英文文獻(xiàn)及譯文

1、一個(gè)索貝爾圖像邊緣檢測(cè)算法描述1摘要：圖像邊緣檢測(cè)是一個(gè)確定圖像邊緣的過(guò)程，在輸入的灰度圖中的各個(gè)點(diǎn)尋找絕對(duì)梯度近似級(jí)對(duì)于邊緣檢測(cè)是非常重要的。為邊緣獲得適當(dāng)?shù)慕^對(duì)梯度幅度主要在與使用的方法。Sobel算子就是在圖像上進(jìn)行2-D的空間梯度測(cè)量。轉(zhuǎn)換2-D像素列陣到性能統(tǒng)計(jì)數(shù)據(jù)集提高了數(shù)據(jù)冗余消除，因此，作為代表的數(shù)字圖像，數(shù)據(jù)量的減少是需要的。Sobel邊緣檢測(cè)器采用一對(duì)3×3的卷積模板，一塊估計(jì)x方向的梯度，另一塊估計(jì)y方向的梯度。Sobel檢測(cè)器對(duì)于圖像中的噪音很敏感，它能有效地突出邊緣。因此，Sobel算子被建議用在數(shù)據(jù)傳輸中的大量數(shù)據(jù)通信。關(guān)鍵詞：圖像處理，邊緣檢測(cè)，Sobe

2、l算子，通信數(shù)據(jù)，絕對(duì)梯度幅度。引言圖像處理在現(xiàn)代數(shù)據(jù)儲(chǔ)存和數(shù)據(jù)傳輸方面十分重要，特別是圖像的漸進(jìn)傳輸，視頻編碼(電話會(huì)議)，數(shù)字圖書館，圖像數(shù)據(jù)庫(kù)以及遙感。它與處理靠算法產(chǎn)生所需的圖像有關(guān)(Milan et al., 2003)。數(shù)字圖像處理(DSP)提高了在極不利條件下所拍攝的圖像的質(zhì)量，具體方法有：調(diào)整亮度與對(duì)比度，邊緣檢測(cè)，降噪，調(diào)整重點(diǎn)，減少運(yùn)動(dòng)模糊等(Gonzalez, 2002)。圖像處理允許更廣泛的范圍被應(yīng)用到輸入數(shù)據(jù)，以避免如噪聲和信號(hào)失真集結(jié)在加工過(guò)程中存在的問題(Baker & Nayar, 1996)。在19世紀(jì)60年代的Jet Propulsion實(shí)驗(yàn)室，美國(guó)

3、麻省理工學(xué)院(MIT)，貝爾實(shí)驗(yàn)室以及一些其他的地方，數(shù)字圖像處理技術(shù)不斷發(fā)展。但是，因?yàn)楫?dāng)時(shí)的計(jì)算設(shè)備關(guān)系，處理的成本卻很高。隨著20世紀(jì)快速計(jì)算機(jī)和信號(hào)處理器的應(yīng)用，數(shù)字圖像處理變成了圖像處理最通用的形式，因?yàn)樗恢皇亲疃喙δ艿?，還是最便宜的。圖像處理過(guò)程中允許一些更復(fù)雜算法的使用，從而可以在簡(jiǎn)單任務(wù)中提供更先進(jìn)的性能，同時(shí)可以實(shí)現(xiàn)模擬手段不能實(shí)現(xiàn)的方法(Micheal, 2003)。因此，計(jì)算機(jī)搜集位表示像素或者點(diǎn)形成的圖片元素，以此儲(chǔ)存在電腦中(Vincent, 2006)。首先，圖像是在空間上的參數(shù)測(cè)量，而大多數(shù)的信號(hào)是在時(shí)間上的參數(shù)測(cè)量。其次，它們包含了大量的信息(Guthe和St

