CN104217403A - Method for converting colored image into grayscale image - Google Patents

Abstract

The invention relates to the field of computers, in particular to a method for converting a colored image into a grayscale image. The method for converting the colored image into the grayscale image disclosed by the invention is implemented by the following two steps: performing initial graying on the image by using a simplest method to obtain a grayscale image; and combining the color contrast information of the original image with the grayscale image to construct an error energy function, and evaluating a final de-coloration result. Through the evaluated grayscale image, global contrast can be well kept, and local detailed information can be well reflected.

Description

A kind of method coloured image being converted to gray level image

Technical field

The present invention relates to computer realm, specifically refer to a kind of method coloured image being converted to gray level image.

Background technology

In recent years along with the development of scientific and technological level, present Digital printing technology can not meet people keep degree requirement to original image.Although commercially occurred colour print technology existing, can keep more detailed information, colour print technology has needs a lot of energy consumptions, and price comparison is expensive, temporarily also cannot popularize in our daily life; Simultaneously a lot of at present digital cameras is a lot of different style according to the Demand Design of client also, and wherein image gray processing style but have lost much important detailed information, cannot meet the requirement to the strict artistic study personnel of image request.For this problem, if new image gray processing algorithm can be proposed, enable result images keep the contrast information of original image as much as possible, Digital printing technology and image stylization technology can be made more to meet the demand of Vehicles Collected from Market.

Summary of the invention

For overcoming above problem, the object of the present invention is to provide a kind of for keeping method coloured image being converted to gray level image of original image contrast.

Coloured image is converted to a method for gray level image, comprises the steps:

1) preliminary gray processing

First extract R, G, B tri-passages of coloured image and by its vectorization, become a column vector; Then formula (1) is used to carry out preliminary gray processing.

H(i)＝0.299*R(i)+0.587*G(i)+0.114*B(i) (1)

Wherein: H (i) represents the gray-scale value of pixel i after preliminary gray processing, R (i), G (i), B (i) represents the gray-scale value of pixel i in R, G, channel B in original image respectively.

Weights before three passages determine the sensitivity of color according to human eye.Due in these three kinds of colors, human eye is the most responsive to green, least responsive to blueness, and therefore G passage accounts for maximum proportion in conversion, and B accounts for minimum proportion.Through the research of theory and practice, we adopt the weighted value shown in formula (1).

2) details strengthens

After obtaining preliminary gray processing result, we need the color contrast of original image to add in the result of preliminary gray processing, therefore construct the error energy function as shown in formula (2):

$E=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}[{\mathrm{\λ}}_1{(g_i-H_i)}^2+{\mathrm{\λ}}_2\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{({\▿g}_{\mathrm{ij}}-{\mathrm{\α}}_{\mathrm{ij}}{\▿C}_{\mathrm{ij}})}^2]---\left(2\right)$

Wherein: N represents the number of pixels that entire image is total; λ ₁, λ ₂represent two weighted values, generally we get λ at acquiescence ₁=1, λ ₂=1.G _irepresent the gray-scale value of pixel i in final colour killing image, H _imeaning consistent with formula (1).K represents the number of the neighbor point existed around each pixel, pixel such as on four edges circle of image only has 3 neighbors, all only have 2 neighbors in 4 pixels at image four drift angle places, and other pixels have 4 neighbors, therefore K has different values to different pixels.And in formula represent the contrast between coloured image neighbor, its concrete formula is as follows.

${\▿C}_{\mathrm{ij}}=\left|\right|{\▿R}_{\mathrm{ij}}\left|\right|+\left|\right|{\▿G}_{\mathrm{ij}}\left|\right|+\left|\right|{\▿B}_{\mathrm{ij}}\left|\right|=\left|\right|R_i-R_j\left|\right|+\left|\right|G_i-G_j\left|\right|+\left|\right|B_i-B_j\left|\right|---\left(3\right)$

Due to colour contrast, we directly adopt the contrast sum of three passages, and grey-scale contrast and colour contrast, mutually near the scope of grey-scale contrast can be made to become extensively, give prominence to the contrast information of local more.

The α of formula (2) _ijrepresent direction, its value can only be 1 or-1, if the direction of getting 1 expression color contrast is positive, get-1 and represent negative, its judgment criterion is as follows:

If a) R _i>>R _jaMP.AMp.Amp G _i>>G _jaMP.AMp.Amp B _i>>B _j, then α is got _ij=1; Otherwise, if R _i<<R _jaMP.AMp.Amp G _i<<G _jaMP.AMp.Amp B _i<<B _j, then α is got _ij=-1.If this method can not judge, then adopt criterion b).

