81. Introduction to the video image denoising filtering algorithm

Why do I need to noise?

Image Denoising is an important part and step in Digital image processing. The effect of denoising has a direct impact on the subsequent image processing, such as segmentation and edge detection. Image signal in the generation, transmission process may be affected by noise pollution, general digital image system common noise mainly include: Gaussian noise (mainly caused by the resistive components inside), salt and pepper noise (mainly the image cutting caused by the white spot noise on the black image or photoelectric conversion process generated by the Poisson noise), etc. , so the front-end filter does not do well, will give the back end of the image processing brings a lot of trouble, in fact, its final response is the image on the display to give people the visual effect, we want to achieve maximum optimization for different applications.

Two. How to Noise

Throughout the online discussion, there are a variety of denoising algorithms, now I know that as described below.

2.1 Classical filtering algorithm

There are three kinds of classical filtering algorithms, mean filter, median filter, Wiener Wiener filter.

2.1.1 Mean value Filter

Mean filter is a simple and practical linear filter, the basic idea is to give the target pixel a template that contains its neighboring pixels, substituting the pixel mean in the template for the original pixel value. In general, in order for the output image to remain in the original grayscale range, the pixel domain and the template of the flight needs divided by 9, in the 3x3 domain, for example, assuming that the current processing pixel is f (m,n), then the simplest of a mean filter module is

　　　　　　　　　　　　　　　　　　　　　　　　

The above formula is modified to get the weighted average filter, as follows:

　　　　　　　　　　　　

Assuming a pair is Mxnde Digital Image f (x, y), after smoothing the resulting digital image is g (x, y), then its grayscale value of each pixel is determined by a number of pixels containing (x, y) of the predetermined field of the gray level average. As shown below:

　　　　　　　　　　　　　　　　　　　　　　　　　　

, S is the predetermined area of the pixel (x, y) of the pixel (x, y), and K is the total number of punctuation points within S.

If an image passes through a low-pass filter, it is equivalent to the image of the mean filter processing, which is mainly through the gray of the mutation points scattered in its adjacent points, in order to achieve a balanced filter effect. In general, the image is smoothed after the mean filtering process, and the noise is suppressed, but for the limit pixel value, this pixel with a large difference from the gray value of the surrounding pixels, the mean filter is more sensitive, which will blur the edge of the image.

2.1.2 Median Filter

A nonlinear smoothing filtering signal processing technique based on ranking statistic theory, which can effectively suppress noise. The characteristics of the median filter is to first determine a pixel as the center of the neighborhood, usually a square neighborhood, it can also be circular, cross-shaped, and so on, and then the neighborhood of the gray values of each pixel sorted, take its median as a new value of the central pixel Gray, where the field is called the window, when the window moves, The image can be smoothed with median filter. Its algorithm is simple, the time complexity is low, but its point, line and apex of the image should not adopt median filter. It is easy to adaptively adapt. The MATLAB program is as follows:

1 i = im2double (Imread ('e:/0.jpg'2 I =3 I1 = Imnoise (I,'Salt & pepper'4 I2 =5 I3 = Imnoise (I,'Gaussian'6 I4 = MEDFILT2 (I3);

2.1.3wiener Wiener Filter

The method of restoring the minimum mean square error between the original image and its restored image is an adaptive filter, which adjusts the effect of the filter according to the local variance. For the removal of Gaussian noise effect is obvious. Restores the goal of minimizing the mean square error between the image F1 (x, y) and the original image f (x, y) MSE. The minimum mean square error MSE is defined as follows:

　　　　　　　　　　　　

The square operation of the error makes the component of the large error much smaller than the small error component, and by selecting Min MSE, the main error of the filter output can be limited, and other optimal criteria can be used for analysis (such as mean error). But these guidelines will make the process of analysis more complex and less effective.

2.2 Morphological filtering

Mathematical morphology mainly includes expansion, corrosion, open operation, closed operation four basic operations, and other forms of operation can be derived from the four basic operations by different combinations. In these four basic operations, the structural elements throughout, it refers to a certain size of the background image, no fixed size, there is no fixed shape, based on the input image and the required information of the shape characteristics, in the morphological transformation algorithm design in conjunction with the design. The selection of structural elements is directly related to the processing result of the input image.

For the binary image, the noise block around the object can be eliminated, and the noise hole inside the object can be eliminated by using the closed operation. For grayscale images, the open and closed operations are used in practical applications to eliminate light details and dark details in smaller sizes. Therefore, combining the two operations can well filter out the light and dark noise, in addition, the combination of structural elements and the two filters to protect the image details more advantages. The MATLAB program for corrosion filtering is as follows:

1%%imdilate Expansion2 CLC3 Clear4 5A1=imread ('. \images\dipum_images_ch09\fig0906 (a) (Broken-text). tif');6Info=imfinfo ('. \images\dipum_images_ch09\fig0906 (a) (Broken-text). tif')7b=[0 1 08    1 1 19    0 1 0];TenA2=imdilate (A1,B);image A1 is expanded by structural element B Onea3=imdilate (a2,b); Aa4=imdilate (a3,b); -  -Subplot (221), Imshow (A1); theTitle'imdilate Swelling Original image'); -  -Subplot (222), Imshow (A2); -Title'image after 1 expansion with B'); +  -Subplot (223), Imshow (A3); +Title'image after 2 expansion with B'); A  atSubplot (224), Imshow (A4); -Title'image after 3 expansion with B'); -   -%imdilate image Expansion Process operation results are as follows:

For the morphological filtering of several MATLAB programs please refer to the link http://www.cnblogs.com/tornadomeet/archive/2012/03/20/2408086.html

2.3 Small Wave Transform

The wavelet transform is relatively complex, the Fourier transform is a series of different frequencies of the positive cosine function to decompose the original function, the transformation is obtained is the original function in the sine cosine of the coefficients of different frequencies. Wavelet transform uses a series of different scale wavelet to decompose the original function, and the coefficients of the original function under different scale wavelets are obtained. Different wavelets are decomposed by translation and scale transformation, which is to get the time characteristic of the original function, and the scale transformation is to get the frequency characteristic of the original function. Wavelet Transform steps:

1. Compare the starting part of the wavelet W (t) and the original function f (t) to calculate the coefficient c. The coefficient c indicates how similar the part function is to the wavelet.

2. Move the wavelet to the right to the K unit, get the wavelet w (t-k), repeat 1. Repeat the department until the function f ends.

3. Expand the wavelet w (t), get the wavelet w (T/2), repeat steps.

4. Continue to expand the wavelet, repeat the double.

For details, please refer to the following link

Http://www.cnblogs.com/tiandsp/archive/2013/04/12/3016989.html

Http://blog.sina.com.cn/s/blog_4b9b714a0100cuzo.html

2.4 Bilateral filtering

What is a bilateral filter? The bilateral filter (bilateral filter) is a filter that can be used for edge-preserving denoising. This denoising effect can be achieved because the filter is composed of two functions. A function is determined by the distance of the geometric space filter coefficients. The other is the filter coefficients determined by the difference in pixel values.

For details of the procedures and formulas, please refer to the following links:

http://blog.csdn.net/abcjennifer/article/details/7616663

2.5guide Filter Guide Filter

Guide filter on-line discussion is relatively small, but it is currently filtering algorithm in the filter effect is relatively good, fast.

Three. Summary

After the discussion of various filtering algorithms, it is known that the effect of the current guidance filtering is better, but these are only verified by MATLAB, and the actual engineering application, but also according to the comprehensive situation to verify.

81. Introduction to the video image denoising filtering algorithm