4、rasser, 2004)；圖像處理是當(dāng)輸入是圖像時(shí)的信息處理方式，就像是幀視頻；輸出不一定是圖像，也有可能是比如圖像的一個(gè)特征(Yuval, 1996)。大多數(shù)圖像處理技術(shù)包括把圖像視為一個(gè)二維信號(hào)，以及包括信號(hào)處理技術(shù)的應(yīng)用標(biāo)準(zhǔn)。這一過(guò)程涉及圖像的增強(qiáng)或操縱，導(dǎo)致產(chǎn)生另一圖像，冗余數(shù)據(jù)的清除和2-D像素陣列到靜態(tài)不相關(guān)數(shù)據(jù)集的轉(zhuǎn)化(Priotr, 2004)。由于圖像包含大量的冗余數(shù)據(jù)，學(xué)者們發(fā)現(xiàn)最重要的信息在它的邊緣(Canny, 1986)。邊作為像素的局部特征和最接近的近鄰，特征邊界(Chaug-Huang, 2002)。它們對(duì)應(yīng)于對(duì)象的界限，表面方向的改變和一個(gè)小幅度的對(duì)失敗的描述

5、。邊通常對(duì)應(yīng)圖像上的點(diǎn)，圖像上灰度明顯地從一個(gè)像素變化到下一個(gè)。邊代表圖像上具有很強(qiáng)對(duì)比度的區(qū)域;以圖像的邊緣代表一幅圖像有一個(gè)基本優(yōu)點(diǎn)，當(dāng)以高頻率保留圖像的大多數(shù)的重要信息時(shí)，數(shù)據(jù)量明顯的減少(Keren, Osadchy, & Gotsman, 2001)。因此，檢測(cè)邊緣幫助提取圖像突然變化區(qū)域的有用的信息特征(Folorunso et al., 2007)。邊緣檢測(cè)是一個(gè)定位圖像邊緣的一個(gè)過(guò)程。在一圖像中邊緣檢測(cè)是理解圖像特征的一個(gè)重要步驟。邊組成了有意義的特征并且包含了重要的信息。它顯著地減少了圖像尺寸的量并且過(guò)濾了一些可能被認(rèn)為相關(guān)性較小的信息，保持了一幅圖像的重要結(jié)構(gòu)特征(

6、Yuval, 1996)。當(dāng)圖像被改時(shí)，大多數(shù)的圖像包含一些當(dāng)邊被檢測(cè)或更換時(shí)被移走的冗余(Osuna etal., 1997)。消除冗余可以通過(guò)邊緣檢測(cè)來(lái)完成。當(dāng)進(jìn)行圖像邊緣檢測(cè)時(shí)，圖像中純?cè)诘拿恳环N冗余都被刪除(Sparr, 2000)。檢測(cè)圖像亮度的急劇變化的目的是要捕捉重要的事件。在保持重要結(jié)構(gòu)特征的前提下，對(duì)一幅圖像進(jìn)行邊緣檢測(cè)會(huì)大大減少要處理的數(shù)據(jù)量并且可能因此過(guò)濾掉那些被認(rèn)為不太有關(guān)的信息。圖像質(zhì)量反映了輸出邊緣的重要信息，并且圖像的尺寸是在減小的。這反過(guò)來(lái)又進(jìn)一步解釋了邊緣檢測(cè)是一種解決了高容量空間圖像占用電腦內(nèi)存的問題的方法。儲(chǔ)存，通過(guò)互聯(lián)網(wǎng)和寬帶傳輸這些問題在進(jìn)行邊緣檢測(cè)時(shí)

7、可以很簡(jiǎn)單的就解決掉(Vincent, 2007)。由于邊緣通常出現(xiàn)在圖像邊界地區(qū)，邊緣檢測(cè)被廣泛應(yīng)用在當(dāng)圖像被分成對(duì)應(yīng)不同對(duì)象區(qū)域的圖像分割。相關(guān)方法不同的方法被用于圖像處理上的邊緣檢測(cè)，其中有Roberts交叉算法。Robert將一幅照片處理成一個(gè)線條制圖，再將線條圖轉(zhuǎn)化成一個(gè)立體的圖像，最后從任何角度顯示所有刪除了的隱藏線條的三維結(jié)構(gòu)(Robert, 1965)。Roberts交叉算法執(zhí)行圖像上的二維空間梯度的卷積。其主要思想是呈現(xiàn)出水平和垂直邊緣，然后把邊緣檢測(cè)結(jié)果放在一起。這兩個(gè)過(guò)濾器突出了具有特殊頻率的區(qū)域，趨向于在圖像中定義一個(gè)物理邊緣。兩個(gè)過(guò)濾器被設(shè)計(jì)的目的是實(shí)現(xiàn)對(duì)圖像的角線邊

