Edge and keypoint detection in facial regions

一种新的视频镜头边界检测及关键帧提取方法
方勇;戚飞虎
【期刊名称】《华南理工大学学报（自然科学版）》
【年(卷),期】2004(032)0z1
【摘要】根据视频邻域片段变化的特点提出了镜头边界系数模型,镜头边界系数具有良好的抗噪能力,且对视频帧的时域变化有较好的描述能力,可用于镜头边界检测与关键帧提取.它可以单独检测镜头边界,也可以与传统的基于帧差的镜头边界检测方法相结合检测镜头边界.在提取关键帧时,根据镜头边界系数的分布,自适应地确定镜头内的关键帧数,用非极大值抑制方法与基于镜头边界系数的优先级方法确定关键帧的位置.实验结果表明,该方法在镜头边界检测性能上要优于已有的基于帧差的镜头边界检测方法,提取的关键帧对镜头的视觉内容具有较好的表达能力,且可在视频回放时实时执行.
【总页数】6页(P18-23)
【作者】方勇;戚飞虎
【作者单位】上海交通大学,计算机科学与工程系,上海,200030;上海交通大学,计算机科学与工程系,上海,200030
【正文语种】中文
【中图分类】TP391
【相关文献】
1.一种新的自适应的视频关键帧提取方法 [J], 王宇;汪荣贵;杨娟
2.一种新的视频镜头扫换边界检测方法 [J], 谢明华;刘辉;王新辉
3.一种压缩视频流的视频分段和关键帧提取方法 [J], 王凤领;
4.一种压缩视频流的视频分段和关键帧提取方法 [J], 王凤领
5.一种新的镜头边界检测和静态视频摘要提取方法 [J], 卜庆凯;胡爱群
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Digital Image Processing and Edge DetectionDigital Image ProcessingInterest in digital image processing methods stems from two principal applica- tion areas: improvement of pictorial information for human interpretation; and processing of image data for storage, transmission, and representation for au- tonomous machine perception.An image may be defined as a two-dimensional function, f(x, y), where x and y are spatial (plane) coordinates, and the amplitude of f at any pair of coordinates (x, y) is called the intensity or gray level of the image at that point. When x, y, and the amplitude values of f are all finite, discrete quantities, we call the image a digital image. The field of digital image processing refers to processing digital images by means of a digital computer. Note that a digital image is composed of a finite number of elements, each of which has a particular location and value. These elements are referred to as picture elements, image elements, pels, and pixels. Pixel is the term most widely used to denote the elements of a digital image.Vision is the most advanced of our senses, so it is not surprising that images play the single most important role in human perception. However, unlike humans, who are limited to the visual band of the electromagnetic (EM) spec- trum, imaging machines cover almost the entire EM spectrum, ranging from gamma to radio waves. They can operate on images generated by sources that humans are not accustomed to associating with images. These include ultra- sound, electron microscopy, and computer-generated images. Thus, digital image processing encompasses a wide and varied field of applications.There is no general agreement among authors regarding where image processing stops and other related areas, such as image analysis and computer vi- sion, start. Sometimes a distinction is made by defining image processing as a discipline in which both the input and output of a process are images. We believe this to be a limiting and somewhat artificial boundary. For example, under this definition, even the trivial task of computing the average intensity of an image (which yields a single number) would not be considered an image processing operation. On the other hand, there are fields such as computer vision whose ultimate goal is to use computers to emulate human vision, including learning and being able to make inferences and take actions based on visual inputs. This area itself is a branch of artificial intelligence (AI) whose objective is to emulate human intelligence. The field of AI is in its earliest stages of infancy in terms of development, with progress having been much slower than originally anticipated. The area of image analysis (also called image understanding) is in be- tween image processing and computer vision.There are no clearcut boundaries in the continuum from image processing at one end to computer vision at the other. However, one useful paradigm is to consider three types of computerized processes in this continuum: low-, mid-, and highlevel processes. Low-level processes involve primitive opera- tions such as imagepreprocessing to reduce noise, contrast enhancement, and image sharpening. A low-level process is characterized by the fact that both its inputs and outputs are images. Mid-level processing on images involves tasks such as segmentation (partitioning an image into regions or objects), description of those objects to reduce them to a form suitable for computer processing, and classification (recognition) of individual objects. A midlevel process is characterized by the fact that its inputs generally are images, but its outputs are attributes extracted from those images ., edges, contours, and the identity of individual objects). Finally, higherlevel processing involves “making sense” of an ensemble of recognized objects, as in image analysis, and, at the far end of the continuum, performing the cognitive functions normally associated with vision.Based on the preceding comments, we see that a logical place of overlap between image processing and image analysis is the area of recognition of individual regions or objects in an image. Thus, what we call in this book digital image processing encompasses processes whose inputs and outputs are images and, in addition, encompasses processes that extract attributes from images, up to and including the recognition of individual objects. As a simple illustration to clarify these concepts, consider the area of automated analysis of text. The processes of acquiring an image of the area containing the text, preprocessing that image, extracting (segmenting) the individual characters, describing the characters in a form suitable for computer processing, and recognizing those individual characters are in the scope of what we call digital image processing in this book. Making sense of the content of the page may be viewed as being in the domain of image analysis and even computer vision, depending on the level of complexity implied by the statement “making sense.” As will become evident shortly, digital image processing, as we have defined it, is used successfully in a broad range of areas of exceptional social and economic value.The areas of application of digital image processing are so varied that some form of organization is desirable in attempting to capture the breadth of this field. One of the simplest ways to develop a basic understanding of the extent of image processing applications is to categorize images according to their source ., visual, X-ray, and so on). The principal energy source for images in use today is the electromagnetic energy spectrum. Other important sources of energy include acoustic, ultrasonic, and electronic (in the form of electron beams used in electron microscopy). Synthetic images, used for modeling and visualization, are generated by computer. In this section we discuss briefly how images are generated in these various categories and the areas in which they are applied.Images based on radiation from the EM spectrum are the most familiar, es- pecially images in the X-ray and visual bands of the spectrum. Electromagnet- ic waves can be conceptualized as propagating sinusoidal waves of varying wavelengths, or they can be thought of as a stream of massless particles, each traveling in a wavelike pattern and moving at the speed of light. Each massless particle contains a certain amount (or bundle) of energy. Each bundle of energy is called a photon. If spectral bands aregrouped according to energy per photon, we obtain the spectrum shown in fig. below, ranging from gamma rays (highest energy) at one end to radio waves (lowest energy) at the other. The bands are shown shaded to convey the fact that bands of the EM spectrum are not distinct but rather transition smoothly from one to the other.Image acquisition is the first process. Note that acquisition could be as simple as being given an image that is already in digital form. Generally, the image acquisition stage involves preprocessing, such as scaling.Image enhancement is among the simplest and most appealing areas of digital image processing. Basically, the idea behind enhancement techniques is to bring out detail that is obscured, or simply to highlight certain features of interest in an image. A familiar example of enhancement is when we increase the contrast of a n image because “it looks better.” It is important to keep in mind that enhancement is a very subjective area of image processing. Image restoration is an area that also deals with improving the appearance of an image. However, unlike enhancement, which is subjective, image restoration is objective, in the sense that restoration techniques tend to be based on mathematical or probabilistic models of image degradation. Enhancement, on the other hand, is based on human subjective preferences regarding what constitutes a “good” enhancement result.Color image processing is an area that has been gaining in importance because of the significant increase in the use of digital images over the Internet. It covers a number of fundamental concepts in color models and basic color processing in a digital domain. Color is used also in later chapters as the basis for extracting features of interest in an image.Wavelets are the foundation for representing images in various degrees of resolution. In particular, this material is used in this book for image data compression and for pyramidal representation, in which images are subdivided successively into smaller regions.Compression, as the name implies, deals with techniques for reducing the storage required to save an image, or the bandwidth required to transmi storage technology has improved significantly over the past decade, the same cannot be said for transmission capacity. This is true particularly in uses of the Internet, which are characterized by significant pictorial content. Image compression is familiar (perhaps inadvertently) to most users of computers in the form of image file extensions, such as the jpg file extension used in the JPEG (Joint Photographic Experts Group) image compression standard.Morphological processing deals with tools for