数字图像检测毕业论文中英文资料对照外文翻译文献综述
中英文资料对照外文翻译文献综述
Edge detection in noisy images by neuro-fuzzy
processing
通过神经模糊处理的噪声图像边缘检测
Abstract
A novel neuro-fuzzy (NF) operator for edge detection in digital images corrupted by impulse noise is presented. The proposed operator is constructed by combining a desired number of NF subdetectors with a postprocessor. Each NF subdetector in the structure evaluates a different pixel neighborhood relation. Hence, the number of NF subdetectors in the structure may be varied to obtain the desired edge detection performance. Internal parameters of the NF subdetectors are adaptively optimized by training by using simple artificial training images. The performance of the proposed edge detector is evaluated on different test images and compared with popular edge detectors from the literature. Simulation results indicate that the proposed NF operator outperforms competing edge detectors and offers superior performance in edge detection in digital images corrupted by impulse noise.
Keywords: Neuro-fuzzy systems; Image processing; Edge detection
摘要
针对被脉冲信号干扰的数字图像进行边缘检测，提出了一种新型的NF边缘检测器，它是由一定数量的NF子探测器与一个后处理器组成。每个子探测器针对一个不同的像素区域进行处理。因此，改变子探测器的数目，可以使边缘检测器具有想要的性能。通过对简单的人工改造的图像进行测试，可以优化每个子探测器的内置参数。通过对
不同的图像进行测试，我们检验了该检测器的性能。而且我们还把它与文献中经常出现的边缘检测器进行比较，仿真结果表明该检测器远优于其它检测器，对被脉冲干扰的数字图像表现出优越的性能。
关键词：神经模糊系统，图像处理，边缘检测。
1. Introduction
Edges in a digital image provide important information about the objects contained within the image since they constitute the boundaries between the objects in the image. Edge detection is a frequently performed operation in many image processing applications because it is usually the first operation that is performed before other image processing tasks such as image segmentation, boundary detection, object recognition and classification, image registration, and so on. Consequently, the success of these subsequent image processing tasks are strictly dependent on the performance of the edge detection operation.
The image intensity shows sudden changes at edges. Therefore, edge detection usually involves the calculation of the derivative of the image intensity function at a given pixel location. If the magnitude of the derivative of the image intensity function is relatively high at a given pixel.
location, then the pixel at that image location is classified as an edge pixel.The most important factor decreasing the performance of edge detection is the noise. Unfortunately, digital images are inevitably degraded by noise during image acquisition and/or transmission due to a number of imperfections encountered in imaging processes and/or communication channels. Most edge detection operators are based on the assumption that images contain large homogeneous regions separated by clear boundaries. However, this assumption loses its validity if the image is corrupted by noise. Therefore, majority of the edge detection operators require a prefiltering of the noisy image by using an appropriate noise filter before edge detection is performed. In this case, however, the
performance of the edge detection operation becomes strictly dependent on the performance of the noise filter. Moreover, the complexity of the system and the processing time are considerably increased.
A number of methods for edge detection implementing different approaches to the digital calculation of the derivative of the image intensity function are available in the literature. The classical methods[1,2]such as the Sobel, Prewitt and Kirsch detectors calculate the first directional derivative to determine the locations of the edges. These detectors are simple to implement but they are usually inaccurate and highly sensitive to noise. The zero-crossing edge detectors [1,2]use the second derivative along with the Laplacian operator. These detectors have fixed detection characteristics in all directions but they are very sensitive to noise too. The Gaussian edge detectors[2]reduce the undesirable negative effects of noise by smoothing the image before performing edge detection. Hence, they exhibit much superior performance over other operators especially in noisy conditions. The Canny detector, which is a Gaussian edge detector, is one of the most popular edge detectors in the literature and it has been widely used in many applications[3–5]. Although the Gaussian detectors exhibit relatively better performance, they are computationally much more complex than classical derivative based edge detectors. Furthermore, their performances quickly decrease as the density of the corrupting noise increases. Therefore, a novel edge detector that is capable of extracting edges from digital images corrupted by noise is highly desirable.
In the last few years, there has been a growing research interest in the applications of soft computing based techniques, such as neural networks and fuzzy logic systems, to various problems in image processing[6–15]. This is due mainly to the fact that neuro-fuzzy (NF) systems are very suitable tools to deal with uncertainty encountered in the process of extracting useful information from noisy images since NF systems combine the ability of neural networks to learn from examples and the capability of fuzzy logic systems to model the uncertainty and imprecision. Hence, NF systems may be employed as powerful tools for edge detection provided that appropriate network topologies and training
strategies are chosen.
