opencv-图像梯度（gradient）

前言：
目标：

• 寻找图像的梯度，边缘等
• 学习cv2.Sobel(),cv2.Scharr(),cv2.Laplacian()

Opencv有三种梯度滤波器或者说是高通滤波器，它们分别是：Sobel，Scharr，Laplacian。

Sobel Derivatives（导数）

cv2.Sobel(src, ddepth, dx, dy[, dst[, ksize[, scale[, delta[, borderType]]]]]) $\rightarrow$dst

• src – input image.

• dst – output image of the same size and the same number of channels as src .

• ddepth – output image depth; the following combinations of src.depth() and ddepth are supported:
  – src.depth() = CV_8U, ddepth = -1/CV_16S/CV_32F/CV_64F
  – src.depth() = CV_16U/CV_16S, ddepth = -1/CV_32F/CV_64F
  – src.depth() = CV_32F, ddepth = -1/CV_32F/CV_64F
  – src.depth() = CV_64F, ddepth = -1/CV_64F
  when ddepth=-1, the destination image will have the same depth as the source; in the case of 8-bit input images it will result in truncated derivatives.

• 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).

• ddepth的取值，主要是图像的深度。
  注意一点的是如果我们的像素数据类型为cv2.CV_8U或者np.uint8，这种数据类型是由黑色向白色变换的是正斜率，而白色向黑丝变换的是负斜率。所以在得到的梯度图像时，会有正数和负数之分。
  如果你想保存这两种变化得到的梯度，最好使用更高级的形式，比如cv2.CV_16S，cv2.CV_64F等等，取其绝对值然后将其转换为cv2.CV_8U就可以了。见下面的例子：
  

img = cv2.imread('box.png',0)
'单边灰度变换的边缘检测'
sobelx8u = cv2.Sobel(img,cv2.CV_8U,1,0,ksize=3)
'双边灰度变换的梯度检验'
sobelx64f = cv2.Sobel(img,cv2.CV_64F,1,0,ksize=5)
abs_sobel64f = np.absolute(sobelx64f)
sobel_8u = np.uint8(abs_sobel64f)

Laplacian Derivatives

拉普拉斯导数,其数学公式为： $\triangle src = \frac{\partial^2 src}{\partial x^2} + \frac{\partial^2 src}{\partial y^2}$
如果ksize = 1，则核为：
$k = \begin{bmatrix} 0 &1 &0 \\ 1& -4 &1 \\ 0&1 &0 \end{bmatrix}$