8、緣。由于Gy圖片呈現(xiàn)從右上角到左下方的邊，Gx圖像將闡明從左上角到右下角的對(duì)角線。這兩個(gè)獨(dú)立的Gx和Gy圖像使用近似公式相組合。Canny邊緣檢測(cè)算子是由John F發(fā)現(xiàn)的。在1986年，Canny使用多級(jí)算法來(lái)檢測(cè)圖像中廣范圍的邊。此外，Canny邊緣檢測(cè)器是一個(gè)復(fù)雜的最優(yōu)邊緣檢測(cè)器，它要花相當(dāng)長(zhǎng)的時(shí)間來(lái)得到計(jì)算結(jié)果。圖像首先通過(guò)高斯模糊來(lái)處理噪音。當(dāng)算法被應(yīng)用時(shí)，角度和大小被得到用來(lái)確定保留邊緣部分。設(shè)置兩個(gè)截止閥值點(diǎn)，當(dāng)圖像中的某些值低于第一個(gè)閥值時(shí)則降到零，當(dāng)值高于第二個(gè)閥值時(shí)提高到一。Canny(1986)認(rèn)為推導(dǎo)一個(gè)最佳的平滑的過(guò)濾器的數(shù)學(xué)問題是給出檢測(cè)的標(biāo)準(zhǔn)，定位以及減少單個(gè)邊的

9、多個(gè)響應(yīng)。他指出最佳過(guò)濾器給出的這些假設(shè)是四指數(shù)項(xiàng)的總和。他還表明這種過(guò)濾器可以很好的被逼近高斯一介導(dǎo)數(shù)。Canny還介紹了非最大抑制的概念，給出presmoothing過(guò)濾器，邊緣點(diǎn)被定義為梯度幅度上假定的一個(gè)在梯度方向最大的點(diǎn)。另一種被使用的算法是Susan邊緣檢測(cè)器。這種邊緣檢測(cè)算法跟著常用的算法獲取一幅圖像并且使用預(yù)先確定的窗口集中在圖像中的每個(gè)像素，該圖像使用本地代理的一套規(guī)則給出一個(gè)邊緣響應(yīng)(Vincent，2006)。該響應(yīng)再經(jīng)過(guò)處理得到作為邊集的輸出。Susan邊緣過(guò)濾器已經(jīng)通過(guò)使用圓形遮罩(內(nèi)核)以及近似的使用或常數(shù)加權(quán)或高斯加權(quán)而給出同位素反應(yīng)被實(shí)現(xiàn)。半徑通常是3.4像素，

10、給出37像素的遮罩，最小的遮罩被認(rèn)為是傳統(tǒng)的3.3遮罩。被使用在所有特征檢測(cè)實(shí)驗(yàn)中的37像素圓形遮罩被安放在圖像中的每個(gè)點(diǎn)上，對(duì)每個(gè)點(diǎn)來(lái)說(shuō)，遮罩上的每個(gè)像素的亮度被拿來(lái)與內(nèi)核進(jìn)行比較。比較方程是： C= (1)三維圖像中，的位置即是核所在的位置，是遮罩上的一些其他點(diǎn)的位置，I是像素的亮度，t是不同閥值上的亮度，C是對(duì)比后的輸出。對(duì)比是遮罩上每個(gè)像素之間的比較，而該遮罩上所有輸出(C)的n如下所示n=C (2)Sobel濾波器設(shè)計(jì)大多數(shù)的邊緣檢測(cè)方法只能在假設(shè)邊緣存在時(shí)使用，即在強(qiáng)度函數(shù)里有一個(gè)不連續(xù)段或圖像中有一個(gè)非常陡峭的強(qiáng)度梯度。使用這種假設(shè)，如果取得圖像強(qiáng)度值的導(dǎo)數(shù)并且找到最大導(dǎo)數(shù)的點(diǎn)，

11、那么邊緣就能確定了。梯度是一個(gè)向量，其組成部分測(cè)量在X和Y方向距離變化時(shí)如何快速地測(cè)出像素值。因此，梯度的部分也許可以通過(guò)使用下面的近似來(lái)找到： (3) (4)沿著X和Y方向，分別用d和d代表距離。在離散圖像中，像素兩點(diǎn)之間的成員組可以用d和d來(lái)代替。d=d=1(像素間距)像素坐標(biāo)上的點(diǎn)是(i，j)，因此 (5) (6)為檢測(cè)是否存在一個(gè)梯度間斷，可以計(jì)算（i，j）梯度上的變化。這可以通過(guò)尋找以下幅度測(cè)量來(lái)完成， M= (7)梯度方向可以通過(guò)下式得出： (8)濾波器的設(shè)計(jì)方法有許多方法可以檢測(cè)邊緣；多數(shù)的不同方法可以被分為這兩類：梯度：梯度方法通過(guò)尋找圖像的一階導(dǎo)數(shù)的最大值和最小值來(lái)檢測(cè)邊緣。

