OpenCV  4.10.0-dev
Open Source Computer Vision
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Motion Deblur Filter

Prev Tutorial: Out-of-focus Deblur Filter
Next Tutorial: Anisotropic image segmentation by a gradient structure tensor

Original author Karpushin Vladislav
Compatibility OpenCV >= 3.0

Goal

In this tutorial you will learn:

  • what the PSF of a motion blur image is
  • how to restore a motion blur image

Theory

For the degradation image model theory and the Wiener filter theory you can refer to the tutorial Out-of-focus Deblur Filter. On this page only a linear motion blur distortion is considered. The motion blur image on this page is a real world image. The blur was caused by a moving subject.

What is the PSF of a motion blur image?

The point spread function (PSF) of a linear motion blur distortion is a line segment. Such a PSF is specified by two parameters: \(LEN\) is the length of the blur and \(THETA\) is the angle of motion.

Point spread function of a linear motion blur distortion

How to restore a blurred image?

On this page the Wiener filter is used as the restoration filter, for details you can refer to the tutorial Out-of-focus Deblur Filter. In order to synthesize the Wiener filter for a motion blur case, it needs to specify the signal-to-noise ratio ( \(SNR\)), \(LEN\) and \(THETA\) of the PSF.

Source code

You can find source code in the samples/cpp/tutorial_code/ImgProc/motion_deblur_filter/motion_deblur_filter.cpp of the OpenCV source code library.