extracting image components that are useful in the representation and description of shape. The material in this chapter begins a transition from processes that output images to processes that output image attributes.Segmentation procedures partition an image into its constituent parts or objects. In general, autonomous segmentation is one of the most difficult tasks in digital image processing. A rugged segmentation procedure brings the process a long way toward successful solution of imaging problems that require objects to be identified individually. On the other hand, weak or erratic segmentation algorithms almost always guarantee eventual failure. In general, the more accurate the segmentation, the more likely recognition is to succeed.Representation and description almost always follow the output of a segmentation stage, which usually is raw pixel data, constituting either the bound- aryof a region ., the set of pixels separating one image region from another) or all the points in the region itself. In either case, converting the data to a form suitable for computer processing is necessary. The first decision that must be made is whether the data should be represented as a boundary or as a complete region. Boundary representation is appropriate when the focus is on external shape characteristics, such as corners and inflections. Regional representation is appropriate when the focus is on internal properties, such as texture or skeletal shape. In some applications, these representations complement each other. Choosing a representation is only part of the solution for trans- forming raw data into a form suitable for subsequent computer processing. A method must also be specified for describing the data so that features of interest are highlighted. Description, also called feature selection, deals with extracting attributes that result in some quantitative information of interest or are basic for differentiating one class of objects from another.Recognition is the process that assigns a label ., “vehicle”) to an object based on its descriptors. As detailed before, we conclude our coverage of digital image processing with the development of methods for recognition of individual objects.So far we have said nothing about the need for prior knowledge or about the interaction between the knowledge base and the processing modules in Fig2 above. Knowledge about a problem domain is coded into an image processing system in the form of a knowledge database. This knowledge may be as sim- ple as detailing regions of an image where the information of interest is known to be located, thus limiting the search that has to be conducted in seeking that information. The knowledge base also can be quite complex, such as an interrelated list of all major possible defects in a materials inspection problem or an image database containing high-resolution satellite images of a region in con- nection with change-detection applications. In addition to guiding the operation of each processing module, the knowledge base also controls the interaction between modules. This distinction is made in Fig2 above by the use of double-headed arrows between the processing modules and the knowledge base, as op- posed to single-headed arrows linking the processing modules.Edge detectionEdge detection is a terminology in and , particularly in the areas of and , to refer to which aim at identifying points in a at which the changes sharply or more formally has point and line detection certainly are important in any discussion on segmentation,edge dectection is by far the most common approach for detecting meaningful discounties in gray level.Although certain literature has considered the detection of ideal step edges, the edges obtained from natural images are usually not at all ideal step edges. Instead they are normally affected by one or several of the following effects: blur caused by a finite and finite ; 2. caused by shadows created by light sources of non-zero radius; 3. at a smooth object edge; or in the vicinity of object edges.A typical edge might for instance be the border between a block of red color and a blockof yellow. In contrast a (as can be extracted by a ) can be a small number of pixels of a different color on an otherwise unchanging background. For a line, there may therefore usually be one edge on each side of the line.To illustrate why edge detection is not a trivial task, let us consider the problem of detecting edges in the following one-dimensional signal. Here, we may intuitively say that there should be an edge between the 4th and 5th pixels.5 76 4 152 148 149If if the intensity differences between the adjacent neighbouring pixels were higher, it would not be as easy to say that there should be an edge in the corresponding region. Moreover, one could argue that this case is one in which there are several , to firmly state a specific threshold on how large the intensity change between two neighbouring pixels must be for us to say that there should be an edge between these pixels is not always a simple problem. Indeed, this is one of the reasons why edge detection may be a non-trivial problem unless the objects in the scene are particularly simple and the illumination conditions can be well controlled.There are many methods for edge detection, but most of them can be grouped into two categories,search-based and based. The search-based methods detect edges by first computing a measure of edge strength, usually a first-order derivative expression such as the gradient magnitude, and then searching for local directional maxima of the gradient magnitude using a computed estimate of the local orientation of the edge, usually the gradient direction. The zero-crossing based methods search for zero crossings in a second-order derivative expression computed from the image in order to find edges, usually the zero-crossings of the or the zero-crossings of a non-linear differential expression, as will be described in the section on following below. As a pre-processing step to edge detection, a smoothing stage, typically Gaussian smoothing, is almost always applied (see also ).The edge detection methods that have been published mainly differ in the types of smoothing filters that are applied and the way the measures of edge strength are computed. As many edge detection methods rely on the computation of image gradients, they also differ in the types of filters used for computing gradient estimates in the x- and y-directions.Once we have computed a measure of edge strength (typically the gradient magnitude), the next stage is to apply a threshold, to decide whether edges are present or not at an image point. The lower the threshold, the more edges will be detected, and the result will be increasingly susceptible to , and also to picking out irrelevant features from the image. Conversely a high threshold may miss subtle edges, or result in fragmented edges.If the edge thresholding is applied to just the gradient magnitude image, the resulting edges will in general be thick and some type of edge thinning post-processing is necessary. For edges detected with non-maximum suppression however, the edge curves are thin by definition and the edge pixels can be linked into edge polygon by an edge linking (edge tracking) procedure. On a discrete grid, the non-maximum suppression stage can be implemented by estimating the gradient direction using first-order derivatives, then rounding off the gradient direction to multiples of 45 degrees, and finally comparing the values of the gradient magnitude in the estimated gradient direction.A commonly used approach to handle the problem of appropriate thresholds for thresholding is by using with . This method uses multiple thresholds to find edges. We begin by using the upper threshold to find the start of an edge. Once we have a start point, we then trace the path of the edge through the image pixel by pixel, marking an edge whenever we are above the lower threshold. We stop marking our edge only when the value falls below our lower threshold. This approach makes the assumption that edges are likely to be in continuous curves, and allows us to follow a faint section of an edge we have previously seen, without meaning that every noisy pixel in the image is marked down as an edge. Still, however, we have the problem of choosing appropriate thresholding parameters, and suitable thresholding values may vary over the image.Some edge-detection operators are instead based upon second-order derivatives of the intensity. This essentially captures the in the intensity gradient. Thus, in the ideal continuous case, detection of zero-crossings in the second derivative captures local maxima in the gradient.We can come to a conclusion that,to be classified as a meaningful edge point,the transition in gray level associated with that point has to be significantly stronger than the background at that we are dealing with local computations,the method of choice to determine whether a value is “significant” or not id to use a we define a point in an image as being as being an edge point if its two-dimensional first-order derivative is greater than a specified criterion of connectedness is by definition an term edge segment generally is used if the edge is short in relation to the dimensions of the key problem in segmentation is to assemble edge segments into longer alternate definition if we elect to use the second-derivative is simply to define the edge ponits in an image as the zero crossings of its second definition of an edge in this case is the same as is important to note that these definitions do not guarantee success in finding edge in an simply give us a formalism to look for derivatives in an image are computed using the derivatives are obtained using the Laplacian.数字图像处理与边缘检测数字图像处理数字图像处理方法的研究源于两个主要应用领域：其一是为了便于人们分析而对图像信息进行改进：其二是为使机器自动理解而对图像数据进行存储、传输及显示。

