// Function calculates PSD(Power spectrum density) by fft with two flags
// flag = 0 means to return PSD
// flag = 1 means to return log(PSD)
public static void calcPSD(ref Mat inputImg, ref Mat outputImg, bool flag = false)
{
Mat[] planes = { new Mat <float>(inputImg.Clone()), Mat.Zeros(inputImg.Size(), MatType.CV_32F) };
Mat complexI = new Mat();
Cv2.Merge(planes, complexI);
Cv2.Dft(complexI, complexI);
Cv2.Split(complexI, out planes); // planes[0] = Re(DFT(I)), planes[1] = Im(DFT(I))
planes[0].Set <float>(0, 0);
planes[1].Set <float>(0, 0);
// compute the PSD = sqrt(Re(DFT(I))^2 + Im(DFT(I))^2)^2
Mat imgPSD = new Mat();
Cv2.Magnitude(planes[0], planes[1], imgPSD); //imgPSD = sqrt(Power spectrum density)
Cv2.Pow(imgPSD, 2, imgPSD); //it needs ^2 in order to get PSD
outputImg = imgPSD;
// logPSD = log(1 + PSD)
if (flag)
{
Mat imglogPSD = new Mat();
imglogPSD = imgPSD + Scalar.All(1);
Cv2.Log(imglogPSD, imglogPSD);
outputImg = imglogPSD;
}
}
public static void filter2DFreq(ref Mat inputImg, ref Mat outputImg, ref Mat H)
{
Mat[] planes = { new Mat <float>(inputImg.Clone()), Mat.Zeros(inputImg.Size(), MatType.CV_32F) };
Mat complexI = new Mat();
Cv2.Merge(planes, complexI);
Cv2.Dft(complexI, complexI, DftFlags.Scale);
Mat[] planesH = { new Mat <float>(H.Clone()), Mat.Zeros(H.Size(), MatType.CV_32F) };
Mat complexH = new Mat();
Cv2.Merge(planesH, complexH);
Mat complexIH = new Mat();
Cv2.MulSpectrums(complexI, complexH, complexIH, 0);
Cv2.Idft(complexIH, complexIH);
Cv2.Split(complexIH, out planes);
outputImg = planes[0];
}
public void Run()
{
Mat img = Cv2.ImRead(FilePath.Image.Lenna, ImreadModes.GrayScale);
// expand input image to optimal size
Mat padded = new Mat();
int m = Cv2.GetOptimalDFTSize(img.Rows);
int n = Cv2.GetOptimalDFTSize(img.Cols); // on the border add zero values
Cv2.CopyMakeBorder(img, padded, 0, m - img.Rows, 0, n - img.Cols, BorderTypes.Constant, Scalar.All(0));
// Add to the expanded another plane with zeros
Mat paddedF32 = new Mat();
padded.ConvertTo(paddedF32, MatType.CV_32F);
Mat[] planes = { paddedF32, Mat.Zeros(padded.Size(), MatType.CV_32F) };
Mat complex = new Mat();
Cv2.Merge(planes, complex);
// this way the result may fit in the source matrix
Mat dft = new Mat();
Cv2.Dft(complex, dft);
// compute the magnitude and switch to logarithmic scale
// => log(1 + sqrt(Re(DFT(I))^2 + Im(DFT(I))^2))
Mat[] dftPlanes;
Cv2.Split(dft, out dftPlanes); // planes[0] = Re(DFT(I), planes[1] = Im(DFT(I))
// planes[0] = magnitude
Mat magnitude = new Mat();
Cv2.Magnitude(dftPlanes[0], dftPlanes[1], magnitude);
magnitude += Scalar.All(1); // switch to logarithmic scale
Cv2.Log(magnitude, magnitude);
// crop the spectrum, if it has an odd number of rows or columns
Mat spectrum = magnitude[