12、例如Roberts，Sobel檢測(cè)有非常尖銳邊緣的特征(見圖1)。拉普拉斯算子：拉普拉斯方法通過(guò)搜索圖像的二階導(dǎo)數(shù)上的零交叉點(diǎn)來(lái)尋找邊緣。例如希爾德雷斯，高斯的拉普拉斯等等。一個(gè)邊緣有一個(gè)坡道的一維形狀并且計(jì)算圖像導(dǎo)數(shù)可以突出其位置(見圖2)。邊的觀點(diǎn)依賴：當(dāng)視角變化是邊也可能變化，并且通常能反映幾何結(jié)構(gòu)，反過(guò)來(lái)也可以反映視角的性能比如表面標(biāo)志和表面形狀。相反的一個(gè)典型邊緣也許是介于紅色塊和黃色塊的邊界。然而，當(dāng)一個(gè)人看到圖像的像素時(shí)，一個(gè)邊的可見部分是夯實(shí)的。 輸入圖像 輸出邊圖1 梯度方法 輸入圖像 輸出邊緣圖2 拉普拉斯方法Sobel算子是梯度算法的一個(gè)例子。這個(gè)算子是一個(gè)離散的微分算子

13、，計(jì)算圖像強(qiáng)度函數(shù)的近似梯度(Sobel和Feldman，1968)。式(5)和(6)上的不同算子對(duì)應(yīng)于用下列標(biāo)志纏繞圖像。，如果這已經(jīng)完成，那么：1. 反過(guò)來(lái)，適當(dāng)遮掩的左上角是疊加在圖像的每個(gè)像素上。2. 通過(guò)使用像素值(i，j)的加權(quán)總和及他鄰居上的遮掩系數(shù)來(lái)得到和3. 這些遮掩被稱作卷積遮掩或有時(shí)也稱卷積內(nèi)核。梯度分量的近似可以分別沿45和135上的方向來(lái)得到，而不是尋找x或y方向上的近似梯度分量。這種情況下 (9) (10)算子的這種形式被稱為Roberts邊緣算子并且是被用來(lái)檢測(cè)圖像邊緣的第一個(gè)集的其中一個(gè)(Robert，1965)。相應(yīng)的卷積遮掩已給出： 和 通過(guò)面具的鄰居上的局

14、部平均值，使用較大規(guī)模的面具的優(yōu)勢(shì)是噪音影響產(chǎn)生的錯(cuò)誤降低了。使用奇數(shù)大小的面具的優(yōu)勢(shì)是算子是集中的，并且可以因此提供一個(gè)基于中心像素(i，j)的近似值。這類算子中的一個(gè)重要的邊緣算子是Sobel邊緣算子。Sobel邊緣算子的面具已給出： 該算子在每個(gè)點(diǎn)計(jì)算圖像強(qiáng)度的梯度，給出了從明到暗最可能增加的方向和在這方向上變化的速度。這結(jié)果因此顯示了圖像在那個(gè)點(diǎn)上如何“突然”或“順利”地變化，并且顯示代表邊緣的圖像的部分，同時(shí)顯示如何導(dǎo)向邊。在實(shí)踐中，規(guī)模(可能性邊緣)計(jì)算更可靠而且比方向計(jì)算更容易解釋。數(shù)學(xué)上，每幅圖像點(diǎn)上的一個(gè)二元函數(shù)(圖像的強(qiáng)度函數(shù))的梯度是一個(gè)2D向量，根據(jù)在水平和垂直方向上的

