OpenCV 低通滤波（可设置频率）

#include
#include
#include
#include 
#include 
using namespace std;
using namespace cv;
int radius = 1;//截断频率
Mat img;
/*(理想低通滤波器，巴特沃斯低通滤波器，高斯低通滤波器)*/
enum LPFILTER_TYPE { ILP_FILTER = 0, BLP_FILTER = 1, GLP_FILTER = 2 };
void fft2Image(InputArray _src, OutputArray _dst);
Mat createLPFilter(Size size, float radius, int type, int n);
void callback_lpFilter(Mat src, int lpType, Mat&result);

int main()
{
    
    
    Mat img = imread("1.jpg", 0);
    //数据类型转换，转换为 浮点型
    Mat src_32;
    img.convertTo(src_32, CV_32FC1, 1.0, 0.0);
    /* -- 第二步：每一个数乘以(-1)^(r+c) -- */
    for (int r = 0; r < src_32.rows; r++)
    {
        for (int c = 0; c < src_32.cols; c++)
        {
            if ((r + c) % 2)
                src_32.at<float>(r, c) *= -1;
        }
    }
    /* -- 第三、四步：补零和快速傅里叶变换 -- */
    Mat src_dft;
    fft2Image(src_32, src_dft);
    //傅里叶谱
    int lpType = 0;
    Mat lowpass;
    callback_lpFilter(src_dft,lpType, lowpass);
    imshow("d", lowpass);
}
void fft2Image(InputArray _src, OutputArray _dst)
{
    //得到Mat类型
    Mat src = _src.getMat();
    //判断位深
    CV_Assert(src.type() == CV_32FC1 || src.type() == CV_64FC1);
    CV_Assert(src.channels() == 1 || src.channels() == 2);
    int rows = src.rows;
    int cols = src.cols;
    //为了进行快速的傅里叶变换，我们经行和列的扩充,找到最合适扩充值
    Mat padded;
    int rPadded = getOptimalDFTSize(rows);
    int cPadded = getOptimalDFTSize(cols);
    //进行边缘扩充,扩充值为零
    copyMakeBorder(src, padded, 0, rPadded - rows, 0, cPadded - cols, BORDER_CONSTANT, Scalar::all(0));
    //快速的傅里叶变换（双通道：用于存储实部 和 虚部）
    dft(padded, _dst, DFT_COMPLEX_OUTPUT);
}
//构造低通滤波器
Mat createLPFilter(Size size, float radius, int type, int n = 2)
{
    Mat lpFilter = Mat::zeros(size, CV_32FC1);
    int rows = size.height;
    int cols = size.width;
    if (radius <= 0)
        return lpFilter;
    //构造理想低通滤波器
    if (type == ILP_FILTER)
    {
        for (int r = 0; r < rows; r++)
        {
            for (int c = 0; c < cols; c++)
            {
                float norm2 = pow(abs(float(r - rows/2)), 2) + pow(abs(float(c - cols/2)), 2);
                if (sqrt(norm2) < radius)
                    lpFilter.at<float>(r, c) = 1;
                else
                    lpFilter.at<float>(r, c) = 0;
            }
        }
    }
    //构造巴特沃斯低通滤波器
    if (type == BLP_FILTER)
    {
        for (int r = 0; r < rows; r++)
        {
            for (int c = 0; c < cols; c++)
            {
                lpFilter.at<float>(r, c) = float(1.0 / (1.0 + pow(sqrt(pow(r - rows / 2, 2.0) + pow(c -cols/2, 2.0)) / radius, 2.0*n)));
            }
        }
    }
    //构造高斯低通滤波
    if (type == GLP_FILTER)
    {
        for (int r = 0; r < rows; r++)
        {
            for (int c = 0; c < cols; c++)
            {
                lpFilter.at<float>(r, c) = float(exp(-(pow(c - cols / 2, 2.0) + pow(r - rows/2, 2.0)) / (2 * pow(radius, 2.0))));
            }
        }
    }
    return lpFilter;
}
//低通滤波src傅里叶变换图像
void callback_lpFilter(Mat src,int lpType, Mat &result)
{
    /* -- 第五步：构造低通滤波器 -- */
    Mat lpFilter = createLPFilter(src.size(), radius, lpType, 2);
    /*-- 第六步：低通滤波器和图像快速傅里叶变换点乘 --*/
    Mat F_lpFilter;
    F_lpFilter.create(src.size(), src.type());
    for (int r = 0; r < F_lpFilter.rows; r++)
    {
        for (int c = 0; c < F_lpFilter.cols; c++)
        {
            //分别取出当前位置的快速傅里叶变换和理想低通滤波器的值
            Vec2f F_rc = src.at(r, c);
            float lpFilter_rc = lpFilter.at<float>(r, c);
            //低通滤波器和图像的快速傅里叶变换对应位置相乘
            F_lpFilter.at(r, c) = F_rc * lpFilter_rc;
        }
    }

    /* -- 第七、八步：对低通傅里叶变换执行傅里叶逆变换，并只取实部 -- */
    
    dft(F_lpFilter, result, DFT_SCALE + DFT_INVERSE + DFT_REAL_OUTPUT);
    /* -- 第九步：同乘以(-1)^(x+y) -- */
    for (int r = 0; r < result.rows; r++)
    {
        for (int c = 0; c < result.cols; c++)
        {
            if ((r + c) % 2)
                result.at<float>(r, c) *= -1;
        }
    }
    //注意将结果转换 CV_8U 类型
    result.convertTo(result, CV_8UC1, 1.0, 0);
    /* -- 第十步：截取左上部分,大小等于输入图像的大小 --*/
    
    
    
}