new Rect(0, 0, magnitude.Cols & -2, magnitude.Rows & -2)];
// rearrange the quadrants of Fourier image so that the origin is at the image center
int cx = spectrum.Cols / 2;
int cy = spectrum.Rows / 2;
Mat q0 = new Mat(spectrum, new Rect(0, 0, cx, cy)); // Top-Left - Create a ROI per quadrant
Mat q1 = new Mat(spectrum, new Rect(cx, 0, cx, cy)); // Top-Right
Mat q2 = new Mat(spectrum, new Rect(0, cy, cx, cy)); // Bottom-Left
Mat q3 = new Mat(spectrum, new Rect(cx, cy, cx, cy)); // Bottom-Right
// swap quadrants (Top-Left with Bottom-Right)
Mat tmp = new Mat();
q0.CopyTo(tmp);
q3.CopyTo(q0);
tmp.CopyTo(q3);
// swap quadrant (Top-Right with Bottom-Left)
q1.CopyTo(tmp);
q2.CopyTo(q1);
tmp.CopyTo(q2);
// Transform the matrix with float values into a
Cv2.Normalize(spectrum, spectrum, 0, 1, NormTypes.MinMax);
// Show the result
Cv2.ImShow("Input Image", img);
Cv2.ImShow("Spectrum Magnitude", spectrum);
// calculating the idft
Mat inverseTransform = new Mat();
Cv2.Dft(dft, inverseTransform, DftFlags.Inverse | DftFlags.RealOutput);
Cv2.Normalize(inverseTransform, inverseTransform, 0, 1, NormTypes.MinMax);
Cv2.ImShow("Reconstructed by Inverse DFT", inverseTransform);
Cv2.WaitKey();
}
/// <summary>
/// 离散傅里叶变换
/// </summary>
/// <param name="source"></param>
/// <returns></returns>
public static Bitmap Dft(this Bitmap source)
{
var fileName = Path.GetTempPath() + "\\" + Guid.NewGuid().ToString() + ".bmp";
File.WriteAllBytes(fileName, source.GetBitmapFileData());
using (var img = Cv2.ImRead(fileName, ImreadModes.Grayscale))
{
fileName = Path.GetTempPath() + "\\" + Guid.NewGuid().ToString() + ".bmp";
var padded = new Mat();
// 计算最佳 DFT 尺寸
var m = Cv2.GetOptimalDFTSize(img.Rows);
var n = Cv2.GetOptimalDFTSize(img.Cols);
Cv2.CopyMakeBorder(img, padded, 0, m - img.Rows, 0, n - img.Cols, BorderTypes.Constant, Scalar.All(0));
var paddedF32 = new Mat();
padded.ConvertTo(paddedF32, MatType.CV_32F);
Mat[] planes = { paddedF32, Mat.Zeros(padded.Size(), MatType.CV_32F) };
var complex = new Mat();
Cv2.Merge(planes, complex);
// 执行 dft
var dft = new Mat();
Cv2.Dft(complex, dft);
// log(1 + sqrt(Re(DFT(I))^2 + Im(DFT(I))^2))
Cv2.Split(dft, out var dftPlanes); // planes[0] = Re(DFT(I), planes[1] = Im(DFT(I))
// planes[0] = magnitude
var magnitude = new Mat();
Cv2.Magnitude(dftPlanes[0], dftPlanes[1], magnitude);
magnitude += Scalar.All(1);
Cv2.Log(magnitude, magnitude);
var spectrum = magnitude[
new Rect(0, 0, magnitude.Cols & -2, magnitude.Rows & -2)];
// 交换象限
var cx = spectrum.Cols / 2;
var cy = spectrum.Rows / 2;
var q0 = new Mat(spectrum, new Rect(0, 0, cx, cy)); // 左上
var q1 = new Mat(spectrum, new Rect(cx, 0, cx, cy)); // 右上
var q2 = new Mat(spectrum, new Rect(0, cy, cx, cy)); // 左下
var q3 = new Mat(spectrum, new Rect(cx, cy, cx, cy)); // 右下
