//快速傅里叶变换
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);
}
//求傅里叶变换的幅度谱 amplitude spectrum
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);
}
//傅里叶谱的灰度级显示
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;
}
//求相位谱 phase spectrum
Mat phaseSpectrum(Mat _srcFFT)
{
//相位谱
Mat phase;
phase.create(_srcFFT.size(), CV_64FC1);
//分离通道
vector<Mat> FFT2Channel;
split(_srcFFT, FFT2Channel);
//计算相位谱
for (int r = 0; r<phase.rows; r++)
{
for (int c = 0; c < phase.cols; c++)
{
//实部 虚部
double real = FFT2Channel[0].at<double>(r, c);
double imaginary = FFT2Channel[1].at<double>(r, c);
// atan2 的返回值范围 [0,180] [-180,0]
phase.at<double>(r, c) = atan2(imaginary, real);
}
}
return phase;
}
int main(int argc, char*argv[])
{
//输入图像
Mat img = imread("lena.jpg", 0);
if (!img.data)
return -1;
//将图像转换为浮点型
Mat fImg;
img.convertTo(fImg, CV_64FC1, 1.0, 0);
//乘以 -1^(r+c)
int rows = fImg.rows;
int cols = fImg.cols;
for (int r = 0; r < rows; r++)
{
for (int c = 0; c < cols; c++)
{
if ((r + c) % 2)
fImg.at<double>(r, c) *= -1;
}
}
//快速傅里叶变换
Mat fft2;
fft2Image(fImg, fft2);
//傅里叶变换的幅度谱
Mat ampSpec;
amplitudeSpectrum(fft2, ampSpec);
//幅度谱的灰度级显示
Mat graySpec = graySpectrum(ampSpec);
imshow("幅度谱的灰度级显示", graySpec);
//相位谱
Mat phaSpec = phaseSpectrum(fft2);
//相位谱的灰度级显示
imshow("相位谱", phaSpec);
waitKey(0);
return 0;
}
原图：
傅里叶图：
中心化的可视化幅度谱：
相位谱：
