【正文】 ，通常采用梯度的方向，并利用此方向找到局部梯度模的最大值?；诹憬徊娴姆椒ㄕ业接蓤D像得到的二階導(dǎo)數(shù)的零交叉點(diǎn)來(lái)定位邊緣。通常用拉普拉斯算子或非線性微分方程的零交叉點(diǎn)，通常采用高斯濾波。已發(fā)表的邊緣檢測(cè)方法應(yīng)用計(jì)算邊界強(qiáng)度的度量， 這與平滑濾波有本質(zhì)的不同. 正如許多邊緣檢測(cè)方法依賴于圖像梯度的計(jì)算， 他們用不同種類的濾波器來(lái)估計(jì)x方向和y方向的梯度.一旦我們計(jì)算出導(dǎo)數(shù)之后，下一步要做的就是給出一個(gè)閾值來(lái)確定哪里是邊緣位置。閾值越低，能夠檢測(cè)出的邊線越多，結(jié)果也就越容易受到圖片噪聲的影響，并且越容易從圖像中挑出不相關(guān)的特性。與此相反，一個(gè)高的閾值將會(huì)遺失細(xì)的或者短的線段。如果邊緣閾值應(yīng)用于正確的的梯度幅度圖像，生成的邊緣一般會(huì)較厚，某些形式的邊緣變薄處理是必要的。然而非最大抑制的邊緣檢測(cè)，邊緣曲線的定義十分模糊，邊緣像素可能成為邊緣多邊形通過(guò)一個(gè)邊緣連接（邊緣跟蹤）的過(guò)程。在一個(gè)離散矩陣中，非最大抑制階梯能夠通過(guò)一種方法來(lái)實(shí)現(xiàn)，首先預(yù)測(cè)一階導(dǎo)數(shù)方向、然后把它近似到45度的倍數(shù)、最后在預(yù)測(cè)的梯度方向比較梯度幅度。一個(gè)常用的這種方法是帶有滯后作用的閾值選擇。這個(gè)方法使用不同的閾值去尋找邊緣。首先使用一個(gè)閾值上限去尋找邊線開始的地方。一旦找到了一個(gè)開始點(diǎn)，我們?cè)趫D像上逐點(diǎn)跟蹤邊緣路徑，當(dāng)大于門檻下限時(shí)一直紀(jì)錄邊緣位置，直到數(shù)值小于下限之后才停止紀(jì)錄。這種方法假設(shè)邊緣是連續(xù)的界線，并且我們能夠跟蹤前面所看到的邊緣的模糊部分，而不會(huì)將圖像中的噪聲點(diǎn)標(biāo)記為邊緣。但是，我們?nèi)匀淮嬖谶x擇適當(dāng)?shù)拈撝祬?shù)的問(wèn)題，而且不同圖像的閾值差別也很大。其它一些邊緣檢測(cè)操作是基于亮度的二階導(dǎo)數(shù)。這實(shí)質(zhì)上是亮度梯度的變化率。在理想的連續(xù)變化情況下，在二階導(dǎo)數(shù)中檢測(cè)過(guò)零點(diǎn)將得到梯度中的局部最大值。另一方面，二階導(dǎo)數(shù)中的峰值檢測(cè)是邊線檢測(cè)，只要圖像操作使用一個(gè)合適的尺度表示。如上所述，邊線是雙重邊緣，這樣我們就可以在邊線的一邊看到一個(gè)亮度梯度，而在另一邊看到相反的梯度。這樣如果圖像中有邊線出現(xiàn)的話我們就能在亮度梯度上看到非常大的變化。為了找到這些邊線，我們可以在圖像亮度梯度的二階導(dǎo)數(shù)中尋找過(guò)零點(diǎn)?？傊瑸榱藢?duì)有意義的邊緣點(diǎn)進(jìn)行分類，與這個(gè)點(diǎn)相聯(lián)系的灰度級(jí)變換必須比在這一點(diǎn)的背景上變換更為有效。由于我們用局部計(jì)算進(jìn)行處理，決定一個(gè)值是否有效的選擇方法就是使用門限。因此，如果一個(gè)點(diǎn)的二維一階導(dǎo)數(shù)比指定的門限大，我們就定義圖像中的此點(diǎn)是一個(gè)邊緣點(diǎn)。術(shù)語(yǔ)“邊緣線段”一般在邊緣與圖像的尺寸比起來(lái)很短時(shí)才使用。分割的關(guān)鍵問(wèn)題是如何將邊緣線段組合成更長(zhǎng)的邊緣。如果我們選擇使用二階導(dǎo)數(shù)，則另一個(gè)可用的定義是將圖像中的邊緣點(diǎn)定義為它的二階導(dǎo)數(shù)的零交叉點(diǎn)。此時(shí)，邊緣的定義同上面講過(guò)的定義是一樣的。應(yīng)注意，這些定義并不能保證在一幅圖像中成功地找到邊緣，它們只是給了我們一個(gè)尋找邊緣的形式體系。圖像中的一階導(dǎo)數(shù)用梯度計(jì)算，二階導(dǎo)數(shù)使用拉普拉斯算子得到。附錄2 英文參考資料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 twodimensional 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 puter. Note that a digital image is posed 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 putergenerated images. Thus, digital image processing enpasses 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 puter 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 puting 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 puter vision whose ultimate goal is to use puters 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 puter vision.There are no clearcut boundaries in the continuum from image processing at one end to puter vision at the other. However, one useful paradigm is to consider three types of puterized processes in this continuum: low, mid, and highlevel processes. Lowlevel processes involve primitive opera tions such as image preprocessing to reduce noise, contrast enhancement, and image sharpening. A lowlevel process is characterized by the fact that both its inputs and outputs are images. Midlevel 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 puter 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 ments, 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 enpasses processes whose inputs and outputs are images and, in addition, enpasses 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