OpenCV 低通滤波

#include<opencv2/core/core.hpp>
#include<opencv2/highgui/highgui.hpp>
#include<opencv2/imgproc/imgproc.hpp>
using namespace std;
using namespace cv;
Mat I;//输入的图像矩阵
Mat F;//图像的快速傅里叶变换
Point maxLoc;//傅里叶谱的最大值的坐标
int radius = 20;//截断频率
const int Max_RADIUS = 100;//设置最大的截断频率
Mat lpFilter;//低通滤波器
int lpType = 0;//低通滤波器的类型
const int MAX_LPTYPE = 2;
Mat F_lpFilter;//低通傅里叶变换
Mat FlpSpectrum;//低通傅里叶变换的傅里叶谱灰度级
Mat result;//低通滤波后的效果
string lpFilterspectrum = "低通傅里叶谱";//显示窗口的名称
//快速傅里叶变换
void fft2Image(InputArray _src, OutputArray _dst);
//幅度谱
void amplitudeSpectrum(InputArray _srcFFT, OutputArray _dstSpectrum)
{
    //判断傅里叶变换是两个通道
    CV_Assert(_srcFFT.channels() == 2);
    //分离通道
    vector<Mat> FFT2Channel;
    split(_srcFFT, FFT2Channel);
    //计算傅里叶变换的幅度谱 sqrt(pow(R,2)+pow(I,2))
    magnitude(FFT2Channel[0], FFT2Channel[1], _dstSpectrum);
}
//幅度谱的灰度级显示
Mat graySpectrum(Mat spectrum)
{
    Mat dst;
    log(spectrum + 1, dst);
    //归一化
    normalize(dst, dst, 0, 1, NORM_MINMAX);
    //为了进行灰度级显示，做类型转换
    dst.convertTo(dst, CV_8UC1, 255, 0);
    return dst;
}
void callback_lpFilter(int, void*);
/*
低通滤波的类型：
(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 };
//构建低通滤波器
Mat createLPFilter(Size size, Point center, float radius, int type, int n = 2);
int main(int argc, char*argv[])
{
    /* -- 第一步：读入图像矩阵 -- */
    I = imread(argv[1], CV_LOAD_IMAGE_GRAYSCALE);
    if (!I.data)
        return -1;
    imwrite("I1.jpg", I);
    //数据类型转换，转换为 浮点型
    Mat fI;
    I.convertTo(fI, CV_32FC1, 1.0, 0.0);
    /* -- 第二步：每一个数乘以(-1)^(r+c) -- */
    for (int r = 0; r < fI.rows; r++)
    {
        for (int c = 0; c < fI.cols; c++)
        {
            if ((r + c) % 2)
                fI.at<float>(r, c) *= -1;
        }
    }
    /* -- 第三、四步：补零和快速傅里叶变换 -- */
    fft2Image(fI, F);
    //傅里叶谱
    Mat amplSpec;
    amplitudeSpectrum(F, amplSpec);
    //傅里叶谱的灰度级显示
    Mat spectrum = graySpectrum(amplSpec);
    imshow("原傅里叶谱的灰度级显示", spectrum);
    imwrite("spectrum.jpg", spectrum);
    //找到傅里叶谱的最大值的坐标
    minMaxLoc(spectrum, NULL, NULL, NULL, &maxLoc);
    /* -- 低通滤波 -- */
    namedWindow(lpFilterspectrum, WINDOW_AUTOSIZE);
    createTrackbar("低通类型:", lpFilterspectrum, &lpType, MAX_LPTYPE, callback_lpFilter);
    createTrackbar("半径:", lpFilterspectrum, &radius, Max_RADIUS, callback_lpFilter);
    callback_lpFilter(0, 0);
    waitKey(0);
    return 0;
}
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);
}
//回调函数：调整低通滤波的类型，及截断频率
void callback_lpFilter(int, void*)
{
    /* -- 第五步：构造低通滤波器 -- */
    lpFilter = createLPFilter(F.size(), maxLoc, radius, lpType, 2);
    /*-- 第六步：低通滤波器和图像快速傅里叶变换点乘 --*/
    F_lpFilter.create(F.size(), F.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 = F.at<Vec2f>(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<Vec2f>(r, c) = F_rc * lpFilter_rc;
        }
    }

    //低通傅里叶变换的傅里叶谱
    amplitudeSpectrum(F_lpFilter, FlpSpectrum);
    //低通傅里叶谱的灰度级的显示
    FlpSpectrum = graySpectrum(FlpSpectrum);
    imshow(lpFilterspectrum, FlpSpectrum);
    imwrite("FlpSpectrum.jpg", FlpSpectrum);
    /* -- 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 --*/
    result = result(Rect(0, 0, I.cols, I.rows)).clone();
    imshow("经过低通滤波后的图片", result);
    imwrite("lF.jpg", result);
}
//构造低通滤波器
Mat createLPFilter(Size size, Point center, 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 - center.y)), 2) + pow(abs(float(c - center.x)), 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 - center.y, 2.0) + pow(c - center.x, 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 - center.x, 2.0) + pow(r - center.y, 2.0)) / (2 * pow(radius, 2.0))));
            }
        }
    }
    return lpFilter;
}