图像的频域变换

最新推荐文章于 2025-06-30 11:10:23 发布

一瞬秒年

最新推荐文章于 2025-06-30 11:10:23 发布

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分类专栏： OpenCV

本文链接：https://blog.youkuaiyun.com/guoruijiushiwo/article/details/75290700

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具体代码如下:

int main(int argc,char *argv[])
{
    Mat image = imread("/Users/hanoi/Desktop/lena.bmp",0);
    printf("width=%d,height=%d\n",image.rows,image.cols);
    
    Mat padded;
    int m = getOptimalDFTSize(image.rows);  // Return size of 2^x that suite for FFT
    int n = getOptimalDFTSize(image.cols);
    // Padding 0, result is @padded
    copyMakeBorder(image, padded, 0, m-image.rows, 0, n-image.cols, BORDER_CONSTANT, Scalar::all(0));
    
    // Create planes to storage REAL part and IMAGE part, IMAGE part init are 0
    Mat planes[] = {Mat_<float>(padded), Mat::zeros(padded.size(), CV_32F) };
    Mat complexI;
    merge(planes, 2, complexI);
    
    dft(complexI, complexI);
    
    // compute the magnitude and switch to logarithmic scale
    split(complexI, planes);
    magnitude(planes[0], planes[0], planes[1]);
    Mat magI = planes[0];
    
    // => log(1+sqrt(Re(DFT(I))^2+Im(DFT(I))^2))
    magI += Scalar::all(1);
    log(magI, magI);
    
    // crop the spectrum
    magI = magI(Rect(0, 0, magI.cols & (-2), magI.rows & (-2)));
    Mat _magI = magI.clone();
    normalize(_magI, _magI, 0, 1, CV_MINMAX);
    
    // rearrange the quadrants of Fourier image so that the origin is at the image center
    int cx = magI.cols/2;
    int cy = magI.rows/2;
    
    Mat q0(magI, Rect(0,0,cx,cy));    // Top-Left
    Mat q1(magI, Rect(cx,0,cx,cy));   // Top-Right
    Mat q2(magI, Rect(0,cy,cx,cy));   // Bottom-Left
    Mat q3(magI, Rect(cx,cy,cx,cy));  // Bottom-Right
    
    // exchange Top-Left and Bottom-Right
    Mat tmp;
    q0.copyTo(tmp);
    q3.copyTo(q0);
    tmp.copyTo(q3);
    
    // exchange Top-Right and Bottom-Left
    q1.copyTo(tmp);
    q2.copyTo(q1);
    tmp.copyTo(q2);
    
    normalize(magI, magI, 0, 1, CV_MINMAX);
    Mat magImg(magI.size(),CV_8UC1);
    magI.convertTo(magImg, CV_8UC1,255,0);
    imwrite("/Users/hanoi/Desktop/lena11.bmp", magImg);
    /*
    imshow("Input image", image);
    imshow("Spectrum magnitude before shift frequency", _magI);
    imshow("Spectrum magnitude after shift frequency", magI);
    
    Mat myImage;
    convertScaleAbs(magI, myImage);
    
    double min = 0.0;
    double max = 0.0;
    minMaxLoc(magI, &min, &max);
    double scale = 255.0 / (max - min);
    double shift = -min * scale;
    convertScaleAbs(magI, myImage,scale,shift);
    imwrite("/Users/hanoi/Desktop/lena11.bmp", myImage);
    waitKey();
    */
    return 0;
}

图像的频率是表征图像中灰度变化剧烈的程度的指标,是灰度在平面空间上的梯度，图像的边缘部分是突变部分，变化较快，因此反应在频域上的是高频分量，图像的噪声大部分情况下是高频部分，图像大部分平缓的灰度变化部分则为低频分量，也就是说，傅立叶变换提供了另外一个角度观察图像，可以将图像从灰度部分转化到频率分布来观察图像的特征。

频域在图像处理中，就我目前知道的用途，是图像的压缩和图像的去燥；

DFT算法的原理要求输入信号的长度是2^n,这样就可以以快速使用傅立叶变化算法(FFT)进行加速，所以程序中使用：

copyMakeBorder(image, padded, 0, m-image.rows, 0, n-image.cols, BORDER_CONSTANT, Scalar::all(0));