var tmp = new Mat();
q0.CopyTo(tmp);
q3.CopyTo(q0);
tmp.CopyTo(q3);
q1.CopyTo(tmp);
q2.CopyTo(q1);
tmp.CopyTo(q2);
// 归一化到 0~255
Cv2.Normalize(spectrum, spectrum, 0, 255, NormTypes.MinMax);
var result = new Mat();
spectrum.ConvertTo(result, MatType.CV_8U);
result.SaveImage(fileName);
return(new Bitmap(fileName));
}
}
public Mat fourier(Mat img)
{
Mat padded = new Mat();
int m = Cv2.GetOptimalDFTSize(img.Rows);
int n = Cv2.GetOptimalDFTSize(img.Cols); // on the border add zero values
Cv2.CopyMakeBorder(img, padded, 0, m - img.Rows, 0, n - img.Cols, BorderTypes.Constant, Scalar.All(0));
// Add to the expanded another plane with zeros
Mat paddedF32 = new Mat();
padded.ConvertTo(paddedF32, MatType.CV_32F);
Mat[] planes = { paddedF32, Mat.Zeros(padded.Size(), MatType.CV_32F) };
Mat complex = new Mat();
Cv2.Merge(planes, complex);
// this way the result may fit in the source matrix
Mat dft = new Mat();
Cv2.Dft(complex, dft);
// compute the magnitude and switch to logarithmic scale
// => log(1 + sqrt(Re(DFT(I))^2 + Im(DFT(I))^2))
Mat[] dftPlanes;
Cv2.Split(dft, out dftPlanes); // planes[0] = Re(DFT(I), planes[1] = Im(DFT(I))
// planes[0] = magnitude
Mat magnitude = new Mat();
Cv2.Magnitude(dftPlanes[0], dftPlanes[1], magnitude);
magnitude += Scalar.All(1); // switch to logarithmic scale
Cv2.Log(magnitude, magnitude);
// crop the spectrum, if it has an odd number of rows or columns
Mat spectrum = magnitude[
new OpenCvSharp.Rect(0, 0, magnitude.Cols & -2, magnitude.Rows & -2)];
// rearrange the quadrants of Fourier image so that the origin is at the image center
int cx = spectrum.Cols / 2;
int cy = spectrum.Rows / 2;
Mat q0 = new Mat(spectrum, new OpenCvSharp.Rect(0, 0, cx, cy)); // Top-Left - Create a ROI per quadrant
Mat q1 = new Mat(spectrum, new OpenCvSharp.Rect(cx, 0, cx, cy)); // Top-Right
Mat q2 = new Mat(spectrum, new OpenCvSharp.Rect(0, cy, cx, cy)); // Bottom-Left
Mat q3 = new Mat(spectrum, new OpenCvSharp.Rect(cx, cy, cx, cy)); // Bottom-Right
// swap quadrants (Top-Left with Bottom-Right)
Mat tmp = new Mat();
q0.CopyTo(tmp);
q3.CopyTo(q0);
tmp.CopyTo(q3);
// swap quadrant (Top-Right with Bottom-Left)
q1.CopyTo(tmp);
q2.CopyTo(q1);
tmp.CopyTo(q2);
// Transform the matrix with float values into a
Cv2.Normalize(spectrum, spectrum, 0, 1, NormTypes.MinMax);
// calculating the idft
Mat inverseTransform = new Mat();
Cv2.Dft(dft, inverseTransform, DftFlags.Inverse | DftFlags.RealOutput);
Cv2.Normalize(inverseTransform, inverseTransform, 0, 1, NormTypes.MinMax);
double minVal = 0.0, maxVal = 0.0;
Cv2.MinMaxIdx(inverseTransform, out minVal, out maxVal);
Cv2.ConvertScaleAbs(inverseTransform, inverseTransform, 255.0 / (maxVal - minVal), -minVal * 255.0 / (maxVal - minVal));
return(inverseTransform);
}