专利名称：Edge detection device, edge detection method, and computer program发明人：堤 隆弘申请号：JP2012158910申请日：20120717公开号：JP5983124B2公开日：20160831专利内容由知识产权出版社提供摘要：PROBLEM TO BE SOLVED: To more reliably detect an edge of a character expressed by dots compared with a conventional manner.SOLUTION: An image formation device 1 includes following means: a first smoothing processing unit 101 for calculating a first smoothing image 41 by performing filter processing with respect to an input image 4 with use of a first filter where a weight is deviated in a first direction; a second smoothing processing unit 102 for calculating a second smoothing image 42 by performing filter processing with respect to an input image 4 with use of a second filter where a weight is deviated in a second direction different from the first direction; an image synthesis processing unit 103 for calculating a synthetic image 43 obtained by synthesizing a first smoothing image 41 with a second smoothing image 42; and a character edge detection unit 104 for detecting an edge 4E from a synthetic image 43.申请人：コニカミノルタ株式会社地址：東京都千代田区丸の内二丁目７番２号国籍：JP代理人：久保 幸雄,坂田 泰弘更多信息请下载全文后查看。

边缘检测-edge detection1.问题描述边缘检测是图像处理和计算机视觉中的基本问题，边缘检测的目的是标识数字图像中亮度变化明显的点。

图像属性中的显著变化通常反映了属性的重要事件和变化。

这些包括（i）深度上的不连续、（ii）表面方向不连续、（iii）物质属性变化（iv）场景照明变化。

边缘检测是图像处理和计算机视觉中，尤其是特征提取中的一个研究领域。

边缘检测的评价是指对边缘检测结果或者边缘检测算法的评价。

诚然，不同的实际应用对边缘检测结果的要求存在差异，但大多数因满足以下要求：1）正确检测出边缘2）准确定位边缘3）边缘连续4）单边响应，即检测出的边缘是但像素的2.应用场合图像边缘检测大幅度地减少了数据量，并且剔除了可以认为不相关的信息，保留了图像重要的结构属性。

有许多方法用于边缘检测，它们的绝大部分可以划分为两类：基于查找一类和基于零穿越的一类。

基于查找的方法通过寻找图像一阶导数中的最大和最小值来检测边界，通常是将边界定位在梯度最大的方向。

基于零穿越的方法通过寻找图像二阶导数零穿越来寻找边界，通常是Laplacian过零点或者非线性差分表示的过零点。

3.研究历史和现状边缘检测作为图像处理的一个底层技术，是一个古老又年轻的课题，有着悠久的历史。

早在1959年，B.Julez就提到过边缘检测，随后，L.G.Robert于1965年对边缘检测进行系统的研究。

3.1一阶微分算子一阶微分算子是最原始，最基本的边缘检测方法，它的理论依据是边缘是图像中灰度发生急剧变化的地方，而图像的提督刻画了灰度的变化速率。

因此，通过一阶微分算子可以增强图像中的灰度变化区域，然后对增强的区域进一步判断边缘。

在点（x,y）的梯度为一个矢量，定义为：梯度模值为：梯度方向为：根据以上理论，人们提出了许多算法，经典的有：Robert算子，Sobel算子等等，这些一阶微分算子的区别在于算子梯度的方向，以及在这些方向上用离散化数值逼近连续导数的方式和将这些近似值合成梯度的方式不同。

Dec. 2020Vol. 41 No 122020 年12 月 第41卷第12期计算机工程与设计COMPUTER ENGINEERING AND DESIGN基于小波的改进边缘检测方法段红燕，杨浩+，李世杰，董中华（兰州理工大学 机电工程学院，甘肃 兰州730050）摘 要：为改善传统二阶边缘检测算子在实际应用中的不足，提出一种基于小波的结合LoG 和Canny 算子的边缘检测方法。

对图像进行小波变换增强，对高频系数拉伸，低频系数压缩，增强边缘信息；在LoG 检测中，用双边滤波代替高斯滤 波，在滤除噪声的同时，提高保边能力，在Canny 检测中，用改进自适应中值滤波平滑图像，用改进的（）su 计算图像的 阈值；将两种边缘进行加权融合。

