【正文】 (一個像素寬度 )有更強的響 4 應。在孔中只嵌有一個黑色像素。嚴格地講，這里強調的是點的檢測。這里 T是一個非負門限， R由式()給出。照例，模板響應是它的中心位置。 間斷檢測 在本節(jié)中，我們介紹幾種用于檢測數(shù)字圖像中三種基本的灰度級間斷技術 :點、線和邊緣。關于門限處理的討論將在幾種面向區(qū)域的分割方法展開的討論之后進行。特別是邊緣檢測近年來已經成為分割算法的主題。第一類性質的應用途徑是基于亮度的不連續(xù)變化分割圖像，比如圖像的邊緣。在其他應用方面，比如自動目標采集，系統(tǒng)設計者無法對環(huán)境進行控制。精確的分割決定著計算分析過程的成敗。就是說當感興趣的對象已經被分離出來時就停止分割。從輸人輸出均為圖像的處理方法轉變?yōu)檩斎藶閳D像而輸出為從這些圖像中提取出來的屬性的處理方法〔這方面在 節(jié)中定義過 )。圖像分割是這一方向的另一主要步驟。例如，在電子元件的自動檢測方面，我們關注的是分析產品的圖像，檢測是否存在特定的異常狀態(tài)，比如，缺失的元件或斷裂的連接線路。因此，應該特別的關注分割的穩(wěn)定性。所以，通常的方法是將注意力集中于傳感器類型的選擇上，這樣可以增強獲取所關注對象的能力，從而減少圖像無關細節(jié)的影響。第二類的主要應用途徑是依據(jù)事先制定的準則將圖像分割為相似的區(qū)域，門限處理、區(qū)域生長、區(qū)域分離和聚合都是這類方法的實例。除了邊緣檢測本身，我們還會討論一些連接邊緣線段和把邊緣“組裝 ”為邊界的方法。之后，我們將討論一種稱為分水嶺分割法的形態(tài)學 2 圖像分割方法。尋找 間斷最一般的方法是以 一個模板進行檢測。有關執(zhí)行模板操作的細節(jié)在 ?；旧希@個公式是測量中心點和它的相鄰點之間加權的差值。即我們著重考慮的差別是那些足以識別為孤立點的差異 (由 T 決定 )。圖 102(c)是將點檢測模板應用于 X射線圖像后得到的結果 .圖 102(d)顯示了當 T取圖 102(c)中像素最高絕襯值的 90%時，應用式 ()所得的結果 (門限選擇將在 節(jié)中詳細討論 )。在一個不變的背景上，當線條經過模板的中間一行時會產生響應的最大值。第 3個模板對于垂直線有最佳響應 。注意每個模板系數(shù)相加的總和為零，表示在灰度級恒定的區(qū)域來自模板的響應為零。從左到右代表圖 103中模板的響應，這里 R 的值由式()給出。在這種情況下，我們應使用與這一方向有關的模板，并設置該模板的輸出門限，如式 ()所示。下列例子說明了這一過程?；谶@個假設，使用圖 103中最后一個模板。方向的部分產生了最強響應。圖 104(c)顯示了使門限等于圖像中最大值后得到的結果。的線段 (圖像中在左上象限中也有此方向上的圖像部分，但寬度不是一個像素 )。 邊緣檢側 盡管在任何關于分割的討論中，點和線檢測都是很重要的，但是邊緣檢測對 3 于灰度級間斷的檢測是 最為普遍的檢測方法。某些前面介紹的概念在這里為了敘述的連續(xù)性將進行簡要的重述。這些像素位于兩個區(qū)域的邊界上。 我們先從直觀上對邊緣建模開始。 實際上，光學系統(tǒng)、取樣和其他圖像采集的不完善性使得到的 邊緣是模糊的，模糊的程度取決于諸如圖像采集系統(tǒng)的性能、取樣率和獲得圖像的照明條件等因素。相反，現(xiàn)在邊緣的點是包含于斜坡中的任意點，并且邊緣成為一組彼此相連接的點集。 圖 106(a)顯示的圖 像是從圖 105(b)的放大特寫中提取出來的。在灰度級不變的區(qū)域一階導數(shù)為零。 斜坡部分與邊緣的模糊程度成正比 圖 106 (a)由一條垂直邊緣分開的兩個不同區(qū)域 ,(b)邊界附近的細 節(jié)顯示了一個灰度級剖面圖和一階與二階導數(shù)的剖面圖 由這些現(xiàn)象我們可以得到的結論是 :一階導數(shù)可以用于檢測圖像中的一個點是否是邊緣的點 (也就是判斷一個點是否在斜坡上 )。將在本節(jié)后面說明，二階導數(shù)的這個過零點的性質對于確定粗邊線的中心非常有用。 盡管到此為止我們的注意力被限制在一維水平剖面線范圍內，但同樣的結 論可以應用于圖像中的任何方向上。s with a line of a different gray level (say, 539。 Vertical 45176。 line detector. (c) Result of thresholding image. (b) produced the strongest responses in Fig. (b). In order to determine which lines best fit the mask, we simply threshold this image. The result of using a threshold equal to the maximum value in the image is 7 shown in Fig. (c).The maximum value is a good choice for a threshold in applications such as this because the input image is binary and we are looking for the strongest responses. Figure (c) shows in white all points that passed the threshold test. In this case, the procedure extracted the only line segment that was one pixel thick and oriented at 450 (the other ponent of the image oriented in this direction in the top, left quadrant is not one pixel thick). The isolated points shown in Fig. (c) are points that also had similarly strong responses to the mask. In the original image, these points and their immediate neighbors are oriented in such as way that the mask produced a maximum response at those isolated locations. These isolated points can be detected using the mask in Fig. (a) and then deleted, or they could be deleted using morphological erosion, as discussed in the last chapter. Edge Detection Although point and line detection certainly are important in any discussion on segmentation, edge detection is by far the most mon approach for detecting meaningful discontinuities in gray level. In this section we discuss approaches for implementing first and secondorder digital derivatives for the detection of edges in an image. We introduced these derivatives in Section in the context of image enhancement. The focus in this section is on their properties for edge detection. Some of the concepts previously introduced are restated briefly here for the sake continuity in the discussion. Basic formulation Edges were introduced informally in Section . In this section we look at the concept of a digital edge a little closer. Intuitively, an edge is a set of connected pixels that lie on the boundary between two regions. However, we already went through some length in Section to explain the difference between an edge and a boundary. Fundamentally, as we shall see shortly, an edge is a local concept whereas a region boundary, owing to the way it is defined, is a more global idea. A reasonable definition of edge requires the ability to measure graylevel transitions in a meaningful way. We start by modeling an edge intuitively. This will lead us to a formalism to 8 which meaningful transitions in gray levels can be measured. Intuitively, an ideal edge has the properties of the model shown in Figure (a). An ideal edge according to this model is a set of connected pixels (in the vertical direction here), each of which is located at an orthogonal step transition in gray level (as shown by the horizontal profile in the figure). In practice, optics, sampling, and other image acquisition imperfections yield edges that are blurred, with the degree of blurring being determined by factors. such as the quality of the image acquisition system, the sampling rate, and illumination conditions under which the image is acquired. As a result, edges are more closely modeled as hav