#include <iostream>
using namespace cv;
using namespace std;
void help();
void calcPSF(Mat& outputImg, Size filterSize, int len, double theta);
void fftshift(const Mat& inputImg, Mat& outputImg);
void filter2DFreq(const Mat& inputImg, Mat& outputImg, const Mat& H);
void calcWnrFilter(const Mat& input_h_PSF, Mat& output_G, double nsr);
void edgetaper(const Mat& inputImg, Mat& outputImg, double gamma = 5.0, double beta = 0.2);
const String keys =
"{help h usage ? | | print this message }"
"{image |input.png | input image name }"
"{LEN |125 | length of a motion }"
"{THETA |0 | angle of a motion in degrees }"
"{SNR |700 | signal to noise ratio }"
;
int main(int argc, char *argv[])
{
help();
CommandLineParser parser(argc, argv, keys);
if (parser.has("help"))
{
parser.printMessage();
return 0;
}
int LEN = parser.get<int>("LEN");
double THETA = parser.get<double>("THETA");
int snr = parser.get<int>("SNR");
string strInFileName = parser.get<String>("image");
if (!parser.check())
{
parser.printErrors();
return 0;
}
Mat imgIn;
imgIn = imread(strInFileName, IMREAD_GRAYSCALE);
if (imgIn.empty()) //check whether the image is loaded or not
{
cout << "ERROR : Image cannot be loaded..!!" << endl;
return -1;
}
Mat imgOut;
// it needs to process even image only
Rect roi = Rect(0, 0, imgIn.cols & -2, imgIn.rows & -2);
//Hw calculation (start)
Mat Hw, h;
calcPSF(h, roi.size(), LEN, THETA);
calcWnrFilter(h, Hw, 1.0 / double(snr));
//Hw calculation (stop)
imgIn.convertTo(imgIn, CV_32F);
edgetaper(imgIn, imgIn);
// filtering (start)
filter2DFreq(imgIn(roi), imgOut, Hw);
// filtering (stop)
imgOut.convertTo(imgOut, CV_8U);
normalize(imgOut, imgOut, 0, 255, NORM_MINMAX);
imwrite("result.jpg", imgOut);
return 0;
}
void help()
{
cout << "2018-08-14" << endl;
cout << "Motion_deblur_v2" << endl;
cout << "You will learn how to recover an image with motion blur distortion using a Wiener filter" << endl;
}
void calcPSF(Mat& outputImg, Size filterSize, int len, double theta)
{
Mat h(filterSize, CV_32F, Scalar(0));
Point point(filterSize.width / 2, filterSize.height / 2);
ellipse(h, point, Size(0, cvRound(float(len) / 2.0)), 90.0 - theta, 0, 360, Scalar(255), FILLED);
Scalar summa = sum(h);
outputImg = h / summa[0];
}
void fftshift(const Mat& inputImg, Mat& outputImg)
{
outputImg = inputImg.clone();
int cx = outputImg.cols / 2;
int cy = outputImg.rows / 2;
Mat q0(outputImg, Rect(0, 0, cx, cy));
Mat q1(outputImg, Rect(cx, 0, cx, cy));
Mat q2(outputImg, Rect(0, cy, cx, cy));
Mat q3(outputImg, Rect(cx, cy, cx, cy));
Mat tmp;
q0.copyTo(tmp);
q3.copyTo(q0);
tmp.copyTo(q3);
q1.copyTo(tmp);
q2.copyTo(q1);
tmp.copyTo(q2);
}
void filter2DFreq(const Mat& inputImg, Mat& outputImg, const Mat& H)
{
Mat planes[2] = { Mat_<float>(inputImg.clone()), Mat::zeros(inputImg.size(), CV_32F) };
Mat complexI;
merge(planes, 2, complexI);
dft(complexI, complexI, DFT_SCALE);
Mat planesH[2] = { Mat_<float>(H.clone()), Mat::zeros(H.size(), CV_32F) };
Mat complexH;
merge(planesH, 2, complexH);
Mat complexIH;
mulSpectrums(complexI, complexH, complexIH, 0);
idft(complexIH, complexIH);
split(complexIH, planes);
outputImg = planes[0];
}
void calcWnrFilter(const Mat& input_h_PSF, Mat& output_G, double nsr)
{
Mat h_PSF_shifted;
fftshift(input_h_PSF, h_PSF_shifted);
Mat planes[2] = { Mat_<float>(h_PSF_shifted.clone()), Mat::zeros(h_PSF_shifted.size(), CV_32F) };
Mat complexI;
merge(planes, 2, complexI);
dft(complexI, complexI);
split(complexI, planes);
Mat denom;
pow(abs(planes[0]), 2, denom);
denom += nsr;
divide(planes[0], denom, output_G);
}
void edgetaper(const Mat& inputImg, Mat& outputImg, double gamma, double beta)
{
int Nx = inputImg.cols;
int Ny = inputImg.rows;
Mat w1(1, Nx, CV_32F, Scalar(0));
Mat w2(Ny, 1, CV_32F, Scalar(0));
float* p1 = w1.ptr<float>(0);
float* p2 = w2.ptr<float>(0);
float dx = float(2.0 * CV_PI / Nx);
float x = float(-CV_PI);
for (int i = 0; i < Nx; i++)
{
p1[i] = float(0.5 * (tanh((x + gamma / 2) / beta) - tanh((x - gamma / 2) / beta)));
x += dx;
}
float dy = float(2.0 * CV_PI / Ny);
float y = float(-CV_PI);
for (int i = 0; i < Ny; i++)
{
p2[i] = float(0.5 * (tanh((y + gamma / 2) / beta) - tanh((y - gamma / 2) / beta)));
y += dy;
}
Mat w = w2 * w1;
multiply(inputImg, w, outputImg);
}
Designed for command line parsing.
Definition utility.hpp:820
Template matrix class derived from Mat.
Definition mat.hpp:2230
n-dimensional dense array class
Definition mat.hpp:812
CV_NODISCARD_STD Mat clone() const
Creates a full copy of the array and the underlying data.
MatSize size
Definition mat.hpp:2160
void copyTo(OutputArray m) const
Copies the matrix to another one.
int cols
Definition mat.hpp:2138
bool empty() const
Returns true if the array has no elements.
int rows
the number of rows and columns or (-1, -1) when the matrix has more than 2 dimensions
Definition mat.hpp:2138
void convertTo(OutputArray m, int rtype, double alpha=1, double beta=0) const
Converts an array to another data type with optional scaling.
Template class for 2D rectangles.
Definition types.hpp:444
Size_< _Tp > size() const
size (width, height) of the rectangle
Template class for specifying the size of an image or rectangle.
Definition types.hpp:335
_Tp height
the height
Definition types.hpp:363
_Tp width
the width
Definition types.hpp:362
void split(const Mat &src, Mat *mvbegin)
Divides a multi-channel array into several single-channel arrays.
void mulSpectrums(InputArray a, InputArray b, OutputArray c, int flags, bool conjB=false)
Performs the per-element multiplication of two Fourier spectrums.
void divide(InputArray src1, InputArray src2, OutputArray dst, double scale=1, int dtype=-1)
Performs per-element division of two arrays or a scalar by an array.
Scalar sum(InputArray src)
Calculates the sum of array elements.
void merge(const Mat *mv, size_t count, OutputArray dst)
Creates one multi-channel array out of several single-channel ones.
void multiply(InputArray src1, InputArray src2, OutputArray dst, double scale=1, int dtype=-1)
Calculates the per-element scaled product of two arrays.
void idft(InputArray src, OutputArray dst, int flags=0, int nonzeroRows=0)
Calculates the inverse Discrete Fourier Transform of a 1D or 2D array.
void dft(InputArray src, OutputArray dst, int flags=0, int nonzeroRows=0)
Performs a forward or inverse Discrete Fourier transform of a 1D or 2D floating-point array.
void pow(InputArray src, double power, OutputArray dst)
Raises every array element to a power.
std::string String
Definition cvstd.hpp:151
#define CV_8U
Definition interface.h:73
#define CV_32F
Definition interface.h:78
softfloat abs(softfloat a)
Absolute value.
Definition softfloat.hpp:444
int cvRound(double value)
Rounds floating-point number to the nearest integer.
Definition fast_math.hpp:200
#define CV_PI
Definition cvdef.h:380
Quat< T > tanh(const Quat< T > &q)
void ellipse(InputOutputArray img, Point center, Size axes, double angle, double startAngle, double endAngle, const Scalar &color, int thickness=1, int lineType=LINE_8, int shift=0)
Draws a simple or thick elliptic arc or fills an ellipse sector.
int main(int argc, char *argv[])
Definition highgui_qt.cpp:3
"black box" representation of the file storage associated with a file on disk.
Definition core.hpp:102
STL namespace.