实验结果表明，所提算法在提高边缘细节信息和去噪性能上具有很好的鲁棒性。

关键词：小波增强；双边滤波；自适应中值滤波；改进Otsu ；融合中图法分类号：TP391. 41 文献标识号：A 文章编号：1000-7024 （2020） 12-3-185-05doi :10.16208/j.issn1000-7024.2020.12.028Improved edge detection method based on waveletDUAN Hong-yan, YANG Hao + , LI Shi-jie, DONG Zhong-hua(School of Mechanical and Electrical Engineering , Lanzhou University of Technology, Lanzhou 730050, Chin)Abstract ： To improve the shortcomings of traditional second-order edge detection operators in the practical application, an edgedetection method based on wavelet combining LoG and Canny operators was proposed. The image was enhanced by wavelet transform, the high frequency coefficient was stretched and the low frequency coefficient was compressed to enhance the edge in ­formation. In LoG detection, bilateral filtering was used instead of Gaussian filtering to filter the noise and improve the edgepreservation ability. In Canny detection, the improved adaptive median filter was used to smooth the image , and the improved Otsu was used to calculate the threshold of the image. The two kinds of edges were weighted fused. Experimental simulation re ­sults show that the proposed algorithm has good robustness in improving edge detail information and de-noising performance.Key words ： wavelet enhancement ； bilateral filtering ； adaptive median filtering ； improved Otsu ； fusion0引言边缘是指图像中灰度值发生剧烈变化的区域，其中包含着图像的基本特征信息，对边缘的检测是对图像特征提取、图像识别和描述的基础。

Ⅰ.单句语法填空1．(2022·浙江模拟)Everybody should be aware of his ____________(strong) and weakness so that we can work better as a team.答案：strength2．(2022·湖北名校联考)—Did you take ____________ the speech the visiting scholar made yesterday?—Not really.He spoke with an Australian accent and a bit too fast for me.答案：in3．—Have you got any particular plans for the coming winter vacation?—Yes.____________ possible，I’m going to visit my grandparents.答案：If4．The factory cut____________the trees without the agreement of the government.答案：down5．____________(concern) about the student，the teacher called his parents to find out why he was so often absent from class.答案：Concerned6．It is ____________(evidence) to all of you that he has made a mistake.答案：evident7．(2022·天津五区县期末)When the streets are full of melting snow，you can’t help ____________ get your shoes wet.答案：but8．He ____________(catch) in the rain and got wet through last night.答案：was caught9．(2022·安徽重点中学检测)The guests made a ____________(complain) that the fish was too small.答案：complaint10．Look ____________ magazines to find pictures that you can stick on your poster.答案：throughⅡ.阅读理解A(2022·豫北、豫东十所名校联考)The way we cook is important.In many countries，the two choices are natural gas and electric­powered stoves.The World Health Organization warns that millions of people are dying every year from indoor air pollution which results from the use of dangerous fuels and cook-stoves in the home.Most of the deaths are in developing countries.To help fight the problem，the WHO announced new guidelines aimed at reducing household pollutants. The WHO’s plan of action for reducing indoor pollutants is based on new findings，which show that the use of toxic(有毒的)fuels in inefficient stoves，space heaters or lights is to blame for many of these deaths.Carlos Dora，an official in the WHO，says people should not use unprocessed coal indoors.He says，“Opening a window or door to let out the harmful air will not correct the situation.It will only pollute the outdoors.You can’t expect that a bit of ventilation(通风) is going to get rid of this. It is really about clean technologies and clean fuels.And，the fuel store has not been stressed enough so far in the global debate.So，that is the new thing.We should be going for clean fuels，avoiding coal and going for the solar.”WHO officials say indoor pollution leads to early deaths from stroke，heart and lung disease and childhood lung cancer.These diseases can often result from high levels of fine particulate matter and carbon monoxide(一氧化碳) released by the burning of solid fuels.These fuels include wood，coal，animal waste，crop waste and charcoal.Women and girls are the main victims.The United Nations found that more than 95 percent of households in sub­Saharan Africa depend on solid fuels for cooking.It says huge populations in India，China and Latin American countries，such as Guatemala and Peru，are also at risk.WHO experts note some new，safe and low­cost technologies that could help are already available.But this is just a start.They are urging developing countries to use cleaner fuels and increase access to cleaner and more modern cooking and heating appliances.【文章大意】本文是一篇科普说明文。

