opencv的Sobel导数、Scharr滤波器、Laplacian算子、Canny边缘检测
本文主要对opencv的Sobel导数、Scharr滤波器、Laplacian算子、Canny边缘检测的函数进行简单的说明。
1、Sobel导数
索贝尔算子（Sobel operator）是图像处理中的算子之一，主要用作边缘检测。在技术上，它是一离散性差分算子，用来运算图像亮度函数的梯度之近似值。在图像的任何一点使用此算子，将会产生对应的梯度矢量或是其法矢量。Sobel导数结合了高斯平滑和微分求导。
假设被作用图像为 
:
-
在两个方向求导:
-
水平变化: 将
与一个奇数大小的内核 
进行卷积。比如，当内核大小为3时, 的计算结果为:
-
垂直变化: 将:math:I 与一个奇数大小的内核
进行卷积。比如，当内核大小为3时, 的计算结果为:
-
-
在图像的每一点，结合以上两个结果求出近似 梯度:
有时也用下面更简单公式代替:
Sobel
Calculates the first, second, third, or mixed image derivatives using an extended Sobel operator.
- C++: void Sobel (InputArray src, OutputArray dst, int ddepth, int dx, int dy, int ksize=3, double scale=1, double delta=0, int borderType=BORDER_DEFAULT ) ¶
-
Parameters: - 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 (seegetDerivKernels() for details).
- double类型的scale，计算导数值时可选的缩放因子，默认值是1，表示默认情况下是没有应用缩放的。我们可以在文档中查阅getDerivKernels的相关介绍，来得到这个参数的更多信息。
- delta – optional delta value that is added to the results prior to storing them in dst.
- borderType – pixel extrapolation method (see borderInterpolate for details).
In all cases except one, the 
separable kernel is used to calculate the derivative. When 
, the 
or 
kernel is used (that is, no Gaussian smoothing is done). ksize = 1 can only be used for the first or the second x- or y- derivatives.
#include
#include
using namespace cv;
int main(void)
{
Mat src = imread("2.jpg", 0);
if (!src.data) {
return -1;
}
namedWindow("Sobel", CV_WINDOW_AUTOSIZE);
imshow("yuan", src);
Mat grayx, grayy;
Mat absgrayx, absgrayy;
Mat dst;
Sobel(src, grayx, -1, 1, 0); //有的参数如果使用默认值，则可以不用写出。
convertScaleAbs(grayx, absgrayx);
Sobel(src, grayy, -1, 0, 1);
convertScaleAbs(grayy, absgrayy);
addWeighted(absgrayx, 1, absgrayy, 1, 0, dst);
imshow("Sobel", dst);
waitKey(0);
return 0;
}
图一：ksize =3时。
图二：ksize = 5时。
注：Sobel导数有一个非常好的性质，即可以定义任意大小的核，并且这些核可以用快速且迭代方式构造，大核对导数有更好的逼近，因为小核对噪声更敏感。
为了更好的理解以上内容，我们必须认识到一点，即Sobel导数并不是真正的导数，因为Sobel算子定义于一个离散的空间之上。Sobel算子真正表示的是多项式拟合，也就是说，x方向上的二阶导数并不是真正的二阶导数。他是对抛物线函数的局部拟合。
2、Scharr滤波器
当内核大小为 
时, 以上Sobel内核可能产生比较明显的误差(毕竟，Sobel算子只是求取了导数的近似值)。 为解决这一问题，OpenCV提供了 Scharr 函数，但该函数仅作用于大小为3的内核。该函数的运算与Sobel函数一样快，但结果却更加精确，其内核为:
Scharr
Calculates the first x- or y- image derivative using Scharr operator.
- C++: void Scharr(InputArray src, OutputArray dst, int ddepth, int dx, int dy, double scale=1, double delta=0, intborderType=BORDER_DEFAULT )
- Python: cv2.Scharr(src, ddepth, dx, dy[, dst[, scale[, delta[, borderType]]]]) → dst
-
Parameters: - src – input image.
- dst – output image of the same size and the same number of channels as src.
- ddepth – output image depth (see Sobel() for the list of supported combination of src.depth() andddepth).
- dx – order of the derivative x.
- dy – order of the derivative y.
- scale – optional scale factor for the computed derivative values; by default, no scaling is applied (seegetDerivKernels() 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).
The function computes the first x- or y- spatial image derivative using the Scharr operator. The call
is equivalent to
#include
#include
using namespace cv;
int main(void)
{
Mat src = imread("2.jpg", 0);
if (!src.data) {
return -1;
}
namedWindow("Sobel", CV_WINDOW_AUTOSIZE);
imshow("yuan", src);
Mat grayx, grayy;
Mat absgrayx, absgrayy;
Mat dst;
Scharr(src, grayx, -1, 1, 0);
//Sobel(src, grayx, -1, 1, 0, 3);
convertScaleAbs(grayx, absgrayx);
Scharr(src, grayy, -1, 0, 1);
//Sobel(src, grayy, -1, 0, 1, 3);
convertScaleAbs(grayy, absgrayy);
addWeighted(absgrayx, 1, absgrayy, 1, 0, dst);
imshow("Sobel", dst);
waitKey(0);
return 0;
}
图三：Scharr滤波器。
注：对于小核，Sobel算子的计数精度比较低。
对于3*3，Scharr滤波器同Sobel滤波器一样快，但精度更高。