opencv - DFT

本文主要使用DFT相关函数实现对水平文本和旋转文本的DFT变换，在幅度谱中识别文本的变换，从而为图像旋转的检测和校正做准备。

#include "opencv2/core/core.hpp"
#include "opencv2/imgproc/imgproc.hpp"
#include "opencv2/highgui/highgui.hpp"
#include <iostream>

using namespace cv;
using namespace std;

void help(char* progName)
{
    cout << endl
        <<  "This program demonstrated the use of the discrete Fourier transform (DFT). " << endl
        <<  "The dft of an image is taken and it's power spectrum（功率谱) is displayed."          << endl
        <<  "Usage:"                                                                      << endl
        << progName << " [image_name -- default lena.jpg] "                       << endl << endl;
}

int main(int argc, char ** argv)
{
    help(argv[0]);
    const char* filename = argc >=2 ? argv[1] : "lena.jpg";

  /*  Mat I = imread(filename, CV_LOAD_IMAGE_GRAYSCALE);*/
    Mat I = imread(filename, 0);
    if( I.empty())
  {
    cout<<"Can't load image!"<<endl;
    return -1;
  }
  //填充输入图像到最优大小一般是2，3，5的倍数
    Mat padded; 
    int m = getOptimalDFTSize( I.rows );
    int n = getOptimalDFTSize( I.cols );
    
    //把填充边界置0
  copyMakeBorder(I, padded, 0, m - I.rows, 0, n - I.cols, BORDER_CONSTANT, Scalar::all(0));

  //因为图像的频域比空域范围更大，故把输入图像转换到浮点类型，
  //并用另一个通道扩展它。这样才可以存储复数值(实部和虚部)
    Mat planes[] = {Mat_<float>(padded), Mat::zeros(padded.size(), CV_32F)};
    Mat complexI;
    merge(planes, 2, complexI);//把0值添加到另一个扩充的平面


    //这样处理的结果可以适合原来的矩阵
    dft(complexI, complexI);


    //计算这个幅度并转换到log领域
    //log(1 + sqrt(Re(DFT(I))^2 + Im(DFT(I))^2))
  //planes[0] = Re(DFT(I)）实部, planes[1] = Im(DFT(I))虚部
  split(complexI, planes);  
    
  //planes[0] = magnitude幅度值
  magnitude(planes[0], planes[1], planes[0]);
    Mat magI = planes[0];

  //转换到log运算
    magI += Scalar::all(1); 
    log(magI, magI);

    //如果它由奇数个行或奇数个列，截取频谱
    magI = magI(Rect(0, 0, magI.cols & -2, magI.rows & -2));

    //重新分配傅里叶变换后图像的象限从而让图像原始(0，0)位置在图像中心
    int cx = magI.cols/2;
    int cy = magI.rows/2;

    Mat q0(magI, Rect(0, 0, cx, cy));   // Top-Left -每个象限创建一个感兴趣区域
    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

  //交换Ⅱ和Ⅳ象限位置(Top-Left with Bottom-Right)
    Mat tmp;    
    q0.copyTo(tmp);
    q3.copyTo(q0);
    tmp.copyTo(q3);

  //交换Ⅰ和Ⅲ象限位置(Top-Right with Bottom-Left)
    q1.copyTo(tmp); 
    q2.copyTo(q1);
    tmp.copyTo(q2);

  // Transform the matrix with float values into a
  // viewable image form (float between values 0 and 1).
    normalize(magI, magI, 0, 1, CV_MINMAX); 

    imshow("Input Image"       , I   );  
    imshow("spectrum magnitude", magI);
    waitKey();

    return 0;
}