In our recent work, we have shown that a NF system may be utilized to remove impulse noise from digital images[16,17]; to construct highly efficient hybrid filters for restoring noisy digital images while preserving edges, lines and other useful information within the image[18]; to detect noise for guiding switching noise filters and reducing their undesirable blurring effects[19,20]; and to improve noise suppression and detail preservation performances of image filters[21]. In addition to these successful applications, we have also shown in a preliminary report[22] that NF systems may be employed for efficient detection of edges in noisy digital images.
In this paper, we extend our preliminary research on edge detection and present a novel NF method for edge detection in digital images corrupted by impulse noise. In the proposed method, the edges in the noisy image are directly determined by a NF network without needing a prefiltering of the noisy input image. The NF network consists of a desired. number of subdetectors and a postprocessor. Each subdetector evaluates a different pixel neighborhood in the filtering window. The proposed NF edge detector is tested on popular images having different image properties and also compared with popular edge detectors from the literature. Experimental results show that the proposed NF edge detector exhibits much better performance than the competing operators and may efficiently be used for the detection of edges in digital images corrupted by impulse noise.
1 绪论
数字图像的边缘提供了重要的图像的信息，它们构成图像中的对象之间的边界。边缘检测是许多图像处理应用程序中经常执行的操作，因为它通常是其他操作之前对图像进行其他图形处理的任务，如图像分割，边缘检测，对象识别和分类，图像注释等等。因此，这些后续的图像处理任务的成功都严格依赖于边缘检测操作的性能.
图像强度在边缘显示突然变化。因此，边缘检测通常涉及计算图像强度函数的导数在一个给定的像素位置的值。如果图像强度函数的
导数在给定的像素的位置达到相对相对较高的程度，该图像位置的像素被列为边缘像素。
降低边缘检测质量的最重要的因素是噪声。不幸的是，在图像的获取和传输时由于成像处理过程中和通信通道中存在的一些缺陷，数字图像的质量不可避免被噪音降低。大多数的边缘检测方法以图像包含由明确的分界的大型均质区域分隔假设为基础。大多数检测器依据这样一个假设：图像包含大量有明显界限的均匀小区域。然而，如果图像被噪音损坏，这个假设就失去其有效性。因此，大部分的边缘检测算子需要在执行图像边缘检测前先使用适当的噪声滤波器过滤噪声。在这种情况下，边缘检测操作的性能严格依赖于噪声滤波器的性能。这样，系统的复杂性和处理时间就大大增加了。
一些边缘检测方法，为逼近图像强度函数倒数的数值解提供补充，可见诸文献。经典的方法[1,2]，如Sobel算子，Prewitt算子和Kirsch探测器计算第一次的方向导数确定边缘的位置。这些检测器是容易实现的，但它们通常不准确和对噪音非常敏感。零交叉边缘检测[ 1,2 ]使用拉普拉斯算子的二阶导数。这些探测器在所有的方向有固定的检测特性，但他们对噪音非常敏感。高斯边缘检测器[ 2 ]在进行边缘检测前可以通过平滑图像减少由噪声引起的不良影响。因此，他们尤其在嘈杂的环境下能表现出更优越的性能。Canny检测器，作为一个高斯边缘检测器，是在文献中最常见的边缘检测器，它已被广泛使用在许多应用程序[ 3-5 ]。虽然高斯探测器具有较好的性能，但它的计算比常见的边缘检测器的导数计算复杂。此外，他们的性能随着噪声的强度的增大迅速下降。因此，一个能够从受噪声干扰的数字图像中有效提取边缘信息的新型边缘探测器是迫切需求的。
过去的几年里，针对在图像处理中遇到的各种问题，基于神经网络和模糊逻辑系统[ 6-15]，已经有越来越多的研究者在研究应用软计算技术。基于这样的事实：从噪声图像提取有用信息的过程中，神经模糊（NF）系统是非常适合用来处理在遇到的不确定性，因为 NF 系统结合神经网络的从例子中学习的能力和模糊逻辑系统模拟不确性和不精确性的能力。因此，NF系统可作为边缘检测的有力工具，以提供适当的网络拓扑结构和选择测试策略。
在我们最近的作品中已经表明，NF系统可用于去除数字图像中的脉冲噪声 [ 16,17 ]；在保存图像的边缘，线和其他有用的信息时，也可以构造高效混合滤波器恢复嘈杂的数字图像 [ 18 ]；检测引导开关噪
声滤波器中的噪声和减少他们的不良的模糊效应[19,20]；改善噪声抑制和详细保存图像滤波器特性 [ 21 ]。除了这些成功的应用，我们也做在一个预备报告，NF系统可用作噪声数字图像的边缘检测[ 22 ]。
在本文中，我们扩展对边缘检测的初步研究，对脉冲噪声干扰的数字图像的边缘检测提出了一种新的NF边缘检测方法。上述方法嘈杂的图像边缘直接由NF网络提供，无需对输入图像加噪声信号，NF 网络由很多子探测器和一个主处理器组成，要求每个子探测器针对一个不同的像素区域。上述的NF边缘检测器在很多常见的图像上做实验，这些图像具有不同的属性；同时也与一些文献中常见的边缘检测器作比较。实验结果表明，上述NF边缘检测器比大多数的检测器表现出更好的性能，而且能有效地用于脉冲噪声干扰的数字图像的边缘检测。
2 Method
2.1 The proposed neuro-fuzzy operator