Pattern Recognition35(2002)1559–1570/locate/patcogA new approach to edge detectionZ.J.Hou,G.W.Wei∗Department of Computational Science,Faculty of Science,National University of Singapore,Singapore117543,Singapore Received23March2000;receivedin revisedform2November2000;accepted22June2001AbstractThis paper introduces the discrete singular convolution(DSC)algorithm for edge detection.Two classes of new edge detectors,DSC edge detector(DSCED)and DSC anti-noise edge detector(DSCANED),are proposed for the detection of multiscale edges.The DSCED is capable of extracting theÿne details of images,whereas DSCANED is robust against noise.The combination of two classes of DSC edge detectors provides an e cient and reliable approach to multiscale edge puter experiments are carried out for extracting edge information from real images, with andwithout the contamination of Gaussian white noise.Sharp image ed ges are obtainedfrom a variety of sample images,including those that are degraded to a peak-signal–noise-ratio(PSNR)of16dB.Some of the best results are attainedfrom a number of stand ardtest problems.The performance of the proposedalgorithm is comparedwith many other existing methods,such as the Sobel,Prewitt and Canny detectors.?2002Pattern Recognition Society.Published by Elsevier Science Ltd.All rights reserved.Keywords:Edge detection;Image processing;Discrete singular convolution;Multiscale1.IntroductionThe edges in an image usually refer to rapid changes in some physical properties,such as geometry,illumi-nation,andre ectivity.Mathematically,a d iscontinuity may be involvedin the function representing such physi-cal properties.In practice,human perception e ects play an important role in determining whether an edge exists or not.Edge detection is a key issue in image processing, computer vision,andpattern recognition.In the context of digital image processing,the concept of discontinuity does not apply and an edge may refer to systematic,rapid variation of gray-level values over number of scales.A variety of algorithms have been proposedfor analyzing image intensity variation,including statistical methods [1–5],di erence methods[6–8]and curveÿtting meth-ods[9–13].∗Corresponding author.Tel.:+65-874-6589;fax:+65-774-6756.E-mail address:cscweigw@.sg(G.W.Wei).Edge detection in noisy environment can be treated as an optimal linearÿlter design problem[14–18].Canny [15]formulated edge detection as an optimization prob-lem andd eÿnedan optimalÿlter,which can be e ciently approximatedby theÿrst d erivative of Gaussian function in the one-dimensional case.Canny’sÿlter was further extended to recursiveÿlters[19],which provide a more e cient way for image noiseÿltering and edge detection. Other edge detection methods include di erentiation-based edge detection using logarithmic image process-ing(LIP)models[20],contrast-based methods[21], relaxation labeling techniques[22]andanisotropic d if-fusion[23,24].In fact,these methods can be combined to achieve better performance.For instance,the sec-ond directional derivative edge detector proposed by Haralick[9]can be regard edas a hybridof the d i er-entiation methodandthe statistical hypothesis testing method,which leads to better performance in a noisy environment.In the last decade,there has been renewed inter-est in wavelet theory,with applications inÿltering,0031-3203/02/$22.00?2002Pattern Recognition Society.Published by Elsevier Science Ltd.All rights reserved. PII:S0031-3203(01)00147-91560Z.J.Hou,G.W.Wei/Pattern Recognition35(2002)1559–1570classiÿcation,andcompression[25].Wavelet andits as-sociatedmultiresolution analysis have also been applied for the characterization of image intensity variations. Mallat et al.[26]have shown that many images can be adequately approximated by wavelet bases.Discrete wavelet transform(DWT)decomposes an image into a set of successively smaller images with di erent scales of resolutions.The magnitude of coe cients in di erent scales of the wavelet transform domain can be modiÿed prior to carrying out the inverse wavelet transform.This procedure can selectively accentuate interesting com-ponents at the expense of undesirable ones.Equipped with wavelet analysis,one can collect quadraticÿlter responses at selectedscales[27],so that an image ed ge is more reasonably identiÿed with appropriateÿlter responses at a number of desired scales.More recently,a discrete singular convolution(DSC) algorithm was proposedas a potential approach for com-puter realization of singular integrations[28,29].The mathematical foundation of the algorithm is the theory of distributions[30]and wavelet analysis.Sequences of ap-proximations to the singular kernels of Hilbert type,Abel type and delta type were constructed.In solving di eren-tial equations,the DSC approach exhibits the accuracy of a global methodfor integration andthe exibility of a local methodfor hand ling complex geometry andbound-ary conditions.In the context of image processing,DSC kernels were usedto facilitate a new anisotropic d i u-sion operator for image restoration from noise[31].Most recently,DSC kernels were usedto generate a new class of wavelets,which include the Mexican hat wavelet as a special case[32].The purpose of this study is to propose a new ap-proach based on the DSC algorithm for edge detection. We illustrate this approach by using a special class of DSC kernels,the DSC kernels of delta type.In particular, DSC kernels constructedfrom functions of the Schwartz class are easy to parison is made between the proposedDSC d etectors andthe Canny d etectors.Ex-periments indicate that the new approach is e ective for image edge detection under severe Gaussian white noise.The rest of the paper is organizedas the following.In Section2,we describe the theory and algorithm for edge detections.The theory of discrete singular distribution (DSC)is brie y reviewed.Two new classes of edge de-tectors are proposedfor multiscale feature extraction in both normal and noisy environment.DSC edge detectors (DSCED)are constructed asÿne-scale edge detectors. Moreover,DSC anti-noise edge detectors(DSCANED) are designed as coarse-scale edge detectors.The applica-tion of the present algorithm is given in Section3.The utility is illustratedby a number of real images.B oth noise free images andnoisy images are treated.The per-formance of the proposedapproach is testedby using an objective measure.The conclusion is given in Section4.2.Theory and algorithm2.1.The discrete singular convolutionIt is most convenient to discuss singular convolution in the context of the theory of distributions.Let T be a distribution andÁ(x)be an element of the space of test functions.A singular convolution is deÿned asF(t)=(T∗Á)(t)=∞−∞T(t−x)Á(x)d x:(1)Here T(t−x)is a singular kernel.The singular convo-lution is the central issue for a wide range of science andengineering problems.Of particular relevance to the present study is the singular kernels of the delta typeT(x)= (n)(x);n=0;1;2;:::;(2)where is the delta distribution.Here the superscript de-notes the n th order derivative.Although the delta dis-tribution is calledDirac d elta function,it is not a func-tion per se.It does not even have a value anywhere.The kernel T(x)= (0)(x)is important for