图像傅里叶变换与逆变换OpenCV实现

代码步骤:
读入图像->傅里叶变换->傅里叶逆变换->读取图像

int main()
{    
    cv::Mat img = cv::imread("lena.jpg");
    DFTtransform(img);
    cv::imshow("DFT img", img);
    cv::waitKey();
    system("pause");
    return 0;
}
//DFTtransform实现
void DFTtransform(cv::Mat& image)
{
    image.convertTo(image, CV_32F);
    std::vector channels;
    split(image, channels);  //分离RGB通道
    cv::Mat image_B = channels[0];
    //expand input image to optimal size
    int m1 = cv::getOptimalDFTSize(image_B.rows);  //选取最适合做fft的宽和高
    int n1 = cv::getOptimalDFTSize(image_B.cols);
    cv::Mat padded;
    //填充0
    cv::copyMakeBorder(image_B, padded, 0, m1 - image_B.rows, 0, n1 - image_B.cols, cv::BORDER_CONSTANT, cv::Scalar::all(0));
    cv::Mat planes[] = { cv::Mat_<float>(padded), cv::Mat::zeros(padded.size(), CV_32F) };
    cv::Mat complexI;
    cv::merge(planes, 2, complexI);  //planes[0], planes[1]是实部和虚部

    cv::dft(complexI, complexI, cv::DFT_SCALE | cv::DFT_COMPLEX_OUTPUT);
    cv::split(complexI, planes);

    //定义幅度谱和相位谱
    cv::Mat ph, mag, idft;
    cv::phase(planes[0], planes[1], ph);
    cv::magnitude(planes[0], planes[1], mag);  //由实部planes[0]和虚部planes[1]得到幅度谱mag和相位谱ph

    /*
    如果需要对实部planes[0]和虚部planes[1],或者幅度谱mag和相位谱ph进行操作,在这里进行更改
    */


    cv::polarToCart(mag, ph, planes[0], planes[1]);  //由幅度谱mag和相位谱ph恢复实部planes[0]和虚部planes[1]
    cv::merge(planes, 2, idft);
    cv::dft(idft, idft, cv::DFT_INVERSE | cv::DFT_REAL_OUTPUT);
    image_B = idft(cv::Rect(0, 0, image.cols & -2, image.rows & -2));
    image_B.copyTo(channels[0]);
    merge(channels, image);
    image.convertTo(image, CV_8U);
}

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