If have one or two to be close in R, G, B tri-gray-scale values of b) two pixels, another two or a gray-scale value difference comparatively large, such as R _i≈ R _j, G _i>>G _j, B _i>>B _j, then α _ij=1, otherwise α _ij=-1.If c) two kinds of methods all cannot judge, then get the grey-scale contrast direction of the gray level image that preceding step draws, i.e. H above _i-H _jdirection.

Below for pixel i, describe the method for solving of formula (2) in detail.Suppose that the size of image is M × N and pixel i has 4 adjacent pixel i+M, i-M, i+1, i-1, then:

$\left\{\begin{array}{c}{E}_i={\mathrm{\&lambda;}}_1{(g_i-H_i)}^2+{\mathrm{\&lambda;}}_2[{(g_i-g_{i+M}-{\&dtri;C}_{i,i+M})}^2+{(g_i-g_{i-M}-{\&dtri;C}_{i,i-M})}^2\\ +{(g_i-g_{i+1}-{\&dtri;C}_{i,i+1})}^2+{(g_i-g_{i,i-1}-{\&dtri;C}_{i,i-1})}^2\end{array}\right.---\left(4\right)$

By formula (4) to g _idifferentiate, obtains

$\left\{\begin{array}{c}\frac{{\&PartialD;E}_i}{{\&PartialD;g}_i}={2\mathrm{\&lambda;}}_1(g_i-H_i)+{2\mathrm{\&lambda;}}_2[(g_i-g_{i+M}-{\&dtri;C}_{i,i+M})+(g_i-g_{i-M}-{\&dtri;C}_{i,i-M})\\ +(g_i-g_{i+1}-{\&dtri;C}_{i,i+1})+(g_i-g_{i,i-1}-{\&dtri;C}_{i,i-1})\end{array}\right.---\left(5\right)$

Order $\frac{{\&PartialD;E}_i}{{\&PartialD;g}_i}=0,$ Then

$\left\{\begin{array}{c}({\mathrm{\&lambda;}}_1+4*{\mathrm{\&lambda;}}_2)g_i-{\mathrm{\&lambda;}}_2(g_{i+M}+g_{i-M}+g_{i+1}+g_{i-1})\\ ={\mathrm{\&lambda;}}_1{H}_i+{\mathrm{\&lambda;}}_2({\&dtri;C}_{i,i+M}+{\&dtri;C}_{i,i-M}+{{\&dtri;C}_{i,i+1}+\&dtri;C}_{i,i-1})\end{array}\right.---\left(6\right)$

Wherein the left side of equation is made up of coefficient and unknown number, and on the right of equation is a constant.

When being sued for peace by the energy function of all pixels, just can obtain total energy function, as shown in formula (2), we also adopt formula (5) and the mode shown in (6) to carry out differentiate to each pixel, and make its derivative equal 0.So, the formula obtained after total energy function differentiate can regard the equation of an AX=B as, and wherein A is the sparse matrix of M*N × M*N size, and the value of its every a line is just as the coefficient value on equation (6) left side.And X is the unknown number matrix of M × N size, i.e. X=[g ₁, g ₂, Lg _mN] ^t, B is the constant matrices of M × N size.Finally, we can pass through solution by iterative method equation, draw final colour killing result.

In computer realm, gray level image is the image that each pixel only has a sample color.This kind of image is shown as the gray scale from the darkest black to the brightest white usually, and the span of its gray-scale value is [0,255].And coloured image comprises R, G, B tri-channel value, the task of coloured image being transformed into gray level image reduces the dimension of image, the information of a part will inevitably be lost like this, thus as a good result will be obtained, the contrast of original image must be kept as much as possible.

And show for human visual perception systematic research at present, human visual system accurately can not perceive the change of hue and luminance, and everyone is not identical to the sensitivity of brightness change yet.The principle simultaneously converted from colour killing, limited gray level is each color that impossible represent correspondingly in color space, and therefore we retain the most responsive contrast changing unit of visually-perceptible as much as possible.Again because human eye is the most responsive for the color change of image adjacent area, so we think that the information between neighbor plays an important role in greyscale transformation.We have proposed the gradient field optimized algorithm of coloured image gray processing.Compare with existing algorithm, this algorithm can not only keep the structural information of original image better, also can retain the local contrast information of original image to greatest extent.