interpolation and T(x)= (n)(x)(n=1;2;:::)are essential for di erentia-tions.However,these kernels cannot directly be applied in numerical computations because of their singular na-ture.One methodto overcome this d i culty is to con-struct an approximation{T }that converges to the sin-gular kernel lim →T →T(x),where 0is a general-izedlimit.In the case of T(x)= (x),the kernel T (x)is a delta sequence kernel.With a su ciently smooth ap-proximation,it is useful to consider a discrete singular convolution(DSC)F (t)=kT (t−x k)f(x k);(3)where F (t)is an approximation to F(t)and x k is an appropriate set of discrete points on which the DSC is well deÿned.Here,in general,f(x)is not requiredto be a test function.An important example of the DSC kernels is Shannon’s delta kernel(x)=sin( x)x:(4) Numerically,Shannon’s delta kernel is a reproducing kernelf(x)=∞−∞f(y)sin (x−y)(x−y)d y∀f∈B2;(5)where∀f∈B2 indicates that,in its Fourier repre-sentation,the L2function f vanishes outside theZ.J.Hou,G.W.Wei/Pattern Recognition35(2002)1559–15701561 interval[− ; ].Here B2 is the Paley–Wiener repro-ducing kernel Hilbert space which is a subspace of theHilbert space L2(R).The Paley–Wiener reproducingkernel Hilbert space has a very useful sampling basis[S k(x)=sin (x−k)= (x−k);(k∈Z)],which providesa discrete representation of every(continuous)functionin B2f(x)=k∈Zf(y k)S k(x)∀f∈B2 ;(6)where symbol Z denotes the set of all integers.Eq.(6)is recognizedas Shannon’s sampling theorem.2.2.DSCÿltersFrom the point of view of signal processing,Shan-non’s delta kernel (x)corresponds to a family of ideallow passÿlters,each with a di erent bandwidth.Theircorresponding wavelet expressions(x)=sin2 x−sin xx;(7)are bandpassÿlters.B oth (x)andits associated wavelet play a crucial role in information theory and theory of signal processing.However,their usefulness is limitedby the fact that (x)and (x)are inÿnite im-pulse response(IIR)ÿlters andtheir Fourier transforms ˆ (!)andˆ(!)are not di putationally, (x)and(x)do not haveÿnite moments in the coor-dinate space;in other words,they are de-localized.This non-local feature in coordinate is related to the bandlim-itedcharacter in the Fourier representation accord ing to the Heisenberg uncertainty principle.To improve the asymptotic behavior of Shannon’s delta kernel in the coordinate representation,a regularization procedure can be usedandthe resulting DSC kernel in its d iscretized form can be expressedas; (x−x k)=sin( = )(x−x k)( = )(x−x k)e −(x−x k)2=2 2 ¿0:(8)Here,it is understood that = = andexpression(8)is usedin d iscrete computations exclusively.An immediate beneÿt of the regularized Shannon’s delta kernel,Eq.(8),is that its Fourier transform is in-ÿnitely di erentiable.Both Shannon’s delta kernel and the regularizedShannon’s d elta kernel are plottedin Fig.1.Qualitatively,all kernels oscillate in the co-ordinate representation.Shannon’s delta kernel has a long tail which is proportional to1=x.Whereas, the regularizedkernels d ecay much faster,especially when is very small.In the Fourier representa-tion,Shannon’s delta kernel is the ideal low pass ÿlter,which is discontinuous at!=12.In contrast, all regularizedkernels have an“optimal”shape in their frequency responses.Of course,they allreduce Fig.1.Graphs of ; (x)andits frequency response.The d otted line: =1;the dot dashed line: =3;the dashed line: =5; the solidline: =∞.to Shannon’s deltaÿlter at the limitlim→∞; (x)=lim→∞sin xx e−x2=2 2=sin xx:(9) 2.3.DSC edge detectorsTo construct edge detectors,we consider a one-dimensional,n th order DSC kernel of the delta type(n) ; (x−x k);n=0;1;2;::::Here (0) ; (x−x k)= ; (x−x k)is a DSCÿlter.The ex-pression given in Eq.(8)is an example of the DSCÿl-ters andmany other examples are given in Ref.[28]. The derivatives (n) ; (x m−x k)(n=1;2;:::)are obtained by di erentiation(n) ; (x m−x k)=dd xn; (x−x k)x=x m;(10)andcan be regard edas high-passÿlters.Theÿlters for n=1–3andtheir frequency responses are plottedin Fig.2.It is seen thatÿlters corresponding to the deriva-tives of Shannon’s delta kernel decay slowly as x in-creases,whereas,regularizedÿlters are functions of the Schwartz class andhave controlledresid ue amplitud e at1562Z.J.Hou,G.W.Wei /Pattern Recognition 35(2002)1559–1570Fig.2.High-pass ÿlters (n ); (x )andtheir frequency responses.The dottedline: =1;the dot dashed line: =3;the dashed line: =5;the solidline: =∞.(a)and(b):n =1;(c)and(d):n =2;(e)and(f):n =rge x values.In the Fourier representation,the deriva-tives of Shannon’s delta kernel are discontinuous atcertain points.In contrast,the derivatives of regularized kernels are all continuous andcan be mad e as close to those of Shannon’s as one wishes.Fig.2also illustrates the impact of parameter on the ÿlters in the time–frequency domain.For ÿxed ,the larger the value is,the slower the ÿlters will decay in the time domain.As a result,the truncation error increases for numerical computations.In the frequency domain,however,these ÿlters become more localizedwith theincrease of .But di erence in values has little impact on the low frequency responses of various ÿlters.To balance the localization of a ÿlter in both the time and frequency domains,an optimal is requiredandcan be attainedfor a given practical problem.Fig.3shows the in uence of parameter on the fre-quency response of (1) ; for a given .It is seen that the frequency response is very sensitive to the change of value.With the decrease of ,the peak of frequency response moves from the high frequency region to the low frequency one.At the limit of →0,the frequencyZ.J.Hou,G.W.Wei /Pattern Recognition 35(2002)1559–15701563Fig.3.Frequency response of DSCED 1with di erent values ( =2).response localizes at a very low frequency region.Ob-viously,the DSC parameter can be utilizedto achievean optimal frequency selection in a practical applica-tion.For example,in many problems,the object to be processedmay be corruptedby noise whose frequency distribution mainly concentrates in the high frequency region.Therefore,a small value can be usedto avoid the noise corruption.For noise free images,the n th order ÿne-scale DSC edge detector (DSCED n )is given by DSCED n (x i ;y j )=W n k =−W n (n ) n ; n (x i −x k )I (x k ;y j )+ W n l =−W n (n ) n ; n (y j −y l )I (x i ;y l );n =1;2;:::;(11)where I is a digital image.In principle,all derivatives (n =1;2;:::)can be employed for edge detection and in general,an appropriate linear combination of them may be requiredbecause image ed ges can exhibit vari-ous shapes.Nevertheless,in most situations,DSCED 1is quite su cient andvery easy to implement.These ed ge detectors are capable of extracting ÿne details.However,they perform less well for images that are corruptedwith much noise.Due to the possible presence of noise,the deÿnition of image edge is not unique and ÿnding edge by di erenti-ation is an ill-posedproblem in a d igital image.Essen-tially,the di erential operator is deÿned based on contin-uous and di erentiable functions.Its discrete version,the di erence operation (or di erence operator as referred in the literature),is strictly applicable only to those sets of discrete values that are attained by the appropriate dis-cretization of the original continuous andd i erentiable functions.Therefore,we deÿne edges at di erent levels of scales andwe call them multiscale ed ges.The con-cept of multiscale edges has an advantage that one can locate an edge at selected scale which is comparable to the physical extension of the feature.A ÿne-scale edge detector,as given in Eq.