像的边缘检测结果进行比较，表明了该算法的有效性。

关键词：边缘检测；模糊熵；图像分割；模糊划分
图像分割是图像分析、计算机视觉和模式识别的一个重要课题，直至现在,许多经典的边缘检测算法已提出。

在最近的几年，模糊理论已经在很多领域运用，如自动化控制,图象处理,模式识别和计算机视觉等。

人们普遍认为在自然条件下图像处理负有一定的模糊性是由于下列因素：①信息的丢失当3-D的物体转换为2-D图像；②在定义上(例如边缘,边界地区,纹理,等等)的二异性；③低级别图像处理后解释的二异性因此，模糊技术经常在图像分割上使用。

利用条件概率与条件熵，Jin Lizuo等人提出了一个新的定义模糊划分熵，并设计了一个新的阈值选择算法基于最大模糊熵。

本文把该方法延伸运用到边缘检测方法，并提出了一个新的模糊边缘检测算法。

在算法中,梯度图像被视为是由一个边缘地区的和平稳的地区组成的，基于条件概率及模糊划分熵。

最优阈值搜寻是模糊最大熵原则实现的。

这有两个主要的区别问题的边缘检测和图像分割。

首先，这一问题实际上是减少了两个级别的阈值问题,目的是通过阈值把图像分割成两个区域:一个边缘地区和平稳地区。

第二,通过梯度图像处理，可以找到最好的紧凑的有代表性的图像边缘和轮廓。

实验结果表明该算法的有效性。

文章的其余部分组织如下：第一部分，我们简述概念模糊概率及模糊划分。

第二部分,我们描述的模糊边缘检测算法。

在第三部分中，实验结果和结论等。

2.4 边缘检测
另边缘图像为e (x , y )，然后计算如下：
200(,)(,)0(,)if g x y T e x y f g x y T ≥⎧=⎨<⎩ (1)
由于其他很多的原因，边沿会变成假的或效果不好的（强度不连续）；其中有噪音和两部分边界断裂是,因非均匀照明。

在这部分中,我们引进了一种简单而有效的程序,清除假的或效果不好的边沿。

程序如下:
1)在边缘图像上，运行一个3×3像素的窗口,窗口的中心在点(x , y )上;
2) 把在窗口中，已经通过边缘分类的点全部加起来，假如这个数字大于4，离开这个边缘点，否则他们代表假的或效果不好的边缘点。

3)实验结果与结论
在这一部分中，所有的实验都是在前面提出的方法上处理。

三幅原始图像和处理过的图像如图2~4所示。

2是一幅飞机的图像，大小为212×200个像素点，成员函数的参数设定(a, b)=(5,157)和图像阈值是81。

3是狒狒的图像，大小为202×200个像素点，成员函数的参数设定(a, b)=(6,164)和图像阈值是85。

4是Lena 的图像，大小为212×208个像素点，成员函数的参数设定(a, b)=(3,147)和图像阈值是75。

在这篇文章中,我们把有条件的概率与模糊最大熵引入到一种新的模糊边缘检测算法.实验结果表明,这种算法不错. 它证实了分割的方法,并和模糊统计结合起来，适合的进一步研究。