15、衍生物給出的分量。在每個(gè)圖像點(diǎn)上，梯度向量指向最可能增大強(qiáng)度的方向，在那個(gè)方向上梯度向量對(duì)應(yīng)的變化速度的長(zhǎng)度。這意味著在一些圖像點(diǎn)上的Sobel算子的結(jié)果，該圖像點(diǎn)是在不變的圖像強(qiáng)度為零向量的地區(qū)里，在邊緣的點(diǎn)上是一個(gè)通過(guò)邊緣的點(diǎn)的向量，從暗到明值。該邊緣檢測(cè)的Sobel模型發(fā)展的算法如下所示。Sobel邊緣檢測(cè)算法的偽代碼輸入：一幅簡(jiǎn)單圖像輸出：檢測(cè)出的邊第一步： 接收輸入的圖像第二步： 應(yīng)用輸入的圖像的模板第三步： 應(yīng)用Sobel邊緣檢測(cè)算法和梯度第四部： 輸入圖像中對(duì)應(yīng)G，G的模板控制第五部： 結(jié)合結(jié)果找到梯度的絕對(duì)大小 (11)第六步： 絕對(duì)量是輸出邊緣二階導(dǎo)數(shù)算子最大的一階導(dǎo)數(shù)將產(chǎn)生

16、在二階導(dǎo)數(shù)的零交叉上。為了得到水平和垂直的邊，我們期待在x及y方向上的二階導(dǎo)數(shù)。這是I的拉普拉斯： (12)拉普拉斯是線性和旋轉(zhuǎn)對(duì)稱。因此，如果圖像上的一個(gè)零交叉的搜索是高斯模型的第一平滑，那么可以用二階導(dǎo)數(shù)來(lái)計(jì)算出；或可以將圖像用高斯的拉普拉斯卷起。 (13)邊緣可以通過(guò)指定它的四個(gè)自由度來(lái)被仿照的：它的位置，方向，和步驟兩側(cè)的恒定強(qiáng)度。數(shù)據(jù)通過(guò)求適合圖像窗口的參數(shù)化模型的最小平方誤差來(lái)匹配，但這樣的做法是普遍的并且計(jì)算代價(jià)很大。通常所做的是圖像數(shù)據(jù)和模型在小窗口中被代表，通過(guò)在一個(gè)特定的二維正交級(jí)數(shù)膨脹上的一階導(dǎo)數(shù)系數(shù)。在這種情況下，優(yōu)化降低到一個(gè)變量：邊緣的方向。結(jié)果與討論Sobel算子

17、在圖像上進(jìn)行一個(gè)二維空間的梯度檢測(cè)。通常情況下，它被用來(lái)尋找輸入的灰度圖上每個(gè)點(diǎn)的近似絕對(duì)梯度幅度。Sobel邊緣檢測(cè)器使用了一對(duì)3*3的卷積模板，一個(gè)X方向上的估計(jì)梯度以及Y方向的其他估計(jì)梯度。卷積通常遠(yuǎn)小于實(shí)際圖像。因此，模板是一段時(shí)間里圖像操縱一個(gè)正方形像素的滑塊。模板是輸入圖像的像素值的改變區(qū)域的滑塊，然后轉(zhuǎn)移一個(gè)像素一直向右知道它到達(dá)一行的末尾，到下一行的開始時(shí)又自動(dòng)開始。值得注意的是第一行和最后一行的像素，以及第一和最后一列不能用3*3模板來(lái)操縱的列。這是因?yàn)榘涯０宓闹行挠玫谝恍械南袼貋?lái)替代，例如，模板會(huì)出到圖像邊界。當(dāng)G模板突出在垂直方向上的邊緣時(shí)G模板突出在水平方向上的邊緣。取

18、得兩者的幅度之后，產(chǎn)生的輸出在兩個(gè)方向上檢測(cè)邊緣。這是通過(guò)：（1） 應(yīng)用原始圖像的噪音平滑（2） 根據(jù)下面表一給出的結(jié)果所示的兩個(gè)內(nèi)核過(guò)濾原始圖像表一 兩核的濾波結(jié)果核1=核2=-101-1-2-1-202000-101121根據(jù)I和I（3） 估計(jì)每個(gè)像素上的梯度幅度： (14)（4） 如果G(i，j)>t，標(biāo)記像素為邊緣點(diǎn)，產(chǎn)生的結(jié)果如圖(表三)表三 圖像邊緣檢測(cè)邊緣檢測(cè)的實(shí)際意義和重要性Sobel邊緣檢測(cè)的下列優(yōu)點(diǎn)證明它優(yōu)于其他邊緣檢測(cè)技術(shù)：邊緣方向：算子的幾何決定在最敏感邊緣方向上的特征。算子可以被優(yōu)化來(lái)找水平，垂直或?qū)蔷€邊緣。噪聲環(huán)境：在有噪音環(huán)境下，邊緣檢測(cè)是困難的，除非噪音

