图像滤波----低通滤波，中值滤波，高通滤波，方向滤波（Sobel），拉普拉斯变换

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①观察灰度分布来描述一幅图像成为空间域，观察图像变化的频率被成为频域。
②频域分析：低频对应区域的图像强度变化缓慢，高频对应的变化快。低通滤波器去除了图像的高频部分，高通滤波器去除了图像的低频部分。

(1)低通滤波
①栗子：

#include <iostream>#include <opencv2/core/core.hpp>#include <opencv2/imgproc/imgproc.hpp>#include <opencv2/highgui/highgui.hpp>int main(){    // Read input image    cv::Mat image= cv::imread("boldt.jpg",0);    if (!image.data)        return 0;     // Display the image    cv::namedWindow("Original Image");    cv::imshow("Original Image",image);  // Blur the image with a mean filter    cv::Mat result;    cv::blur(image,result,cv::Size(5,5))；       // Display the blurred image    cv::namedWindow("Mean filtered Image");    cv::imshow("Mean filtered Image",result);

结果：每个像素变为相邻像素的平均值， 快速的强度变化转化为平缓的过度

②栗子：近的像素添加更多的权重。：高斯滤波器

cv::GaussianBlur(image,result,cv::Size(5,5),1.5);

(2)中值滤波 ：非线性滤波
有效去除椒盐噪点

cv::medianBlur(image,result,5);

（3）方向滤波（Sobel）
强调图像中的高频分量，使用高通滤波器进行边缘检测。
Sobel算子是一种经典的边缘检测线性滤波器，可被认为是图像在垂直和水平方向变化的测量。

#include <iostream>#include <iomanip>#include <opencv2/core/core.hpp>#include <opencv2/imgproc/imgproc.hpp>#include <opencv2/highgui/highgui.hpp>#include "laplacianZC.h"int main(){     //Read input image    cv::Mat image= cv::imread("boldt.jpg",0);    if (!image.data)        return 0;     // Display the image    cv::namedWindow("Original Image");    cv::imshow("Original Image",image);    // Compute Sobel X derivative    cv::Mat sobelX;    cv::Sobel(image,sobelX,CV_8U,1,0,3,0.4,128);    // Display the image    cv::namedWindow("Sobel X Image");    cv::imshow("Sobel X Image",sobelX);    // Compute Sobel Y derivative    cv::Mat sobelY;    cv::Sobel(image,sobelY,CV_8U,0,1,3,0.4,128);    // Display the image    cv::namedWindow("Sobel Y Image");    cv::imshow("Sobel Y Image",sobelY);    // Compute norm of Sobel     得到sobel的摸    cv::Sobel(image,sobelX,CV_16S,1,0);    cv::Sobel(image,sobelY,CV_16S,0,1);    cv::Mat sobel;    //compute the L1 norm    sobel= abs(sobelX)+abs(sobelY);    double sobmin, sobmax;    cv::minMaxLoc(sobel,&sobmin,&sobmax);    std::cout << "sobel value range: " << sobmin << "  " << sobmax << std::endl;    // Print window pixel values    for (int i=0; i<12; i++) {        for (int j=0; j<12; j++)            std::cout << std::setw(5) << static_cast<int>(sobel.at<short>(i+135,j+362)) << " ";        std::cout << std::endl;    }    std::cout << std::endl;    std::cout << std::endl;    std::cout << std::endl;    // Conversion to 8-bit image    // sobelImage = -alpha*sobel + 255    cv::Mat sobelImage;    sobel.convertTo(sobelImage,CV_8U,-255./sobmax,255);    // Display the image    cv::namedWindow("Sobel Image");    cv::imshow("Sobel Image",sobelImage);    // Apply threshold to Sobel norm (low threshold value)    cv::Mat sobelThresholded;    cv::threshold(sobelImage, sobelThresholded, 225, 255, cv::THRESH_BINARY);    // Display the image    cv::namedWindow("Binary Sobel Image (low)");    cv::imshow("Binary Sobel Image (low)",sobelThresholded);    // Apply threshold to Sobel norm (high threshold value)    cv::threshold(sobelImage, sobelThresholded, 190, 255, cv::THRESH_BINARY);    // Display the image    cv::namedWindow("Binary Sobel Image (high)");    cv::imshow("Binary Sobel Image (high)",sobelThresholded);

结果：

（4）图像的拉普拉斯变换
是一种基于图像导数的高通线性滤波器，计算二阶倒数已衡量图像的弯曲度。

// Compute Laplacian 3x3    cv::Mat image = cv::imread("boldt.jpg", 0);    cv::Mat laplace;    cv::Laplacian(image,laplace,CV_8U,1,1,128);    // Display the image    cv::namedWindow("Laplacian Image");    cv::imshow("Laplacian Image",laplace);    // Print window pixel values    for (int i=0; i<12; i++) {        for (int j=0; j<12; j++)            std::cout << std::setw(5) << static_cast<int>(laplace.at<uchar>(i+135,j+362))-128 << " ";        std::cout << std::endl;    }    std::cout << std::endl;    std::cout << std::endl;    std::cout << std::endl;    // Compute Laplacian 7x7    cv::Laplacian(image,laplace,CV_8U,7,0.01,128);    // Display the image     cv::namedWindow("Laplacian Image");    cv::imshow("Laplacian Image",laplace);    // Print window pixel values    for (int i=0; i<12; i++) {        for (int j=0; j<12; j++)            std::cout << std::setw(5) << static_cast<int>(laplace.at<uchar>(i+135,j+362))-128 << " ";        std::cout << std::endl;    }    // Extract small window    cv::Mat window(image,cv::Rect(362,135,12,12));    cv::namedWindow("Image window");    cv::imshow("Image window",window);    cv::imwrite("window.bmp",window);    // Compute Laplacian using LaplacianZC class    LaplacianZC laplacian;    laplacian.setAperture(7);    cv::Mat flap= laplacian.computeLaplacian(image);    double lapmin, lapmax;    cv::minMaxLoc(flap,&lapmin,&lapmax);    std::cout << "Laplacian value range=[" << lapmin << "," << lapmax << "]\n";    laplace= laplacian.getLaplacianImage();    cv::namedWindow("Laplacian Image (7x7)");    cv::imshow("Laplacian Image (7x7)",laplace);    // Print Laplacian values    std::cout << std::endl;    for (int i=0; i<12; i++) {        for (int j=0; j<12; j++)            std::cout << std::setw(5) << static_cast<int>(flap.at<float>(i+135,j+362)/100) << " ";        std::cout << std::endl;    }    std::cout << std::endl;    // Compute and display the zero-crossing points    cv::Mat zeros;    zeros= laplacian.getZeroCrossings(lapmax);    cv::namedWindow("Zero-crossings");    cv::imshow("Zero-crossings",zeros);    // Compute and display the zero-crossing points (Sobel version)    zeros= laplacian.getZeroCrossings();    zeros= laplacian.getZeroCrossingsWithSobel(50);    cv::namedWindow("Zero-crossings (2)");    cv::imshow("Zero-crossings (2)",zeros);    // Print window pixel values    for (int i=0; i<12; i++) {        for (int j=0; j<12; j++)            std::cout << std::setw(2) << static_cast<int>(zeros.at<uchar>(i+135,j+362)) << " ";        std::cout << std::endl;    }    // Display the image with window    cv::rectangle(image,cv::Point(362,135),cv::Point(374,147),cv::Scalar(255,255,255));    cv::namedWindow("Original Image with window");    cv::imshow("Original Image with window",image);    cv::waitKey();    return 0;}