数字图像处理英文原版及翻译

Digital Image Processing and Edge Detection

Digital Image Processing

Interest in digital image processing methods stems from two principal application areas: improvement of pictorial information for human interpretation; and processing of image data for storage, transmission, and representation for autonomous 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, pixels, 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 high level processes. Low-level processes involve primitive opera- tions such as image preprocessing 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 (e.g., edges, contours, and the identity of individual objects). Finally, higher level 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 (e.g., 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, especially 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 are grouped 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 an 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 transmit it.Although 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 boundary of a region (i.e., 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 (e.g., “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 Fig 2 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 simple 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 connection 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 Fig 2 above by the use of double-headed arrows between the processing modules and the knowledge base, as opposed to single-headed arrows linking the processing modules.

Edge detection

Edge detection is a terminology in image processing and computer vision, particularly in the areas of feature detection and feature extraction, to refer to algorithms which aim at identifying points in a digital image at which the image brightness changes sharply or more formally has discontinuities.Although point and line detection certainly are important in any discussion on segmentation,edge detection 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:1.focal blur caused by a finite depth-of-field and finite point spread function; 2.penumbral blur caused by shadows created by light sources of non-zero radius; 3.shading at a smooth object edge; 4.local specularities or interreflections in the vicinity of object edges.

A typical edge might for instance be the border between a block of red color and a block of yellow. In contrast a line (as can be extracted by a ridge detector) 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.

If the intensity difference were smaller between the 4th and the 5th pixels and 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 edges.Hence, 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 zero-crossing 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 Laplacian of the zero-crossings of a non-linear differential expression, as will be described in the section on differential edge detection following below. As a pre-processing step to edge detection, a smoothing stage, typically Gaussian smoothing, is almost always applied (see also noise reduction).

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 noise, 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 thresholding with hysteresis. 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 rate of change 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 point.Since we are dealing with local computations,the method of choice to determine whether a value is “significant” or not id to use a threshold.Thus 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 edge.The term edge segment generally is used if the edge is short in relation to the dimensions of the image.A key problem in segmentation is to assemble edge segments into longer edges.An 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 derivative.The definition of an edge in this case is the same as above.It is important to note that these definitions do not guarantee success in finding edge in an image.They simply give us a formalism to look for them.First-order derivatives in an image are computed using the gradient.Second-order derivatives are obtained using the Laplacian.

数字图像处理和边缘检测

数字图像处理

在数字图象处理方法的兴趣从两个主要应用领域的茎：改善人类解释图像信息;和用于存储，传输，和表示用于自主机器感知图像数据的处理。

图像可以被定义为一个二维函数f（X，Y），其中x和y是空间（平面）的坐标，和f中的任何一对坐标（X，Y）的振幅被称为强度或灰度级在该点的图像的。当x，y 和f的振幅值都是有限的，离散的数量时，我们称之为图像的数字图像。数字图像处理领域是指由数字计算机的装置处理的数字图像。请注意，数字图像是由有限数量的元素，其中每一个具有特定的位置和值的。这些元件被称作象素，图像元素，像素和像素。象素是最广泛地用于表示一个数字图象的元件的术语。

视觉是最先进的我们的感官，所以这并不奇怪，图像在人类感知的一个最重要的角色。然而，与人类不同，谁被限定于电磁（EM）的可视带频谱，成像设备覆盖几乎整个电磁波谱，从伽马到无线电波。他们可以通过源生成的图像进行操作，人类是不习惯与图像相关联。这些包括超声，电子显微镜，以及计算机生成的图像。因此，数字图像处理包括广泛的应用和不同的领域。

有关于那里的图像处理站等相关领域，如图像分析和计算机VI-锡永，启动作者之间没有一致的。有时区分被定义图像处理作为一门学科，其中输入和处理的输出是图像进行。我们认为，这是一个限制的，有点人工边界。例如，这个定义下，即使计算图像的平均强度（它产生单号）的简单的任务将不被认为是一个图像处理操作。在另一方面，还有诸如计算机视觉，其最终目标是使用计算机来模拟人的视觉，包括学习和能够作出推断，并根据视觉输入的操作领域。这个区域本身是人工智能（AI），其目的是模仿人类智能的一个分支。 AI的领域是其最早在发展方面起步阶段的阶段，已经远远低于原先预期的进展。图像分析（也称为图像理解）的区域是在之间的图像处理和计算机视觉。

