CN105631833A - Local and linear total variation-based filtering method - Google Patents

Abstract

The invention relates to the image filtering field and provides a local and linear total variation-based filtering method. According to the technical scheme of the method, firstly, each pixel (i) is adopted as a center and an n*n window is obtained. Secondly, the system of each window is transformed as ai* and bi*. Finally, a filtering output result is obtained. By adopting the method, the detail information of an image is better retained. Meanwhile, gray-scale images and color images can be quickly filtered. The method is simple in algorithm, small in calculated amount, better in edge filtering characteristics and efficient in image denoising, smoothing, detail enhancement, image compression within the high dynamic range and the like.

Description

A kind of local linear total variation filtering method

Technical field

The present invention relates to a kind of image filtering one local linear total variation filtering method.

Background technology

Image filtering, namely in the impact of the condition decline low noise of the minutia of maintenance image as much as possible, it is computing basic and important in computer vision application. in general, image filtering can be divided into two big classes: linear filtering and nonlinear filtering. due to non-Gaussian system and the piecewise smooth characteristic of image, linearly (convolution) filtering algorithm, such as mean filter, gaussian filtering etc., although method is simple, speed is fast, but while filtering noise, will also result in smooth phenomenon, make the edge blurry of image. therefore, the non-linear filtering method keeping edge is increasingly subject to people's attention, and it is widely used in computer vision and image processing field.

In the nonlinear filtering algorithm at various maintenance edges, bilateral filtering is one of filtering method of current popular. Two-sided filter is referred to as " non-linear Gaussian filter ", different from conventional filter, two-sided filter not only allows for the aggregate distance between neighborhood territory pixel and also in relation with gray scale color similarity between pixel, give bigger weight to distance in field close to the pixel similar with gray scale (color), otherwise then give less weight. Being highly useful although bilateral filtering there is many applications in which, but how to reduce its computation complexity, it is with challenge that the raising speed of service reduces precision simultaneously.

Summary of the invention

In order to solve the problems referred to above, it is proposed that the edge local linear of a kind of novelty becomes filtering method entirely.

A kind of local linear total variation filtering method, it is characterised in that: comprise the following steps:

Step 1: take the window of n*n centered by pixel i, haveWherein,WithFor windowInterior image block, a_iAnd b_iFor with windowRelevant variation coefficient, can be changed into;

Step 2: to each window, in order to seek optimal solution, by the object function in formula about a_i, b_iDerivation, and make it be equal to zero, can obtain, whereinWithRespectively observed imagefAt wicketInterior average and variance, N_wFor wicketThe number of middle pixel,For observed imagefAt wicketThe average of inside gradient modulus value; To wicketAny pixel, have;

Step 3: to all of sliding window,i=1,2 ... N(N is total number of pixel contained by image), respective a is calculated_i ^*And b_i ^*Afterwards, final filtering output result is

Wherein,��

The present invention is with each pixeliCentered by, take the window of n*n; To each window, transformation system a_i ^*And b_i ^*; Finally draw the output result of filtering. The present invention occasionally can retain the detailed information of image preferably, and gray scale and coloured image are carried out Filtering Processing rapidly; Algorithm is simple, and amount of calculation is little, has good holding edge filter characteristic.

Detailed description of the invention

A kind of local linear total variation filtering method, with pixeliCentered by take the window of n*n, haveWherein,WithFor windowInterior image block, a_iAnd b_iFor with windowRelevant variation coefficient. Then, at wicketIn, above-mentioned formula is write as component form and isIn order to obtain optimal solution, to the object function in this formula about a_i, b_iDerivation, and make it be equal to zero, it is computed obtainingWherein,WithRespectively observed imagefAt wicketThe average of inside gradient modulus value and variance; N _w For wicketThe number of pixel,For observed imagefAt wicketThe average of inside gradient modulus value.

There is a_i ^*And b_i ^*Afterwards, to wicketAny pixel, hasTo all of sliding window,i=1,2 ... N(N is total number of pixel contained by image), respective a is calculated_i ^*And b_i ^*Afterwards, final filtering output resultWherein,

��

The present invention is with each pixeliCentered by, take the window of n*n; To each window, transformation system a_i ^*And b_i ^*; Finally draw the output result of filtering. The present invention occasionally can retain the detailed information of image preferably, and gray scale and coloured image are carried out Filtering Processing rapidly; Algorithm is simple, and amount of calculation is little, has good holding edge filter characteristic. In image denoising, smooth, details enhancing and high dynamic range compression etc., table newly goes out efficient performance.

Claims (1)

1. a local linear total variation filtering method, it is characterised in that: comprise the following steps:

Step 1: take the window of n*n centered by pixel i, haveWherein,WithFor windowInterior image block, a_iAnd b_iFor with windowRelevant variation coefficient, can be changed into

; Step 2: to each window, in order to seek optimal solution, by the object function in formula about a_i, b_iDerivation, and make it be equal to zero, can obtain, whereinWithRespectively observed imagefAt wicketInterior average and variance, N_wFor wicketThe number of middle pixel,For observed imagefAt wicketThe average of inside gradient modulus value; To wicketAny pixel, have;

Step 3: to all of sliding window,i=1,2 ... N(N is total number of pixel contained by image), respective a is calculated_i ^*And b_i ^*Afterwards, final filtering output result isWherein,��