19、和邊緣都包含高頻率的內(nèi)容。企圖減少噪音會(huì)產(chǎn)生模糊和扭曲的邊緣。被使用在含有噪音的圖像上通常是在更大的范圍才使用算子，所以它們可以平均足夠的數(shù)據(jù)來(lái)使局部噪聲產(chǎn)生折扣。這能導(dǎo)致檢測(cè)邊緣上的不夠準(zhǔn)確的定位。邊緣結(jié)構(gòu)：不是所有的邊緣都涉及強(qiáng)度的變化。比如折射或焦距不良的影響可能導(dǎo)致對(duì)象邊界通過(guò)強(qiáng)度上的逐步改變而被確定。算子是用來(lái)順應(yīng)這種逐漸變化的情況。更新的基于小波變換的技術(shù)實(shí)際上是為了區(qū)分每個(gè)邊緣的過(guò)度性質(zhì)的特征，例如，頭發(fā)的邊緣和臉的邊緣。邊緣在圖像處理的許多應(yīng)用上起著非常重要的作用，特別是為了分析控制光照條件下人造物體的場(chǎng)景的機(jī)器視覺系統(tǒng)。檢測(cè)一幅圖片的邊緣大大減少了數(shù)據(jù)量并且可以過(guò)濾掉無(wú)用的信

20、息，同時(shí)保留了圖像中的重要結(jié)構(gòu)性質(zhì)。因此，邊緣檢測(cè)是一種知識(shí)管理的形式。結(jié)論Sobel算子更能處理圖像上的二維空間梯度檢測(cè)。通常情況下它被用來(lái)尋找每個(gè)I點(diǎn)上的近似絕對(duì)梯度幅度，該I點(diǎn)為輸入灰度圖像上的點(diǎn)。Sobel邊緣檢測(cè)器使用一對(duì)3*3卷積模板，一個(gè)在X方向上的估計(jì)梯度，另一個(gè)在Y方向上的估計(jì)梯度。Sobel比其他算子比較容易實(shí)現(xiàn)。將一個(gè)二維像素陣列轉(zhuǎn)移成統(tǒng)計(jì)的不相關(guān)數(shù)據(jù)集可以增強(qiáng)去除冗余數(shù)據(jù)的能力，因此，數(shù)字圖像可以通過(guò)減少所需的數(shù)據(jù)量來(lái)表示?？紤]到數(shù)據(jù)通信特別是網(wǎng)絡(luò)，大規(guī)模數(shù)據(jù)傳輸會(huì)造成互動(dòng)網(wǎng)絡(luò)用戶的嚴(yán)重問題。邊緣檢測(cè)有助于優(yōu)化網(wǎng)絡(luò)寬帶，并且它還是跟蹤網(wǎng)絡(luò)流動(dòng)的數(shù)據(jù)是所需要的。它有助于為

21、模式識(shí)別提供有用的功能。即使Sobel算子比計(jì)算機(jī)更慢，但它的更大的卷積核使輸入圖像更大程度的平滑，并且可以因此使算子對(duì)噪聲減少敏感度。模板寬度越大，它對(duì)噪音的敏感度就越低，而且算子也可以類似邊緣產(chǎn)生跟高的輸出值。即使是在現(xiàn)實(shí)世界圖片的邊上，Sobel算子有效地突出了噪音，檢測(cè)到的邊可以很厚。Canny邊緣檢測(cè)器以及類似的算法解決了這些方法，通過(guò)第一次稍微的模糊圖像，而不是應(yīng)用算法試邊緣有效地變薄成一個(gè)像素。這可能是一個(gè)很慢的過(guò)程，因此，Sobel算子在圖像數(shù)據(jù)傳輸中發(fā)現(xiàn)海量數(shù)據(jù)通信時(shí)被強(qiáng)烈建議。Sobel算子是基于用小的，分離的，以及在水平和垂直方向上整數(shù)取值濾波器來(lái)卷積圖像的，因此，相對(duì)于

