【正文】 ly identified from the image background. So we adopt the bination of binary image and mathematical morphology to detect edge. It is called Binary morphology.Suppose that the region is shown in form of the set A. Its border is β（A）.B is an appropriate structure element, and it is symmetrical around the origin. Firstly we corrupt A with B recorded as A⊙B={x︱(B)x∈A},where (B)X is a translation B along the vector. The interior of region is available with A⊙B .And A( A⊙B) is the borderline naturally. Then β(A) is obtained. The equation of edge extraction can be said βA=A( A⊙B) . Structuring element is larger, the edge gained will be Wider. E. Simulative results analysisIn order to know about the advantages and disadvantages of these edge detection operators, we detect edge using these different operators respectively. The simulation results are shown in and . original image Binary image edge extractionFig. 9 detecting edge with Binary morphologyoriginal image roberts operator sobel operatorprewitt operator canny operator log operatorFig. 10 several edge detection algorithm parisonFrom the simulation results we can conclude that: the effect of detecting edge with sobel operator after wavelet denoising and with Binary morphology directly is better. So these two methods can be used. But finally we choose Binary morphology method based on specific measurement errors.IV. BORDERLINE CLOSED Although image is denoised before detecting edge, yet noises are still introduced when detecting edge. When noise exists, the borderline, which is obtained using derivative algorithm to detect image, usually produces the phenomenon of break. Under this situation, we need to connect the edge pixels. Thus, we will introduce a kind of method closing the borderline with the magnitude and direction of pixels gradient.The basis of connecting edge pixels is that they have definite similarity. Two aspects information can be gained using gradient algorithm to process image. One is the magnitude of gradient。因此，要對(duì)圖像進(jìn)行預(yù)處理以消除噪聲。通過設(shè)定閾值，把這些微分值視為邊緣強(qiáng)度采集點(diǎn)。對(duì)于連續(xù)函數(shù)，LOG算子在點(diǎn)(x,y)的定義為： (11)LOG算子是對(duì)圖像過濾和計(jì)數(shù)微分處理的過程。它可以檢測(cè)到真正的微弱邊緣。原始圖像 二值圖像 邊緣提取圖9 基于二值形態(tài)學(xué)的邊緣檢測(cè)原始圖像 羅伯茨算子 sobel 算子prewitt 算子 坎尼算子 log 算子圖10 幾種邊緣檢測(cè)算子比較從仿真結(jié)果可以得出結(jié)論：用Sobel算子和二值形態(tài)學(xué)方法檢測(cè)的邊緣效果都比較好。為了解決這個(gè)問題，本文中用小波變換來降噪。如果所有的邊緣像素連接起來，將得到閉合的邊界。內(nèi)部區(qū)域用A⊙B表示，并且A( A⊙B)是自然邊緣，然后β(A)可以求出。Canny算子的理論基礎(chǔ)如方程(12)至(15)所示 ：高斯函數(shù)： (12)正常邊緣： (13)邊緣增強(qiáng)： (14)最大增強(qiáng)： (15) 對(duì)二維圖像，Canny算子可以產(chǎn)生邊界梯度的方向和強(qiáng)度兩個(gè)信息。圖6 原始圖像圖7 邊緣檢測(cè)Sobel算子圖從模擬繪制的圖7中我們可以知道，邊緣的位置非常準(zhǔn)確。因此，邊緣檢測(cè)包含以下兩個(gè)部分：1）使用邊緣檢測(cè)算子提取邊緣點(diǎn)； 2）刪除一些邊緣點(diǎn)并對(duì)邊緣點(diǎn)進(jìn)行補(bǔ)充，進(jìn)行曲線擬合得到一條完整的邊界。用于邊緣檢測(cè)的算子包括微分算子，LOG算子，Canny算子和二值形態(tài)學(xué)算子。s blur and distortion, consequently it is very difficult to extract image feature. Moreover, due to such factors it is also difficult to detect edge. The method of image edge and outline characteristic39。邊緣特征提取已經(jīng)在許多領(lǐng)域廣泛應(yīng)用。因?yàn)檫吘壥悄繕?biāo)和背景的邊界，所以在數(shù)字圖像處理中邊緣檢測(cè)是非常重要的，并且只有在獲得圖像邊界以后，我們才能區(qū)分目標(biāo)和背景。Sobel算子具有和Prewitt算子類似的功能，Sobel算子在邊緣檢測(cè)的應(yīng)用中更廣泛。梯度是高斯濾波器的導(dǎo)數(shù)。假設(shè)該區(qū)域顯示形狀設(shè)為A，它的邊緣為β（A）。一種是大小梯度，另一種是方向梯度。例如，抑制噪聲和保持圖像細(xì)節(jié)不能同時(shí)達(dá)到最佳效果。四．邊界跟蹤 雖然在邊緣檢測(cè)之前已經(jīng)進(jìn)行了圖像去噪，但是當(dāng)進(jìn)行邊緣檢測(cè)時(shí)仍會(huì)引入噪聲。因此可以完成圖像的處理與分析。最后進(jìn)行二值化處理，連接邊緣點(diǎn)?；叶茸兓实姆较蛉绶匠?1)所示 ：?f?α=?f?xcosα+?f?ysinα (1)在連續(xù)的情況下，微分函數(shù)為：df=?f?xdx+?f?ydy，微分函數(shù)f(x,y) 的方向?qū)?shù)在某一時(shí)刻有最大值，這一點(diǎn)的方向是：arctan[?f?y/?f?x]，方向?qū)?shù)最大為：(?f?x)2+(?f?y)2，這一矢量的方向和模量稱為梯度函數(shù)f，即?fx,y=?f?x,?f?x，因此，算子的梯度模板方程如方程(2)所示:G[f(x,y)](?f?x)2+(?f?y)2 (2)對(duì)于數(shù)字圖像，梯度模板算子如方程（3）所示： (3)微分算子主要包括Roberts和Sobel算子。由于小波去噪使用不同的頻率帶通濾波器對(duì)信號(hào)濾波，它消除反映主要噪聲頻率的一些系數(shù)，保留下的系數(shù)參與完成逆變換，從而能很好的抑制噪聲。t achieve optimal effect simultaneously. Hence we will acquire satisfactory result if choosing suitable edge detection operator according to specific situation in practice.中文翻譯基于數(shù)字圖像處理技術(shù)的邊緣特征提取一．引言邊緣是指周圍像素灰度有階躍變化或屋頂變化的那些像