有一端与计算机视觉的其他在从图像处理连续无皆伐边界。然而，一个有用的范例是考虑三种类型的计算机化过程中这种连续：低，中和高一级的进程。低级别的过程涉及的原始操作系统蒸发散如图像预处理，以降低噪声，对比度增强和图像锐化。一个低级别的方法的特征在于以下事实既其输入和输出都是图像。上的图像中级处理涉及的任务，例如分割（分割图像划分成多个区域或对象），这些对象的描述，以减少他们适于计算机处理的形式，以及各个对象的分类（识别）。一个中层方法的特征在于以下事实，它的输入端通常是图像，但它的输出是从这些图像（例如，边缘，轮廓，和各个对象的身份）萃取属性。最后，更高层次的处理涉及“决策意识”识别出的对象的合奏的，如在图像分析，并且，在连续体的远端，执行通常与视觉有关的认知功能。

基于前述的评论，我们看到，图像处理和图像分析之间的重叠的逻辑位置是识别单个区域或物体的图像中的区域。因此，我们要求在这本书中的数字图像处理什么包括其输入和输出都图像，此外，包括从图像中提取的属性，直至并包括各个对象的识别过程的进程。作为一个简单的例子，以澄清这些概念，考虑文本的自动分析的面积。获取包含文本的区域的图像，预处理的图像，提取（分割）的单个字符，描述了适合计算机处理的形式特点，并认识到这些单个字符的过程是在我们所说的数字范围在这本书中的图像处理。网页的内容的决策意识可被视为在图像分析和甚至计算机视觉的领域之外，取决于复杂的由语句“决策意识”。作为隐含的水平不久将变得很明显，数字图像处理，如我们所定义的，是在广泛的范围内的特殊的社会和经济价值的领域成功地使用。

数字图像处理的应用的领域是如此不同，某种形式的组织是在试图捕获该区域的广度理想的。一来开发的图像处理应用的程度的一个基本的了解的最简单的方法是根据它们的来源（例如，视觉，X-射线，等）进行分类的图像。对于目前使用的图像的主要能量源是电磁能量光谱。能量的其他重要来源包括声学，超声，及电子（在电子显微镜中使用的电子束的形式）。合成影像，用于建模和可视化，由计算机生成的。在本节中，我们简要讨论的图像是如何在这些不同的类别和它们的应用领域中产生。

基于从电磁波谱的辐射图像是在X射线最熟悉的，尤其是图像和光谱的视觉频带。电磁铁集成电路波可概念化为传播不同波长的正弦波，或者它们可以被认为是无质量颗

粒的流，以波浪图案每行驶和以光的速度移动。每个无质量颗粒含有能量的一定量的（或束）。能量的每个束被称为一个光子。如果谱带是按照每光子能量分组，我们得到图2所示的光谱。下面，在一端向另一无线电波（最低能量）从伽马射线（最高能量）。该频带被阴影显示传达事实的电磁波谱的频带不分明而是从一个到另一个平滑地过渡。

图像采集是第一过程。还要注意被给予一个形象，已经在数字形式的收购可能是简单。通常，图像获取阶段涉及预处理，如缩放。

图像增强是数字图像处理的最简单和最吸引人的领域。基本上，后面增强技术的想法是带出被遮蔽，或简单地以突出的图像中感兴趣的特定特征的细节。增强一个熟悉的例子是，当我们增加，因为图像的对比度“它看起来更好。”为了记住，增强是图像处理的一个非常主观的领域是很重要的。图像复原是也与提高图像的外观涉及的区域。然而，与增强，这是主观的，图像恢复是客观的，在这个意义上，恢复技术往往是基于图像退化的数学或概率模型。增强，而另一方面，是基于对什么是“好”的增强效果人的主观偏好。

彩色图像处理是已经在重要性越来越受到由于在通过互联网的使用数字图像的显著增加的区域。它涵盖了在数字域颜色模型的一些基本概念和基本的色彩处理。颜色也被用于在后面的章节作为一个提取图像的感兴趣的特征的基础。