The invention discloses a kind of by the method for image from color conversion to gray scale, realized by two steps, first by the simplest method, image is carried out preliminary gray processing, obtain a gray level image; And then the color contrast information of original image is combined with gray level image, build an error energy function, try to achieve final colour killing result.The gray level image of trying to achieve like this can not only keep global contrast well, also can embody local detail information well.

Accompanying drawing explanation

Fig. 1 is the algorithm of algorithm of the present invention and Grundland and Dodgson ^[1]with the comparison diagram of the algorithm [2] of the people such as Gooch.

Fig. 2 is the algorithm of the people such as algorithm of the present invention and Rasche ^[3]and the algorithm of the people such as Smith ^[4]effect contrast figure.

Fig. 3 is the algorithm of the people such as algorithm of the present invention and Lu ^[5]and the algorithm of the people such as Smith ^[4]effect contrast figure.

Original image in accompanying drawing is coloured image, and owing to can not there is coloured image in patent application specification restriction article, therefore, here the result after original image gray processing is directly shown as original image by the rgb2gray function in matalab by we.

Embodiment

Set forth the present invention further below in conjunction with specific embodiment, should be understood that following examples are only not used in for illustration of the present invention and limit the scope of the invention.

Embodiment

The size of image is M × N, for pixel i, and pixel i has 4 adjacent pixel i+M, i-M, i+1, i-1, when implementing coloured image gray processing, our concrete steps of algorithm are as follows: 1. first read a width coloured image, and the data of image are integers, and we will convert thereof into double precision and float

Point-type; The size of image is M × N, and pixel i has 4 adjacent pixels

i+M,i-M,i+1,i-1

2. the double precision coloured image formula (1) first step obtained carries out preliminary gray processing conversion;

H(i)＝0.299*R(i)+0.587*G(i)+0.114*B(i)

(1)

Wherein,

H (i) represents the gray-scale value of pixel i after preliminary gray processing;

R (i), G (i), B (i) represents the gray-scale value of pixel i in R, G, channel B in original image respectively.

3. press formula (3) and calculate the color contrast of original image, and with a), b), c) three criterions judge face

The direction of color contrast;

${\&dtri;C}_{\mathrm{ij}}=\left|\right|{\&dtri;R}_{\mathrm{ij}}\left|\right|+\left|\right|{\&dtri;G}_{\mathrm{ij}}\left|\right|+\left|\right|{\&dtri;B}_{\mathrm{ij}}\left|\right|=\left|\right|R_i-R_j\left|\right|+\left|\right|G_i-G_j\left|\right|+\left|\right|B_i-B_j\left|\right|---\left(3\right);$

α _ijrepresent direction, its value is 1 or-1, if the direction of getting 1 expression color contrast is positive, get-1 and represent negative, its judgment criterion is as follows:

If a) R _i>>R _jaMP.AMp.Amp G _i>>G _jaMP.AMp.Amp B _i>>B _j, then α is got _ij=1; Otherwise, if

R _i<<R _jaMP.AMp.Amp G _i<<G _jaMP.AMp.Amp B _i<<B _j, then α is got _ij=-1;

If b) criterion a) cannot judge, then adopt: if having one or two to be close in R, G, B of two pixels tri-gray-scale values, another two or gray-scale value difference comparatively large, such as R _i≈ R _j, G _i>>G _j, B _i>>B _j, then α _ij=1, otherwise α _ij=-1;

If c) a) and b) two kinds of criterions all cannot judge, then get step 1) the grey-scale contrast direction of gray level image that draws, i.e. H _i-H _jdirection.