Explanation

A motion blur image recovering algorithm consists of PSF generation, Wiener filter generation and filtering a blurred image in a frequency domain:

// it needs to process even image only
Rect roi = Rect(0, 0, imgIn.cols & -2, imgIn.rows & -2);
//Hw calculation (start)
Mat Hw, h;
calcPSF(h, roi.size(), LEN, THETA);
calcWnrFilter(h, Hw, 1.0 / double(snr));
//Hw calculation (stop)
imgIn.convertTo(imgIn, CV_32F);
edgetaper(imgIn, imgIn);
// filtering (start)
filter2DFreq(imgIn(roi), imgOut, Hw);
// filtering (stop)

A function calcPSF() forms a PSF according to input parameters \(LEN\) and \(THETA\) (in degrees):

void calcPSF(Mat& outputImg, Size filterSize, int len, double theta)
{
Mat h(filterSize, CV_32F, Scalar(0));
Point point(filterSize.width / 2, filterSize.height / 2);
ellipse(h, point, Size(0, cvRound(float(len) / 2.0)), 90.0 - theta, 0, 360, Scalar(255), FILLED);
Scalar summa = sum(h);
outputImg = h / summa[0];
}

A function edgetaper() tapers the input image’s edges in order to reduce the ringing effect in a restored image:

void edgetaper(const Mat& inputImg, Mat& outputImg, double gamma, double beta)
{
int Nx = inputImg.cols;
int Ny = inputImg.rows;
Mat w1(1, Nx, CV_32F, Scalar(0));
Mat w2(Ny, 1, CV_32F, Scalar(0));
float* p1 = w1.ptr<float>(0);
float* p2 = w2.ptr<float>(0);
float dx = float(2.0 * CV_PI / Nx);
float x = float(-CV_PI);
for (int i = 0; i < Nx; i++)
{
p1[i] = float(0.5 * (tanh((x + gamma / 2) / beta) - tanh((x - gamma / 2) / beta)));
x += dx;
}
float dy = float(2.0 * CV_PI / Ny);
float y = float(-CV_PI);
for (int i = 0; i < Ny; i++)
{
p2[i] = float(0.5 * (tanh((y + gamma / 2) / beta) - tanh((y - gamma / 2) / beta)));
y += dy;
}
Mat w = w2 * w1;
multiply(inputImg, w, outputImg);
}

The functions calcWnrFilter(), fftshift() and filter2DFreq() realize an image filtration by a specified PSF in the frequency domain. The functions are copied from the tutorial Out-of-focus Deblur Filter.

Result

Below you can see the real world image with motion blur distortion. The license plate is not readable on both cars. The red markers show the car’s license plate location.

Below you can see the restoration result for the black car license plate. The result has been computed with \(LEN\) = 125, \(THETA\) = 0, \(SNR\) = 700.

Below you can see the restoration result for the white car license plate. The result has been computed with \(LEN\) = 78, \(THETA\) = 15, \(SNR\) = 300.

The values of \(SNR\), \(LEN\) and \(THETA\) were selected manually to give the best possible visual result. The \(THETA\) parameter coincides with the car’s moving direction, and the \(LEN\) parameter depends on the car’s moving speed. The result is not perfect, but at least it gives us a hint of the image’s content. With some effort, the car license plate is now readable.

Note
The parameters \(LEN\) and \(THETA\) are the most important. You should adjust \(LEN\) and \(THETA\) first, then \(SNR\).

You can also find a quick video demonstration of a license plate recovering method YouTube.