小波是代表不同程度分辨率影像的基础。特别是，这种材料是在这本书的图像数据压缩和金字塔形表示，在其中图像被依次细分成更小的区域中。

压缩，正如其名称所暗示的，以用于减少保存的图像，或发送它。虽然存储技术所需的带宽所需的存储技术涉及在过去十年中显著提高，同样不能说是为传输容量。这是真实的尤其是在互联网上，它的特征是显著图画内容的用途。图像压缩是熟悉的（也许无意中），以在图像文件的扩展，例如以JPEG（联合图像专家组）图像压缩标准中使用的JPG文件的扩展名的形式的计算机大多数用户。

形态处理与用于提取在代表性和形状的描述有用的图像组件工具交易。本章中的材料开始从图像输出到流程，输出图像属性工艺过渡。

分割程序分割图像成其组成部分或对象。在一般情况下，自主分割是在数字图像处理的最困难的任务之一。坚固的分割过程带来的过程向着要求对象单独确定成像问题成功解决一个很长的路要走。在另一方面，弱或不稳定的分割算法几乎总能保证最终失败。在一般情况下，更精确的分割，越容易识别是成功的。

表示和描述几乎总是跟随一个分割阶段，这通常是原始像素数据的输出，构成任一

区域的边界对齐（即，该组从另一分离一个图像区域中的像素的）在该区域或所有的点本身。在这两种情况下，将数据转换为适合于计算机处理的形式是必要的。必须作出的第一个决定是该数据是否应该被表示为边界或作为一个完整的区域。当重点是外部形状的特征，如角落和语调边界表示是适当的。当重点是内部属性，如纹理或骨骼形状的区域表示是适当的。在一些应用中，这些表示相互补充。选择的表示是只为反式形成原始数据转换成适合于随后的计算机处理的形式的解决方案的一部分。一种方法，也必须用于描述使感兴趣的特征被突出显示数据中指定。说明，也叫特征选择，处理与该提取导致一些感兴趣的定量信息或者基本从另一个区分一个类对象的属性。

识别是那一个标签（例如，“车辆”）分配给根据它的描述符的对象的过程。如前详细描述的，我们的结论我们的数字图像处理的覆盖率为识别各个对象的方法的发展。

到目前为止，我们已经避谈需要事先知识或有关的知识基础，并在上面的图2中的处理模块之间的交互。一个问题领域知识的知识数据库的形式被编码为图像处理系统。这方面的知识可以是详细说明，其中所感兴趣的信息是已知位于的图像的区域，从而限制了具有在寻求该信息来进行搜索一样简单。知识库也可以是相当复杂的，例如在材料的检查问题或含有与变化检测应用连接的区域的高分辨率卫星图像的图像数据库中的所有主要可能的缺陷的一个相互联系列表。除了引导每个处理模块的操作，知识库还控制模块之间的相互作用。这种区别在图2所使用的处理模块和知识库之间双头箭头所作以上，相对于单头箭联的处理模块。

边缘检测

边缘检测是在图像处理和计算机视觉一个术语，特别是在特征检测和特征提取的区域，是指算法，旨在在其中图像的亮度急剧或多个改变正式具有间断。虽然数字图像在识别点点和线检测当然是在上分割的任何讨论重要，边缘检测是迄今为止在灰度电平检测有意义的间断最常用的方法。

虽然某些文献认为是理想的台阶边缘的检测，从自然图像得到的边缘通常不是在所有理想台阶边缘。相反，它们通常受到一个或几个以下效果：由 1.焦点模糊深度的领

域和有限点扩散函数的有限; 2.半影带来的模糊由非零半径光源产生的阴影 3.在遮光光滑物体边缘; 4.本地镜面反射或interreflections在对象边缘的附近。。

例如一个典型的边缘可能是红色的块和黄色的块之间的边界。对比度的线（如可通过一个脊检测器中提取）可以在原本不变背景少数不同颜色的像素。对于线，有可能因此通常是在该行的每一侧一个边缘。