4. list error energy function corresponding to image by formula (2) again;

$E=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}[{\mathrm{\&lambda;}}_1{(g_i-H_i)}^2+{\mathrm{\&lambda;}}_2\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{({\&dtri;g}_{\mathrm{ij}}-{\mathrm{\&alpha;}}_{\mathrm{ij}}{\&dtri;C}_{\mathrm{ij}})}^2]---\left(2\right)$

Wherein,

N represents the number of pixels that entire image is total;

λ ₁, λ ₂represent two weighted values, λ ₁=1, λ ₂=1;

G _irepresent the gray-scale value of pixel i in final colour killing image;

H _irepresent the gray-scale value of pixel i after preliminary gray processing;

K represents the number of the neighbor point existed around each pixel;

${\&dtri;g}_{\mathrm{ij}}=g_i-g_j;$

5. press formula (4) again, (5), error energy function is converted to corresponding AX=B equation by (6);

$\left\{\begin{array}{c}{E}_i={\mathrm{\&lambda;}}_1{(g_i-H_i)}^2+{\mathrm{\&lambda;}}_2[{(g_i-g_{i+M}-{\&dtri;C}_{i,i+M})}^2+{(g_i-g_{i-M}-{\&dtri;C}_{i,i-M})}^2\\ +{(g_i-g_{i+1}-{\&dtri;C}_{i,i+1})}^2+{(g_i-g_{i,i-1}-{\&dtri;C}_{i,i-1})}^2\end{array}\right.---\left(4\right)$

By formula (4) to g _idifferentiate, obtains

$\left\{\begin{array}{c}\frac{{\&PartialD;E}_i}{{\&PartialD;g}_i}={2\mathrm{\&lambda;}}_1(g_i-H_i)+{2\mathrm{\&lambda;}}_2[(g_i-g_{i+M}-{\&dtri;C}_{i,i+M})+(g_i-g_{i-M}-{\&dtri;C}_{i,i-M})\\ +(g_i-g_{i+1}-{\&dtri;C}_{i,i+1})+(g_i-g_{i,i-1}-{\&dtri;C}_{i,i-1})\end{array}\right.---\left(5\right)$

Order $\frac{{\&PartialD;E}_i}{{\&PartialD;g}_i}=0,$ Then

$\left\{\begin{array}{c}({\mathrm{\&lambda;}}_1+4*{\mathrm{\&lambda;}}_2)g_i-{\mathrm{\&lambda;}}_2(g_{i+M}+g_{i-M}+g_{i+1}+g_{i-1})\\ ={\mathrm{\&lambda;}}_1{H}_i+{\mathrm{\&lambda;}}_2({\&dtri;C}_{i,i+M}+{\&dtri;C}_{i,i-M}+{{\&dtri;C}_{i,i+1}+\&dtri;C}_{i,i-1})\end{array}\right.---\left(6\right)$

Wherein the left side of equation is made up of coefficient and unknown number, and on the right of equation is a constant.

When being sued for peace by the energy function of all pixels, just can obtain total energy function, as shown in formula (2), we also adopt formula (5) and the mode shown in (6) to carry out differentiate to each pixel, and make its derivative equal 0.So, the formula obtained after total energy function differentiate can regard the equation of an AX=B as, and wherein A is the sparse matrix of M*N × M*N size, and the value of its every a line is just as the coefficient value on equation (6) left side.And X is the unknown number matrix of M × N size, i.e. X=[g ₁, g ₂... g _mN] ^t, B is the constant matrices of M × N size.

6. the mode of last iterative obtains final gray-scale value, obtains final gray level image.

In order to more directly highlight the superiority of this algorithm, the result of the result of algorithm of the present invention and five kinds of algorithms compares by we, is the algorithm of the people such as the Gooch of classics respectively ^[2]with the algorithm of the people such as Rasche ^[3], pass through the algorithm of two kinds of better performances ground algorithm-Grunalana and Doagson that draws of test ^[1]with the algorithm of the people such as Smith ^[4], and the algorithm of the people such as the good Lu done in coloured image gray processing field in recent years.

As accompanying drawing 1 displaying is the algorithm of oneself and the algorithm of Grunalana and Doagson ^[1]with the comparison diagram of the algorithm of the people such as Gooch.As can be seen from figure we, the algorithm of the people such as Gooch ^[2]result can keep the local contrast information of image, but can lose global contrast information, and it can make whole image seem fuzzyyer.And the algorithm of Grunalana and Doagson ^[1]although on global information keeps, than the algorithm of the people such as Gooch ^[2]obviously good a lot, but a lot of local contrast information can be have lost, as the contrast information of petal in the details of the clothes in piece image and the second width image.And our algorithm is on contrast keeps, all will go up well many than these two kinds of algorithms, in piece image, our result can be clear that the texture information on clothes and on floor; In the second width image, our result can keep the particle shape of texture on petal and earth well.

