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(下個隨筆)。。。

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字圖像的一階梯度，常見的應用和物理意義是邊緣檢測。

函數：

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

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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33的矩陣（圖1）算子使用兩個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閾值，則認為該點為邊緣點

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Gx方向的相關模板：

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Gy方向的相關模板：

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具體計算如下：

圖像的每一個像素的橫向及縱向灰度值通過以下公式結合，來計算該點灰度的大小：

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通常，為了提高效率使用不開平方的近似值：

#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將像素值轉換為double型，不然計算后為負值的像素會被截斷為0 sobelx = cv.convertScaleAbs(sobelx) #轉換為uint8類型（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方向一起計算（效果不好，應分開計算，再求權重和） sobelxy11 = cv.convertScaleAbs(sobelxy11) sobelxy = cv.addWeighted(sobelx,0.5,sobely,0.5,0) #圖像權重和 cv.imshow("orginal",img) #dst = cv.addWidget(src1,alpha,src2,beta,gamma) cv.imshow("sobelx",sobelx) #src1 圖一 alpha->圖一的權重 src2->圖二 beta->圖二的權重 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函數同時對想x，y方向檢測的效果并不好，一般不用。

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scharr算子：

函數：

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sabel算子的增強，可以看到上圖中很多細小的邊緣都沒檢測到，那么scharr算子就是解決這個問題的，它比sabel算子更精確，速度和復雜程度卻一樣，只是因為用的核不一樣

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sabel算子的增強 scharr算子等價于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，只不過是用的二階微分，看官網的一些解釋：

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) #關鍵代碼就這兩行，拉普拉斯算子不用再求x，y的權重和，因為這個函數都計算好了 cv.imshow("orginal",img) cv.imshow("laplacian",r) cv.waitKey() cv.destroyAllWindows()

　　

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Canny邊緣檢測：

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

threshold1和threshold2是兩個閾值，越小檢測效果越好

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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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轉載于:https://www.cnblogs.com/ling2000/p/10588294.html

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