圖像梯度的算法有很多方法：sabel算子，scharr算子，laplacian算子，sanny邊緣檢測(cè)(下個(gè)隨筆)。。。

這些算子的原理可參考：https://blog.csdn.net/poem_qianmo/article/details/25560901

下面是我的一些理解：

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sabel算子：

sobel算子主要用于獲得數(shù)字圖像的一階梯度，常見(jiàn)的應(yīng)用和物理意義是邊緣檢測(cè)。

函數(shù)：

Python: cv2.Sobel(src, ddepth, dx, dy[, dst[, ksize[, scale[, delta[, borderType]]]]]) → dst? （參數(shù)就不一一說(shuō)了，常用的就那幾個(gè)，其他默認(rèn)即可）

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Parameters:

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src – Source image. dst – Destination image of the same size and the same number of channels as src . ddepth – Destination image depth. xorder – Order of the derivative x. yorder – Order of the derivative y. ksize – Size of the extended Sobel kernel. It must be 1, 3, 5, or 7. scale – Optional scale factor for the computed derivative values. By default, no scaling is applied. See getDerivKernels() for details. delta – Optional delta value that is added to the results prior to storing them in dst . borderType – Pixel extrapolation method. See borderInterpolate() for details.

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原理

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算子使用兩個(gè)33的矩陣（圖1）算子使用兩個(gè)33的矩陣（圖1）去和原始圖片作卷積，分別得到橫向Ｇ（ｘ）和縱向Ｇ（ｙ）的梯度值，如果梯度值大于某一個(gè)閾值，則認(rèn)為該點(diǎn)為邊緣點(diǎn)

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Gx方向的相關(guān)模板：

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Gy方向的相關(guān)模板：

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具體計(jì)算如下：

圖像的每一個(gè)像素的橫向及縱向灰度值通過(guò)以下公式結(jié)合，來(lái)計(jì)算該點(diǎn)灰度的大小：

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通常，為了提高效率使用不開(kāi)平方的近似值：

#sobels算子 img = cv.imread("E:/pictures/lena.jpg",cv.IMREAD_UNCHANGED) sobelx= cv.Sobel(img,cv.CV_64F,1,0) #cv.CV_64F將像素值轉(zhuǎn)換為double型，不然計(jì)算后為負(fù)值的像素會(huì)被截?cái)酁? sobelx = cv.convertScaleAbs(sobelx) #轉(zhuǎn)換為uint8類(lèi)型（x方向） sobely = cv.Sobel(img,cv.CV_64F,0,1) sobely = cv.convertScaleAbs(sobely) sobelxy11 = cv.Sobel(img,cv.CV_64F,1,1) #直接x，y方向一起計(jì)算（效果不好，應(yīng)分開(kāi)計(jì)算，再求權(quán)重和） sobelxy11 = cv.convertScaleAbs(sobelxy11) sobelxy = cv.addWeighted(sobelx,0.5,sobely,0.5,0) #圖像權(quán)重和 cv.imshow("orginal",img) #dst = cv.addWidget(src1,alpha,src2,beta,gamma) cv.imshow("sobelx",sobelx) #src1 圖一 alpha->圖一的權(quán)重 src2->圖二 beta->圖二的權(quán)重 gamma->修正值 cv.imshow("sobely",sobely) #dst = src1*alpha+src2*beta+gamma cv.imshow("sobelxy",sobelxy) cv.imshow("sobelxy11",sobelxy11) cv.waitKey() cv.destroyAllWindows()

用sobel函數(shù)同時(shí)對(duì)想x，y方向檢測(cè)的效果并不好，一般不用。

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scharr算子：

函數(shù)：

Python: cv2.Scharr(src, ddepth, dx, dy[, dst[, scale[, delta[, borderType]]]]) → dst

Parameters:

src – Source image. dst – Destination image of the same size and the same number of channels as src . ddepth – Destination image depth. xorder – Order of the derivative x. yorder – Order of the derivative y. scale – Optional scale factor for the computed derivative values. By default, no scaling is applied. See getDerivKernels() for details. delta – Optional delta value that is added to the results prior to storing them in dst . borderType – Pixel extrapolation method. See borderInterpolate() for details.