为了说明为什么边缘检测并不是一个简单的任务，让我们考虑在下面的一维信号检测边缘的问题。在这里，我们可直观地说，应该有第四和第五像素之间的边缘。

如果强度差分别为第4和第5个像素，并且如果邻近的相邻像素之间的强度差较高，这将不那么容易地说，应在相应区域的边缘之间较小。此外，人们可以说，这起案件是在其中有几个边缘。于是，牢固说明在两个相邻像素之间的强度发生多大变化必须是我们的一个特定的阈值的说，应该有这些像素之间的边缘并不总是一个简单的问题。事实上，这就是为什么边缘检测可以是不平凡的问题，除非在场景中的对象是特别简单和照明条件可以得到很好的控制的原因之一。

有边缘检测方法很多，但其中大部分可分为两大类，搜索和基于零交叉为主。基于搜索的方法，通过首先计算的边缘强度，通常一阶导数表达的措施，如梯度值，然后利用的当地方位的计算估计梯度幅度的局部方向最大值搜索检测边缘边缘，通常是梯度方向。过零基础的方法搜索过零点中，以便找到边缘，通常是非线性的差异表达的过零点的拉普拉斯的过零点从图像计算的第二阶导数的表达，如将下面跟随差分边缘检测的部分加以说明。作为前处理步骤，边缘检测，平滑阶段，典型高斯平滑，几乎总是施加（也见降噪）。

已经主要发表的边缘检测方法的种类平滑被应用的过滤器和边缘强度的措施被计算的方式有所不同。由于许多边缘检测方法依赖于图像梯度的计算，它们也不同用于在

x和y方向计算梯度估算类型的过滤器。

一旦我们计算的边缘强度（典型梯度大小）的测量，下一阶段是施加的阈值，来决定的边缘是否是在图像点存在与否。阈值越低，更多的边将被检测，其结果将越来越容易受到噪声，并且还从该图像拾取出不相关的特征。相反高的门槛可能会错过微妙的边缘，或导致支离破碎的边缘。

如果边缘阈值被施加到刚梯度幅值图像，所得到的边缘一般将厚减薄后处理某种类型的边缘的是必要的。对于非最大抑制然而检测到的边缘，边缘曲线的定义薄，边缘像素可通过边缘连接（边缘跟踪）的过程被链接到边的多边形。上的离散的网格中，非最大抑制阶段可以通过使用一阶导数估计梯度方向来实现，则梯度方向四舍五入至45度的倍数，最后比较所估计的梯度的梯度幅值的值方向。

常用的方法来处理相应的阈值阈值问题是通过使用阈值与迟滞。该方法使用多个阈值，以找到边缘。我们首先使用上阈值找到一个边缘的开始。一旦我们有一个起点，我们随后通过像素跟踪边缘的路径通过图像的像素，标记的边缘时，我们是上述的下限阈值。我们不再标志着我们的优势只有当值低于我们的门槛较低。这种方法使得假设边缘可能是在连续曲线，并允许我们按照我们先前看到的边缘的微弱部分，而不意味着图像中的每个噪声像素被标记为关闭为边缘。尽管如此，但是，我们必须选择合适的阈值参数的问题，并且适合阈值可以在图像上变化。

一些边缘检测算子在强度的二阶导数而不是基于。这实质上捕获的强度梯度的变化率。因此，在理想的连续的情况下，检测的过零点在第二衍生物捕获在梯度局部最大值。

我们可以得出的是，被分类为有意义的边缘点的结论，与该点相关联的灰度级过渡必须比在我们正在处理本地计算该点。自背景显著强，选择的方法确定值是否为“显著”与否id来使用阈值。从而我们的图像中定义的一个点作为是为边缘点，若其二维一阶导数大于连通的指定标准是更大通过定义一个边缘。这个术语边缘片段通常用于如果边缘是短相对于在分割的图片。这个关键问题的尺寸被组装边缘片段成更长边缘。用来替代定义，如果我们选择使用第二衍生物是简单地定义边缘点图像中作为在这种情况下的边缘的其第二衍生物。关于这个定义的过零点是一样。它重要的是要注意，这些定义并

不是成功的保证找到边缘在图片中。他们只是给我们一个形式主义寻找他们。一阶导数的图像中使用来计算使用拉普拉斯得到了梯度。再使用拉普拉斯得到二阶导数。