- 操作系统：手机安装 Termux ,Termux 内安装 ubuntu
- Termux 0.119.0-beta.3
- 内嵌 ubuntu 24.04
- 编译器：GNU g++ 14.2.0
- 编辑器：Emacs 29.3
- OpenCV：4.13.0
目标
- 什么是降解图像模型
- 失焦图像的 PSF 是什么
- 如何恢复模糊的图像
- 什么是维纳过滤器
理论
什么是退化/降级图像模型
以下是频域表示中图像退化的数学模型：
S=H⋅U+NS = H\cdot U + NS=H⋅U+N
其中 S 是模糊（退化）图像的光谱，U 是原始真实（未退化）图像的光谱，H 是点扩散函数（PSF）的频率响应，N 是加性噪声（干扰）的频谱
圆形 PSF 是失焦畸变的良好近似值。这样的 PSF 仅由一个参数指定 - 半径 R 。本工作中使用了圆形 PSF
如何恢复模糊的图像
恢复（去模糊）的目的是获得原始图像的估计值。频域中的恢复公式为：
U′=Hw⋅SU' = H_w\cdot SU′=Hw⋅S
其中 U′U'U′ 是原始图像 UUU 的估计光谱，HwH_wHw 是恢复过滤器，例如，维纳过滤器
什么是维纳过滤器
维纳滤镜/滤波器是一种恢复模糊图像的方法。假设PSF是真实对称信号，原始真实图像的功率谱和噪声未知，那么简化的维纳公式为：
Hw=H∣H∣2+1SNR H_w = \frac{H}{|H|^2+\frac{1}{SNR}} Hw=∣H∣2+SNR1H
其中 SNRSNRSNR 为信噪比，为了通过维纳滤光片恢复失焦图像，它需要知道 SNRSNRSNR 和 RRR 圆的 PSF
源代码
cpp
#include <iostream>
#include "opencv2/highgui.hpp"
#include "opencv2/imgproc.hpp"
#include "opencv2/imgcodecs.hpp"
using namespace cv;
using namespace std;
void help();
void calcPSF(Mat& outputImg, Size filterSize, int R);
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);
const String keys =
"{help h usage ? | | print this message }"
"{image |original.jpg | input image name }"
"{R |5 | radius }"
"{SNR |100 | 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 R = parser.get<int>("R");
int snr = parser.get<int>("SNR");
string strInFileName = parser.get<String>("image");
samples::addSamplesDataSearchSubDirectory("doc/tutorials/imgproc/out_of_focus_deblur_filter/images");
if (!parser.check())
{
parser.printErrors();
return 0;
}
Mat imgIn;
imgIn = imread(samples::findFile( 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(), R);
calcWnrFilter(h, Hw, 1.0 / double(snr));
//Hw calculation (stop)
// filtering (start)
filter2DFreq(imgIn(roi), imgOut, Hw);
// filtering (stop)
imgOut.convertTo(imgOut, CV_8U);
normalize(imgOut, imgOut, 0, 255, NORM_MINMAX);
imshow("Original", imgIn);
imshow("Debluring", imgOut);
imwrite("result.jpg", imgOut);
waitKey(0);
return 0;
}
void help()
{
cout << "2018-07-12" << endl;
cout << "DeBlur_v8" << endl;
cout << "You will learn how to recover an out-of-focus image by Wiener filter" << endl;
}
void calcPSF(Mat& outputImg, Size filterSize, int R)
{
Mat h(filterSize, CV_32F, Scalar(0));
Point point(filterSize.width / 2, filterSize.height / 2);
circle(h, point, R, 255, -1, 8);
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);
}解释说明
-
失焦图像恢复算法包括PSF生成、维纳滤波器生成和频域模糊图像滤波：
cpp// 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(), R); calcWnrFilter(h, Hw, 1.0 / double(snr)); //Hw calculation (stop) // filtering (start) filter2DFreq(imgIn(roi), imgOut, Hw); // filtering (stop) -
函数 calcPSF() 根据输入参数半径 R 形成圆形 PSF
cppvoid calcPSF(Mat& outputImg, Size filterSize, int R) { Mat h(filterSize, CV_32F, Scalar(0)); Point point(filterSize.width / 2, filterSize.height / 2); circle(h, point, R, 255, -1, 8); Scalar summa = sum(h); outputImg = h / summa[0]; } -
根据上述公式，函数 calcWnrFilter() 合成简化的维纳滤波器 HwH_wHw
cppvoid 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); } -
函数 fftshift() 重新排列 PSF。这段代码只是从离散傅里叶变换教程中复制的：
cppvoid 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); } -
函数filter2DFreq() 过滤频域中的模糊图像：
cppvoid 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]; }
结果