Fig. 1a shows the general structure of the proposed NF edge detection operator. The operator is constructed by combining a desired number of NF subdetectors with a postprocessor. All NF subdetectors in the structure operate onFig. 1.(a) The general structure of the proposed neuro-fuzzy edge detection operator. The pixels applied to the inputs of each NF subdetector in the structure are chosen so as to utilize the information from a different pixel neighborhood; (b) The filtering window of the operator; (c) Some of the possible pixel neighborhood topologies. the same 3-by-3 pixel filtering window, which is shown in Fig. 1b. Each NF subdetector evaluates a different neighborhood relation between the center pixel of the filtering window and two of its neighbors. Some of the many possible neighborhood topologies are shown inFig. 1c. The higher the number of NF subdetectors, the better the edge detection
performance, but the higher the computational cost.
2.方法
2.1 神经模糊算子
上述 NF 边缘检测算子的总体结构如图1所示。它是由一定数量的NF子探测器与一个后处理器组成。所有的NF子探测器都在图1(a)结构框图中。
NF边缘检测算子的一般结构如图1所示。(a)结构图中的每个NF 子探测器要针对的像素是经过选择的，以便利用像素附近不同的信息；（b）检测算子的滤波窗口；（c）像素的一些可能的邻域拓扑。图
1(b)是对3×3的像素进行滤波的窗口。滤波窗口中心像素和与它相领的像素之间的关系对每个NF子探测器来说都是不同的。一些可能的邻域拓扑显示在图1(c)中。NF子探测器越高级，边缘检测性能越
好，但其计算量越大。
2.2 The neuro-fuzzy subdetectors
Each NF subdetector is a first-order Sugeno type fuzzy inference system with 3-inputs and 1-output. The internal structures of the NF subdetectors are identical to each other. Each input has 3generalized belltype membership functions and the output has a linear membership function. The input–output relationship of any of the NF subdetectors is as follows:
LetX1, X2, X3 denote the inputs of the NF subdetector andYdenote its output. Each possible combination of inputs and their associated
membership functions is represented by a rule in the rule base of the NF subdetector. Since the NF subdetector has 3 inputs and each input has 3 membership functions, the rule base contains a total of 27 (33) rules, which are as follows:
Here the parametersa, b, canddare constants that characterize the shape of the membership functions. The optimal values of these parameters are determined by training,which will be discussed in detail later on.
The output of the NF subdetector is the weighted average of the individual rule outputs. The weighting factor,wk,of each rule is calculated by evaluating the membership expressions in the antecedent of the rule. This is accomplished by first converting the input values to fuzzy
membership values by utilizing the input membership functions and then applying the andoperator to these membership values. Theand operator corresponds to the multiplication of input membership values. Hence, the weighting factors of the rules are calculated as follows:
Once the weighting factors are obtained, the output of the NF subdetector can be found by calculating the weighted average of the individual rule outputs
Readers interested in the details of fuzzy systems may refer to an excellent book on this subject[23].
2.2 模糊神经的组成
每个NF子探测器都是一个具有3个输入和1个输出的一阶S型模糊推理系统。NF子探测器的内部结构组成都是相同的，有3个广义布尔型的隶属度函数的输入和1个线性的隶属度函数输出。所有NF子探测器的输入输出关系如下列函数方程式所示。
令X1，X2，X3表示NF 子探测器的输入和Y表示其输出。每个输入系数及其相关的隶属度函数都要符合NF子探测器的输入规则。虽然每个NF子探测器有3个输入，并且每个输入有3个功能，但是基本输入规则有27个，如下所示:
在这里参数A，B，C和D都是常数，表示隶属函数的具体特性。那些最适合的参数值是由实践得出的，这将在后面做详细讨论。
NF 子探测器总的输出是每一个规则输出下的加权平均值。加权因子
Wk是通过评价隶属度函数得出的。首先通过隶属函数将输入值转换
为模糊隶属度值，然后应用对这些隶属度值进行“合成”运算，“合
成”运算可取隶属度值的合取运算。因此，加权因子的计算规则如下：
一旦得到加权因子，NF 子探测器的输出即是各种规则下的输出的加权平均值。
2.3 The postprocessor
The outputs of the NF subdetectors are fed to a postprocessor, which generates the final NF network output.