22、角度計(jì)算更便宜。另一方面，梯度近似產(chǎn)生相對(duì)粗陋，特別是圖像上的高頻率變化。外文原文A Descriptive Algorithm for Sobel Image Edge DetectionAbstract Image edge detection is a process of locating the edge of an image which is important in finding the approximate absolute gradient magnitude at each point I of an input grayscale image. The proble

23、m of getting an appropriate absolute gradient magnitude for edges lies in the method used. The Sobel operator performs a 2-D spatial gradient measurement on images. Transferring a 2-D pixel array into statistically uncorrelated data set enhances the removal of redundant data, as a result, reduction

24、of the amount of data is required to represent a digital image. The Sobel edge detector uses a pair of 3 x 3 convolution masks, one estimating gradient in the x-direction and the other estimating gradient in ydirection. The Sobel detector is incredibly sensitive to noise in pictures, it effectively

25、highlight them as edges. Hence, Sobel operator is recommended in massive data communication found in data transfer.Keywords: Image Processing, Edge Detection, Sobel Operator, Data Communication andAbsolute Gradient Magnitude.IntroductionImage processing is important in modern data storage and data t

26、ransmission especially in progressive transmission of images, video coding (teleconferencing), digital libraries, and image database, remote sensing. It has to do with manipulation of images done by algorithm to produce desired images (Milan et al., 2003). Digital Signal Processing (DSP) improve the

27、 quality of images taken under extremely unfavourable conditions in several ways: brightness and contrast adjustment, edge detection, noise reduction, focus adjustment, motion blur reduction etc (Gonzalez, 2002). The advantage is that image processing allows much wider range of algorithms to be appl

28、ied to the input data in order to avoid problems such as the build-up of noise and signal distortion during processing (Baker & Nayar, 1996). Many of the techniques of digital image processing were developed in the 1960's at the Jet Propulsion Laboratory, Massachusetts Institute of Technolog

29、y (MIT), Bell laboratory and few other places. But the cost of processing was fairly high with the computing equipments of that era.With the fast computers and signal processors available in the 2000's, digital image processing became the most common form of image processing and is general used

30、because it is not only the most versatile method but also the cheapest. The process allows the use of much more complex algorithms for image processing and hence can offer both more sophisticated performance at simple tasks, and the implementation of methods which would be impossible by analog means

31、 (Micheal, 2003). Thus, images are stored on the computers as collection of bits representing pixel or points forming the picture elements (Vincent, 2006). Firstly, images are a measure of parameter over space, while most signals are measures of parameter over time. Secondly, they contain a great de

32、al of information (Guthe & Strasser, 2004); image processing is any form of information processing for which the input is an image, such as frames of video; the output is not necessarily an image, but can be for instance be a set of features of the image (Yuval, 1996).Most image-processing techn

33、iques involve treating the image as a two-dimensional signal and applying standard signal-processing techniques to it. The process involves the enhancement or manipulation of an image which resulted in another image, removal of redundant data and the transformation of a 2-D pixel array into a static

34、ally uncorrelated data set (Priotr, 2004). Since images contain lots of redundant data, scholars have discovered that the most important information lies in it edges (Canny, 1986). Edges being the local property of a pixel and its immediate neighbourhood, characterizes boundary (Chaug-Huang, 2002).

35、They correspond to object boundaries, changes in surface orientation and describe defeat by a small margin. Edges typically correspond to points in the image where the gray value changes significantly from one pixel to the next. Edges represents region in the image with strong intensity contrast; re

36、presenting an image by its edges has the fundamental advantage that the amount of data is reduced significantly while retaining most of images vital information with high frequencies (Keren, Osadchy, & Gotsman, 2001). Thus, detecting Edges help in extracting useful information characteristics of

37、 the image where there are abrupt changes (Folorunso et al., 2007).Edge detection is a process of locating an edge of an image. Detection of edges in an image is a very important step towards understanding image features. Edges consist of meaningful features and contained significant information. It

38、s reduce significantly the amount of the image size and filters out information that may be regarded as less relevant, preserving the important structural properties of an image (Yuval, 1996). Most images contain some amount of redundancies that can sometimes be removed when edges are detected and r

39、eplaced, when it is reconstructed (Osuna et al., 1997). Eliminating the redundancy could be done through edge detection. When image edges are detected, every kind of redundancy present in the image is removed (Sparr, 2000).The purpose of detecting sharp changes in image brightness is to capture impo