(11),is capable of extracting features at all scales,though it is sensitive to noise.How-ever,a coarse-scale edge detector is not too sensitive to ÿne details and is capable of performing well under noisy conditions.One way to extract the present multi-scale edges is to use the wavelet multiresolution analysis.Another practical way for detecting multiscale edges is to construct edge detectors by a combination of ÿltering and edge detection.In the present work,the n th order DSC anti-noise edge detector (DSCANED n ),or the n th order coarse-scale DSC edge detector,is proposed as DSCANED n (x i ;y j )= W n k =−W n W 0 l =−W 0 (n ) n ; n (x i −x k ) (0) 0; 0(y j −y l )I (x k ;y l )+ W 0 k =−W 0W nl =−W n (0) 0; 0(x i −x k ) (n ) n ; n (y j −y l )I (x k ;y l );n =1;2;::::(12)Note that the di erentiation matrices in Eqs.(11)and (12)are,in general,banded.This is advantageous in large-scale computations.Although the present DSCED n andDSCANED n are designed as ÿne and coarse edge detectors,respectively,they operate on the same grid.It is possible to carry out the operations after appropriate down samplings.This multiscale procedure may be better for detecting edges under noisy conditions.For simplicity,the details of this procedure are not presented in this paper.3.Results and discussionTo explore the utility andd emonstrate the e ciency of the proposedapproach,we carry out computer exper-iments on gray-level images.To this end,we select a few classes of standard images,which are either natural or human-made.A summary of the images used in the present study is plotted in Fig.4.The golfcar,boat and pitcher images are non-texturedhuman-mad e images andthe tire is a texturedhuman-mad e image.The egg andpepper images are natural andnon-texturedimages,andthe pinecone image is a natural andtexturedimage.The cameraman,Lena andB arbara images are ÿgure im-ages,of which the Barbara image contains line textures.The square is a synthetic image.The settings of these images vary from in-door scenes to out-door views.The1564Z.J.Hou,G.W.Wei /Pattern Recognition 35(2002)1559–1570Fig.4.A collection of sample images,where the ÿrst eight images are of the size of 512×512andthe last three are of 256×256.The ÿrst ten images are real ones andthe last one is synthetic.resolution of all images is 8-bit per pixel.The ÿrst eight images are of the size of 512×512pixels,while the last three images are of 256×256.For deÿniteness and sim-plicity,we set the parameter W =2for all experiments in this section.Most edge detection techniques utilize a post-processing thresholding immediately after feature ex-traction to thin and =or extended ge contours.There are many well-establishedthreshold ing [33,34]anded ge thinning techniques.In the present work,the edge detec-tion consists of two steps:edge magnitude calculation,andthreshold ing.For simplicity,a ÿxedthresholdis usedin the experiments,although there are ad aptive thresholding techniques that could be implemented.In general,there is no deÿnite “rule”to select a threshold for edge detection.A useful way is to “tune”the thresh-oldsuch that the resulting ed ge images have the same percentage of pixels in gradient images that are classiÿed as edge pixels.Unfortunately,there is no deÿnite rule to determine the percentage for a real image.A common practice is to assume the percentage of edge pixels is about 5–10%[20]for a normal image.In the present study,we set the percentage to 9%.The procedure d escribedhere is also appliedfor the implementation of other standard edge detectors,which are used for comparison in the present study.In the rest of this section,we conduct three groups of computer experiments to test the proposedapproach.Group one is designed to investigate the performance of the present algorithm on the edge detection of clean im-ages.Group two is to examine the ability of the presentalgorithm on extracting edges from noisy images.The last group is designed to objectively compare the perfor-mances of di erent edge detectors by using a computer generatedimage.They are,respectively,d escribedin the following three subsections.A brief discussion is given in the last subsection.3.1.Clean imagesIn this subsection,we examine the performance of the ÿne-scale edge detectors,DSCED 1.The DSCED 1used here is a 5×1mask.Two conventional approaches,the Sobel detector and the Prewitt detector,are also em-ployedfor comparison.It is well-known that both the Sobel andPrewitt d etectors are constructedby using the ÿnite di erence in one direction in association with a low-pass ÿlter in the normal direction for denoising.Fig.5presents a comparison of the performance of ÿve edge detectors on the sample images.Here,the ÿrst three columns are,respectively,obtainedby using theDSCED 1methodwith di erent parameters (Column 1: 1=3; 1=1:5;Column 2: 1=1; 1=1:5;Column 3: 1=1; 1=0:4).The performance of the Sobel andPre-witt detectors are given in the fourth and ÿfth columns,respectively.From Fig.5,we can see the impact of the parameters on the performance of DSCED 1.The edge map of Column 1is much sharper than that of Column 2.This is due to the fact that a smaller 1value leads to larger frequency response at the high frequency region,as shown in Fig.2b.As a result,unwantednoise-like ÿne structures are produced in Column 2.Z.J.Hou,G.W.Wei/Pattern Recognition35(2002)1559–15701565Fig.5.Edge images obtained by using di erent detectors.Columns1–3are obtained by using the DSCED1with di erent parameters (column1: 1=3; 1=1:5,column2: 1=1; 1=1:5,column3: 1=1; 1=0:4).Column4is obtainedby using the Sobel detector and column5by the Prewitt detector.As seen from Fig.3,a smaller 1value leads to a narrow bandfrequency response.Thus,tuning 1is an alternative way to improve the performance of DSCED1. The e ect of 1can be observedby a comparison between Columns2and3.Indeed,the performance of DSCED1 is improvedgenerally in Column3by using a smaller 1 value.The performance of DSCED1is further compared with that of standard methods,presented in the last two columns.The Sobel detector(Columns4)and Prewitt detector(Column5)provide similar results.The visual di erences between these results and those of DSCED1 in Columns1and3are marginal.B oth the Sobel and Prewitt detectors are two-dimensional(3×3),whereas the DSC detectors are one-dimensional(5×1).Therefore, the DSC detectors are slightly more e cient for edge detection of these images.It is notedthat none of the above-mentionedÿve ed ge detectors resolves the facial feature of the Barbara image, which is a well-known di cult case.To illustrate the po-tential of the DSC detectors,we also conduct two tests by using DSCANED1which couples a high-passÿlter with a low-pass one.The DSCANED1parameters are chosen as 1=2; 1=0:2; 0=3; 0=0;W n=2;n=0;1. These results are depicted in Fig.6,along with those ob-tainedby using the Sobel andPrewitt d etectors.Clearly, the DSC detector gives rise to excellent facial features for