What Fig. 2 showed is this algorithm and the algorithm of the people such as Rasche ^[3]and the algorithm of the people such as Smith ^[4]effect contrast figure.From figure, we can clearly find out, the people such as Rasche ^[3]although result can keep substantially global structure, a lot of local contrast information can be lost.And the algorithm of the people such as Smith ^[4]although local contrast information can be kept preferably, but still the obvious contrast information of a part can be lost.As the lower left part of the first sub-picture, the contrast of its adjacent area is just obviously little, although the face color block of personage can identification, clear not.From figure, we can find, our algorithm can keep the contrast information of the overall situation and local better.

The algorithm of the people such as Lu ^[5]it is the more outstanding algorithm done in image gray processing field in recent years, this algorithm not only considers that the structural information of the overall situation also maintains the local contrast information of a part, and the constraint relaxed color contrast direction, automatically select suitable symbol with bimodal distribution function.But this method still can lose the important local contrast information of part, and different images is also different to the requirement of parameter, user not easily debugs out best result.As shown in Figure 3, the second row is the result of this chapter algorithm, the 3rd, fourth line is all algorithms of the people such as Lu ^[5]as a result, the result of fourth line adopts the people such as Lu ^[5]at the default value that article proposes, and the result of the third line is the optimum obtained after debugging.As can be seen from figure we, if we directly adopt the people such as Lu ^[5]propose default value at article and carry out gray processing coloured image, result images can be made to thicken unclear, and defect is also existed to the distribution of gray level; Repeatedly adjust parameter through us, when finding that its parameter value is 0.9, its image optimum, this result is come a lot clear than default value, but still have lost a lot of contrast informations.And our result can not only keep the contrast of the overall situation well, also local contrast information can be kept well.Can find in comparison diagram from figure, our algorithm on Hemifusus ternatanus than the algorithm of the people such as Lu ^[5]go out well many, the information such as text color in such as the first Zhang Tuzhong old man wrinkle on the face and on hand and second image on child's clothes.

In addition, the total algorithm framework of this algorithm and document: the coloured image based on gradient field turns the method (Zhang Weixiang, Zhou Bingfeng) of gray level image ^[7]be different, their algorithm is in LCrCb spatially compute gradient value, and they change brightness value according to the size of luminance gradient value and color gradient value, and build Poisson equation.And first algorithm of the present invention is carry out preliminary gray processing to obtain preliminary gray level image, then direct compute gradient value on rgb space, last preliminary gray level image and Grad combine, and construct energy function.Although our algorithm is similar with the name of their algorithm, content is completely different.

List of references:

[1] gram Lu Lan. mark and Dodge gloomy. Neil. Anthony. colour killing: fast, the colour of contrast strengthen is to the conversion [J] of gray scale. pattern-recognition, 2007,40 (11): 2891 – 2896.M.Grundland and N.A.Dodgson.Decolorize:Fast, contrast enhancing, color to grayscale conversion [J] .Pattern Recognition, 2007,40 (11): 2891 – 2896.

[2] ancient strange. Amy, Ao Er. gloomy polite, Tong Bolin. Jack, Gu Qi. Bruce. colored change gray scale: the algorithm that fades [J] that conspicuousness keeps. Association for Computing Machinery's computer graphics proceedings, 2005,24 (3): 634 – 639.

Amy A.Gooch,Sven C.Olsen,Jack Tumblin,Bruce Gooch.Color2gray:salience-preserving color removal[J].ACM Transactions on Graphics,2005,24(3):634–639.

[3] Lars is thorough. Ka Er, Gai Site. Robert, dimension Manfred Stohl. James. for the Hemifusus ternatanus color image reproduction algorithm [J] of monochromasia and the two primary colors persons of looking. IEEE-USA's computer graphics and application periodical, 2005,25 (3): 22 – 30.

K.Rasche,R.Geist,J.Westall.Detail preserving reproduction of color images for monochromats and dichromats[J].IEEE Computer Graphics and Applications,2005,25(3):22–30.

[4] Smith. Kai Leju, Lan Desi. Pi Aier, Te Longte. Ju Erle, Mace Ke Weisiji. Karol. significantly gray processing: a simply and fast perception sharp picture video conversion method. computer graphics forum, 2008,27 (2): 193 – 200.

K.Smith,P.Landes,J.Thollot,K.Myszkowski.Apparent greyscale:A simple and fast conversion to perceptually accurate images and video[J].Computer Graphics Forum,2008,27(2):193–200.