40、rtant events. Applying an edge detector to an image may significantly reduce the amount of data to be processed and may therefore filter out information that may be regarded as less relevant, while preserving the important structural properties of an image. The image quality reflects significant inf

41、ormation in the output edge and the size of the image is reduced. This in turn explains further that edge detection is one of the ways of solving the problem of high volume of space images occupy in the computer memory. The problems of storage, transmission over the Internet and bandwidth could be s

42、olved when edges are detected (Vincent, 2007). Since edges often occur at image locations representing object boundaries, edge detection is extensively used in image segmentation when images are divided into areas corresponding to different objects.Related MethodsDifferent methods are used to detect

43、 edges in image processing among these is Roberts Cross Algorithms. Robert process a photograph into a line drawing, transform the line drawing into a three-dimensional representation and finally display the three-dimensional structure with all the hidden lines removed, from any point of view (Rober

44、t, 1965). The Roberts cross algorithm (Mario& Maltoni, 1997) performs a 2-D spatial gradient convolution on the image. The main idea is to bring out the horizontal and vertical edges individually and then to put them together for the resulting edge detection. The two filters highlight areas of h

45、igh special frequency, which tend to define the edge of an object in an image. The two filters are designed with the intention of bringing out the diagonal edges within the image. The Gx image will enunciate diagonals that run from thee top-left to the bottom-right where as the Gy image will bring o

46、ut edges that run topright to bottom-left. The two individual imagesGx andGy are combined using the approximation equationThe Canny edge detection operator was developed by John F. Canny in 1986 and uses a multistage algorithm to detect a wide range of edges in images. In addition, canny edge detect

47、or is a complex optimal edge detector which takes significantly longer time in result computations. The image is firstly run through a Gaussian blur to get rid of the noise. When the algorithm is applied, the angle and magnitude is obtained which is used to determine portions of the edges to retain.

48、 There are two threshold cut-off points where any value in the image below the first threshold is dropped to zero and values above the second threshold is raised to one.Canny (1986) considered the mathematical problem of deriving an optimal smoothing filter given the criteria of detection, localizat

49、ion and minimizing multiple responses to a single edge. He showed that the optimal filter given these assumptions is a sum of four exponential terms. He also showed that this filter can be well approximated by first-order derivatives of Gaussians. Canny also introduced the notion of non-maximum supp

50、ression, which means that given the presmoothing filters, edge points are defined as points where the gradient magnitude assumes a local maximum in the gradient direction.Another algorithm used is the Susan edge detector. This edge detection algorithm follows the usual method of taking an image and

51、using a predetermined window centered on each pixel in the image applying a locally acting set of rules to give an edge response (Vincent, 2006). The response is then processed to give the output as a set of edges. The Susan edge filter has been implemented using circular masks (kernel) to give isot

52、opic responses with approximations used either with constant weighting within it or with Gaussian weighting. The usual radius is 3.4 pixels, giving a mask of 37 pixels, and the smallest mask considered is the traditional 3´3 mask. The 37 pixels circular mask used in all feature detection experi

53、ments is placed at each point in the image and for each point the brightness of each pixel within the mask is compared with that of nucleus. The comparison equation isC= （1）whereis the position of the nucleus in the dimensional image,is the position of any other point within the mask, is the brightn

54、ess of any pixel, t is the brightness in difference threshold and C is the output of the comparison. This comparison is done for each pixel within the mask where total n of the outputs (c) is given asn=C （2）Sobel Filter DesignMost edge detection methods work on the assumption that the edge occurs wh

55、ere there is a discontinuity in the intensity function or a very steep intensity gradient in the image. Using this assumption, if one take the derivative of the intensity value across the image and find points where the derivative is maximum, then the egde could be located. The gradient is a vector,

56、 whose components measure how rapid pixel value are changing with distance in the x and y direction. Thus, the components of the gradient may be found using the following approximation: （3） （4）where dx anddy measure distance along the x and y directions respectively. In discrete images, one can consider dx and dy in terms of numbers of pixel between two points. dx = dy = 1 (pixel spacing) is the point at which pixel coordinates are(i, j ) thus, （5） （6）In order to detect the presence of a gradient discontinuity, one could calculate the change in thegradient at (i, j ) .This can be do