The postprocessor actually calculates the average value of the subdetector outputs and compares this value with a threshold. The threshold value is the half of the available dynamic range for the pixel luminance values. For 8-bit images, where the pixel values range between 0 and 255, the threshold value is 128. The input–output relationship of the postprocessor may be explained as follows.
LetY1,Y2,...,YKrepresent the outputs of the NF subdetectors in the structure of the NF network, respectively, whereKis the number of NF subdetectors used. The output of the postprocessor is calculated in two steps. In the firs tstep, the average value of the individual NF subdetectors outputs are calculated.In the second step, this value is converted to 0 (black) or 255 (white) by comparing it with the threshold wherey(r, c)is the output of the postprocessor, which is also the output of the proposed NF edge detection operator.
2.3 后续处理
NF子探测器的输出送给后处理器，最终生成整个网络的输出。
这个后处理器实际上计算子探测器输出的平均值并与阀值比较。阀值是像素亮度值调节范围的一半。如8位图像的像素值，是在0和255之间，该阈值是128。后处理器的输入输出关系介绍如下。令Y1，Y2，、、、，Yk表示NF子探测器的输出，通常K是NF子探测器的数目。后处理器的输出包括两个步骤。
第一步计算NF子探测器输出的平均值。
第二步，此值通过与阈值的比较被转换为0（黑色）或255（白色）。
其中Y（R，C）是处理器的输出，也是NF边缘检测器的输出。
2.4 Training of the neuro-fuzzy subdetectors
The internal parameters of the proposed NF edge detector are optimized by training. Each NF subdetector in the structure is trained individually.Fig. 2represents the setup used for training. Here, the parameters of the NF subdetectors under training are iteratively adjusted so that its output converges to the output of theideal edge detector which, by definition, can correctly detect the locations of the edge pixels of the image fed to its input. The ideal edge detector is conceptual only and does not necessarily exist in reality. It is only the output of the ideal edge detector that is necessary for training, and this is represented by the target training image.
Fig. 3shows the images used for training. The images are 128-by-128 pixel artificial images that can easily be generated by computer. The image shown inFig. 3aisthebase training image. Each square box in this image has a size of 4-by-4 pixels and the 16 pixels contained within each box have the same luminance value. The image inFig. 3bisthe input training image and obtained by corrupting the base training image by impulse noise. The image inFig. 3cisthe target training image. It is a black and white image and its black pixels indicate the locations of the true edges of the input training image. Hence it represents the output of the ideal edge detector for the input training images.
The images in Fig. 3b and c are employed as the input and the target (desired) images during training, respectively. The parameters of the subdetector under training are then tuned by using the Levenberg–Marquardt optimization algorithm [23–25]so as to minimize the learning error.
2.4 模糊神经网络的组成
NF边缘检测器的内部参数是通过实践测试进行优化。结构框图中每个NF子探测器是单独测试的。图2表示实践用的设置。在这里，NF参数在实践中反复地调整，使其输出达到理想的边缘检测器的输出要求。理想的边缘检测器，可以正确地检测出被输入的图像像素的边缘位置。理想的边缘检测器仅是概念，实际上并不存在。仅对理想的边缘检测器进行测试确实是必要的，它代表实际边缘检测器测试的最终目标。
图3是用于测试的图像，是128×128像素的人工图像，可以通过计算机很容易地获得。图3a所示的图像为最初测试图像。在这幅图像中每一方箱的尺寸都是4×4像素而且每个方箱中的16像素具有相同的亮度值。图3b中的图像是通过脉冲噪声干扰最初测试图像而得到的要输入的测试图像。图3c图像是测试的目标图像。它是黑色和白色的图像，而且其黑色像素表示的是要输入的测试图像的真实边缘位置。因此，它代表了理想边缘检测器对要输入的测试图像的输出。在测试过程中图3b和图3C的图像分别代表输入和目标图像。
2.5 Processing of the noisy input image
The overall procedure of applying the proposed NF edge detection