[5] Lu Cewu, Xu Li, Jia Jiaya. the colour killing algorithm [C] that contrast keeps. IEEE-USA calculates photography international conference collection of thesis, 2012,1 – 7.Cewu Lu, Li Xu and Jiaya Jia.Contrast Preserving Decolorization [C] .Proceedings of IEEE International Conference on Computational Photography, 2012,1 – 7.

[6] Ka Dike. Martin. the colored perception evaluation [J] to greyscale image transitions. computer graphics forum, 2008,27 (7): 1745 – 1754.

M. perceptual Evaluation of Color-to-Grayscale Image Conversions [J] .Computer Graphics Forum, 2008,27 (7): 1745 – 1754. [7] Zhang Weixiang, Zhou Bingfeng. the coloured image based on gradient field turns the method [J] of gray level image. camera work, 2007,7:20 – 22.

Claims (1)

1. coloured image is converted to a method for gray level image, it is characterized in that: comprise the steps:

1) preliminary gray processing

First extract R, G, B tri-passages of coloured image and by its vectorization, become a column vector; Then formula (1) is used to carry out preliminary gray processing:

H(i)＝0.299*R(i)+0.587*G(i)+0.114*B(i) (1)

Wherein,

H (i) represents the gray-scale value of pixel i after preliminary gray processing;

R (i), G (i), B (i) represents the gray-scale value of pixel i in R, G, channel B in original image respectively;

2) details strengthens

After obtaining preliminary gray processing result, the color contrast of original image is added in the result of preliminary gray processing, builds the error energy function shown in formula (2):

$E=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}[{\mathrm{\&lambda;}}_1{(g_i-H_i)}^2+{\mathrm{\&lambda;}}_2\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{({\&dtri;g}_{\mathrm{ij}}-{\mathrm{\&alpha;}}_{\mathrm{ij}}{\&dtri;C}_{\mathrm{ij}})}^2]---\left(2\right)$

Wherein,

N represents the number of pixels that entire image is total;

λ ₁, λ ₂represent two weighted values, λ ₁=1, λ ₂=1;

G _irepresent the gray-scale value of pixel i in final colour killing image;

H _irepresent the gray-scale value of pixel i after preliminary gray processing;

K represents the number of the neighbor point existed around each pixel;

${\&dtri;g}_{\mathrm{ij}}=g_i-g_j;$

represent the contrast between coloured image neighbor, calculate as formula (3):

${\&dtri;C}_{\mathrm{ij}}=\left|\right|{\&dtri;R}_{\mathrm{ij}}\left|\right|+\left|\right|{\&dtri;G}_{\mathrm{ij}}\left|\right|+\left|\right|{\&dtri;B}_{\mathrm{ij}}\left|\right|=\left|\right|R_i-R_j\left|\right|+\left|\right|G_i-G_j\left|\right|+\left|\right|B_i-B_j\left|\right|---\left(3\right);$

α _ijrepresent direction, its value is 1 or-1, if the direction of getting 1 expression color contrast is positive, get-1 and represent negative, its judgment criterion is as follows:

If a) R _i>>R _jaMP.AMp.Amp G _i>>G _jaMP.AMp.Amp B _i>>B _j, then α is got _ij=1; Otherwise, if

R _i<<R _jaMP.AMp.Amp G _i<<G _jaMP.AMp.Amp B _i<<B _j, then α is got _ij=-1;

If b) criterion a) does not meet and maybe cannot judge, then adopt: if having one or two to be close in R, G, B of two pixels tri-gray-scale values, another two or gray-scale value difference comparatively large, such as R _i≈ R _j, G _i>>G _j, B _i>>B _j, then α _ij=1; Otherwise, if R _i≈ R _j, G _i<<G _j, B _i<<B _j, then

α _ij＝-1；

If c) a) and b) two kinds of criterions all cannot judge, then α _ijget step 1) gray scale pair of gray level image that obtains

Than degree direction, even H _i-H _jfor positive number, then α _ij=1; Otherwise, if H _i-H _jfor negative, then α _ij=-1;

The error energy function obtained each pixel by formula (2) is to g _idifferentiate, and make and the energy function of all pixels is sued for peace, just can obtain total energy function, so, the formula obtained after total energy function differentiate can regard the equation of an AX=B as;

Finally, by solution by iterative method equation, draw final result.