# # theory # #in the image captured by the camera, there is often a certain amount of noise. This noise is generally non-correlated in the spatial domain and is an additive noise. For images captured by a camera, it can be expressed as a non-noisy image and a composition of additive noise, namely:
$$\begin{equation} \label{imgeq}g (x, y)=f (x, y)+\eta (x, y)\end{equation}$$of which: $g (x, y)$ for capture image, $f (x, y)$ for noise- free images, $\eta (x, y) $. The process of noise removal is from known$g (x, y)$ to approximate get$f (x, y)$ for the process. For multiple images taken in the same scene, $f _{i} (x, y) $ is the same, while $\eta_{i} (x, y) $ is random and unrelated, the mean value of the K-image image of the same scene can be represented as follows $$\begin{equation} \label{ IMGAVRG}
\BAR{G} (x, y) =\frac{1}{k}\sum_{i=1}^k[f_{i} (x, y) +\eta_{i} (x, y)]=f (x, y) +\frac{1}{k}\sum_{i=1}^k\eta_{i} (x, y)\end{equation}
$$Because the noise is random and irrelevant, the expectation of its average image $$\begin{equation} \label{imgexp}
e\{\bar{g} (x, y) \}=f (x, y)\end{equation}
$$Variance of the average image$$\begin{equation} \label{imgvar}
\sigma_{\bar{g} (x, y)}^{2}=\frac{1}{k}\sigma_{\eta (x, y)}^{2}\end{equation}
$$That is, $$\begin{equation} \LABEL{IMGSD}
\SIGMA_{\BAR{G} (x, y)}=\frac{1}{\sqrt{k}}\sigma_{\eta (x, y)}\end{equation}
$$-$\eqref{Imgexp}$ We can find that the average value of multiple images in the same scene is a noise-free image, but there are some disturbances, and the standard deviation of these disturbances $\eqref{imgsd}$ determines the intensity of the noise. The essence of our image denoising is to reduce the standard deviation in the space domain. From type $\EQREF{IMGSD}It is not difficult to find out that noise can be reduced by increasing the $k$ value, that is, by increasing the number of average images. But at the same time we can find: $\sigma\varpropto\frac{1}{\sqrt{k}}$,$\frac{\partial\sigma}{\partial k}=-\frac{1}{2\sqrt{k^3}}$, with $k$ The increase of the value, the change of $\sigma$ is getting smaller, the effect of increasing the number of images is very small when using average method to denoise.
# # experiment # ## # # Purpose # # #1. Verify that multi-image averaging can be de-noising in the same scenario. 2. with the increase of the number of images, the noise of the image becomes smaller. # # # Data Set # # #179 photos of the same scene, collected in a short time. Here is one of the pictures
Its local details:
You can see that the noise on the image is much more. # # # program Design # # #程序的处理过程为:*reading Images* Averaging*Display Image
Program Source code:matlab
"' matlab% get image file Namesdir = ' IMGs '; imgfiles = Dir ([dir, '/*.jpg ']); [N, c]= size (imgfiles); % get the image sizeimg = im2double (Imread ([DIR, '/', Imgfiles (1). name]); figure (1); Imshow (IMG); IMG = img/n;% Calculate the averagefor m = 2:n img = img + im2double (imread ([DIR, '/', Imgfiles (m). Name])/N;ENDFI Gure (2); Imshow (IMG);
C + + (OpenCV2.4) "Cpp#include <opencv2/core/core.hpp> #include <opencv2/imgproc/imgproc.hpp> #include <opencv2/highgui/highgui.hpp> #include <sstream> #include <exception> #include <iostream> void denoise () { const int N = 179; Cv::mat avrg_img; for (int i = 0; i < N; i++) { Std::ostringstream oss; oss << "imgs/img (" << i+1 << "). jpg"; & nbsp Cv::mat image = Cv::imread (Oss.str ()); //Convert to double Image.convertto (image, cv_32f, 1.0/255.0); if (i = = 0) { Cv::namedwindow ("Noisy image") ; Cv::imshow ("NOisy image ", image); avrg_img = image/n; } else avrg_img + = image/n; } CV:: Namedwindow ("denoised image"); cv::imshow ("denoised image", avrg_img); Avrg_ Img.convertto (avrg_img, CV_8UC3, 255.0); cv::imwrite ("Denoised.jpg", avrg_img);} int Main () { try{ denoise (); } catch (std::exception &e) { Std::cerr << E.what () << std::endl; } cv::waitkey (); return 0;} The "# # # test # # #对179张图片进行测试, the results are as follows: Comparison of the original: it can be seen that the noise is significantly reduced, thus verifying the feasibility of multi-image averaging method to de-noising. Change the average number of pictures, $K $ take ${2,3 ... 10}$, you can get a series of images, as shown in the following GIF: As you can see, from the original to the $k=2$, the noise reduction is significant, but from $k=9$ to $k=10$, the noise changes less, validating the previous mathematical model. # # Reference # #
[1] Gonzalez. Digital image processing [M]. Vancouver translation. Beijing: Electronic industry press. 2011.6
From for notes (Wiz)
Multi-image averaging method for noise reduction