the Barbara image.3.2.Noisy imagesTo investigate the performance of the DSC algorithm under noisy environment,we consider a number of low grade images.Fig.7presents a summary of the noisy images,which are generated by adding independently, identically distributed(i.i.d.)Gaussian noise,and the peak-signal–noise-ratio(PSNR)for each image is16dB. Fig.8illustrates the resulting edge images detected from noisy environment,obtainedby DSCANED1(Column 1),the Sobel detector(Column2)and the Prewitt de-tector(Column3).The e ect of noise is signiÿcant and the“edges”re ecting small illumination changes are invisible.For deÿniteness and simplicity,DSCANED1 parameters remain the same as those speciÿedin the last subsection.It is possible that other combinations of the parameters couldd eliver similar results andthe DSCANED1parameters couldbe further optimizedto obtain a global optimal.A discussion of such a global optimization procedure is beyond the scope of the1566Z.J.Hou,G.W.Wei /Pattern Recognition 35(2002)1559–1570Fig.6.A comparison of edge images obtained by using di erent detectors.Column 1:the DSCANED 1;column 2:the Sobel detector;column 3:the Prewittdetector.Fig.7.A collections of noisy sample images (PSNR =16dB).present work,andthe interestedread ers are referredto Ref.[15].In general,the detected edges are blurred due to the presence of noise.The two conventional detectors,the Sobel and Prewitt,detect not only spatially extendededges,but also many spurious features due to noise.As a result,the contrast of their edge images is poor.In con-trast,much sharper edge images are successfully attained by the DSC detector,as shown in Column 1of Fig.8.The di erence in contrast stems from the fact that the DSCANED 1detects edges at a coarse scale,in which the high frequency noise has been remarkably smoothedout.As mentioned in the introduction,the Canny detec-tor [15]was formulatedas an optimization problem for being usedund er noise environment.It was pointed out by Srinivasan et al.[35]that the Canny detector can be e ciently approximatedby the following two ÿlters [35]:C 1=−x2e −(x 2+y 2)=2 2;(13)C 2=−y2e −(x 2+y 2)=2 2;(14)which represent,respectively,the edge detectors along the horizontal andvertical d irections.The parameter is taken as =1:5,which,as suggestedby other re-searchers [35,36],is nearly optimal in association with a 5×5mask.The resulting edge images are included in Column 4of Fig.8for a comparison.Obviously,there is no visual di erence between those obtained by using the DSC detector and the Canny detector.These exper-iments indicate the performance of the DSC based edge detector is as good as that of the Canny detector.3.3.An objective comparisonTo validate the DSC detector further,we present an alternative evaluation in this subsection.Edge detection systems couldbe comparedin many ways.For exam-ple,the image gradients may be compared visually [36],Z.J.Hou,G.W.Wei/Pattern Recognition35(2002)1559–15701567Fig.8.Edge images of the noisy sample images,column1–4are obtained by using,respectively,the DSCANED1,the Sobel detector,the Prewitt detector and the Canny detector.where an edge image is evaluated by a group of peopleandthe average score couldbe an ind ex of quality.Forsynthetic images,where the exact location of edges isknown,Abd ou andPratt[37]proposedaÿgure of meritto objectively evaluate the performance of edge detec-tors.Theirÿgure of merit is deÿned asF=1max(N I;N D)N Di=111+ d2i;(15)where d i is the distance between a pixel declared as edge point and the nearest ideal edge pixel, is a penalty constant,N I and N D are the numbers of ideal and detected edge pixels respectively.It is a common practice to eval-uate the performance of an edge detector for synthetic images by introducing random noise in the images.A plot of F against the peak-signal–noise-ratio gives the degradation in the performance of the detector.The value of F is less than or equal to1.The larger the value,the better the performance.Performance comparison is basedon a synthetic square image,as shown in Fig.6.Theÿgure of merit F for each of the methods studied is calculated with respect to d i erent PSNR,andthe results are plottedin Fig.9. When the noise level is low,the F values are very close to1andthe performances of all the four d etectors are1568Z.J.Hou,G.W.Wei /Pattern Recognition 35(2002)1559–1570Fig.9.The ÿgure of merit for the synthetic square image.Triangle:the DSCANED 1;star:the Canny detector;plus:the Prewitt detector;circle:the Sobel detector.very satisfactory.With the increase of the noise level,the F values of two di erence detectors decrease,and are less than 0.5when PSNR is about 10dB.In contrast,the Canny detector and the DSC detector achieve large F values over the domain of interest,suggesting their superiority to other two detectors.It is noted that the performance of ANDSCED 1is better than that of the Canny detector for small PSNR values.3.4.DiscussionIn the presence of noise,the direct application of the di erentiation operation in edge detection will encounter di culty,as illustrated by the preceding experiments.The di erentiation operation is sensitive to noise and the problem is mathematically ill-posed.To o set the e ect of noise,a direct approach is to remove noise before the di erentiation,usually by convolving the raw input image with a Gaussian function,which leads to the well-known Marr’s detector [27].This problem can also be solvedby using regularization techniques d eveloped for dealing with mathematically ill-posed problems [14].Poggio et al.[38]provedthat the variational formula-tion of Tikhonov regularization leads to a Gaussian-like convolution ÿlter.In the present method,the idea todeal with noise basically falls into this framework,i.e.taking di erentiation after a low-pass ÿlter con-volution.It is well-known that the performance of the Canny detector depends on the computational bandwidth W and standard deviation .These parameters can be utilized to obtain edges which is optimized with respect to the space of parameters ( ∈R +;W ∈Z +)for each given im-age.In particular,the parameter gives rise to excel-lent time–frequency localization.However,the Canny ÿlter does not provide much freedom for frequency se-lection.In contrast to the Canny detector,the DSC de-tector has one more parameter, ,which is very e cient for frequency selection as shown in Fig.3.Thus,DSC detector should perform at least as well as the Canny detector.B oth the Canny andDSC d etectors have a parameter n which a ects signiÿcantly the time–frequency local-ization of the ÿlter,as can be seen from Fig.2.The Gaus-sian factor determines the regularity and smoothness of the DSC kernel andcan be usedto suppress spurious oscillations,i.e.,the Gibbs phenomenon,which is un-wantedin many applications,such as image processing,audio ÿltering and numerical computation.Appropriate choice of n can judiciously balance between the degree。

一种新的提取轮廓特征点的方法
陈燕新;戚飞虎
【期刊名称】《红外与毫米波学报》
【年(卷),期】1998(017)003
【摘要】给出了一种新的提取轮廓特征点的方法,该方法是通过考察以轮廓点为中心的圆盘内目标及背景所占面积大小来提取轮廓特征点的.理论和实验表明该方法不仅运算量小而且具有很好的检测及定位能力.
【总页数】6页(P171-176)
【作者】陈燕新;戚飞虎
【作者单位】上海交通大学计算机科学与工程系,上海,200030;上海交通大学计算机科学与工程系,上海,200030
【正文语种】中文
【中图分类】TB866
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