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scharr算子是對(duì)sabel算子的增強(qiáng)，可以看到上圖中很多細(xì)小的邊緣都沒(méi)檢測(cè)到，那么scharr算子就是解決這個(gè)問(wèn)題的，它比sabel算子更精確，速度和復(fù)雜程度卻一樣，只是因?yàn)橛玫暮瞬灰粯?/span>

是scharr 的卷積核，他的原理和sabel算子一樣。

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#scharr算子 scharr算子是對(duì)sabel算子的增強(qiáng) scharr算子等價(jià)于ksize=-1的sabel算子 img = cv.imread("E:/pictures/lena.jpg",cv.IMREAD_GRAYSCALE) scharrx= cv.Scharr(img,cv.CV_64F,1,0) #scharrx算子要滿(mǎn)足dx>=0&&dy>=0&&dx+dy=1 scharrx = cv.convertScaleAbs(scharrx) scharry = cv.Scharr(img,cv.CV_64F,0,1) scharry = cv.convertScaleAbs(scharry) scharrxy = cv.addWeighted(scharrx,0.5,scharry,0.5,0) #sabel算子和 scharr算子的比較 sobelx= cv.Sobel(img,cv.CV_64F,1,0) sobelx = cv.convertScaleAbs(sobelx) sobely = cv.Sobel(img,cv.CV_64F,0,1) sobely = cv.convertScaleAbs(sobely) sobelxy = cv.addWeighted(sobelx,0.5,sobely,0.5,0) cv.imshow("orginal",img) cv.imshow("sobelxy",sobelxy) cv.imshow("scharrxy",scharrxy) cv.waitKey() cv.destroyAllWindows()

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laplacian算子：

Laplace算子和Sobel算子一樣，屬于空間銳化濾波操作，只不過(guò)是用的二階微分，看官網(wǎng)的一些解釋：

The function calculates the Laplacian of the source image by adding up the second x and y derivatives calculated using the Sobel operator:

This is done when ksize > 1 . When ksize == 1 , the Laplacian is computed by filtering the image with the following aperture:

cv.Laplace(src, dst, ksize=3) → None

Parameters:

src – Source image. dst – Destination image of the same size and the same number of channels as src . ddepth – Desired depth of the destination image. ksize – Aperture size used to compute the second-derivative filters. See getDerivKernels() for details. The size must be positive and odd. scale – Optional scale factor for the computed Laplacian values. By default, no scaling is applied. See getDerivKernels() for details. delta – Optional delta value that is added to the results prior to storing them in dst . borderType – Pixel extrapolation method. See borderInterpolate() for details.

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#拉普拉斯算子 img = cv.imread("E:/pictures/erode1.jpg",cv.IMREAD_GRAYSCALE) r = cv.Laplacian(img,cv.CV_64F) r = cv.convertScaleAbs(r) #關(guān)鍵代碼就這兩行，拉普拉斯算子不用再求x，y的權(quán)重和，因?yàn)檫@個(gè)函數(shù)都計(jì)算好了 cv.imshow("orginal",img) cv.imshow("laplacian",r) cv.waitKey() cv.destroyAllWindows()

　　

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Canny邊緣檢測(cè)：

Python: cv2.Canny(image, threshold1, threshold2[, edges[, apertureSize[, L2gradient]]]) → edges

threshold1和threshold2是兩個(gè)閾值，越小檢測(cè)效果越好

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import cv2 as cv import numpy as npimg = cv.imread("E:/pictures/lena.jpg") result1 = cv.Canny(img,50,100) result2 = cv.Canny(img,100,200) cv.imshow("orginal",img) cv.imshow("result1",result1) cv.imshow("result2",result2) cv.waitKey() cv.destroyAllWindows()

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轉(zhuǎn)載于:https://www.cnblogs.com/ling2000/p/10588294.html

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