CN102063705A - Method for synthesizing large-area non-uniform texture - Google Patents

Abstract

The invention belongs to the field of computer image processing, relating to a method for synthesizing a large-area non-uniform texture. The method comprises the following steps: determining a region to be repaired, extracting the boundary of the region to be repaired, determining the center point of the region to be repaired, and setting energy values at the center point and boundary points of the region to be repaired of an image; dividing the region to be repaired of the image into a plurality of subregions; acquiring a set containing a plurality of distribution points from the boundary of each subregion, wherein all the sets of the distribution points contain the center point of the region to be repaired; selecting a radical basis function; respectively solving the energy value of each distribution point of each subregion; solving the energy value of each point of each subregion; creating an energy distribution model of the region to be repaired; determining a directional priority coefficient, and defining a new priority coefficient by combining amount of information and a structural coefficient; and synthesizing and repairing the texture. According to the invention, wrong mismatching can be reduced, and the requirement for actually synthesizing the large-area texture of a non-uniform texture image can be met.

Description

The non-homogeneous texture synthesis method in a kind of big zone

Technical field

The invention belongs to the Computer Image Processing field, relate to a kind of image repair method.

Background technology

Image repair is the research focus of various fields such as computer graphics and computer vision.At present, zonule image repair problem (as added text, cut removal etc.) solves substantially, and current research focus mainly concentrates on the reparation research of big area image.Have based on the image repair method of PED and to be easy to generate fuzzy shortcoming, consequent CDD, TV scheduling algorithm have run into very big difficulty in big area image reparation, and based on the synthetic image repair technology of texture, then, become the main flow that current big area image is repaired with the repairing effect of its relative ideal.

In the process that big area image is repaired, direction that texture is propagated and progress have determined to repair the feature of image, and directly have influence on the whole repairing effect of image.Existing method generally is to determine the texture direction of propagation according to the tangential direction of isophote, and the synthetic progress of each point then mainly decides by repairing priority coefficient.Owing to lack effective index in the building-up process, can not effectively control to the texture synthetic direction of propagation and progress.Therefore, in case the phenomenon of mistake coupling takes place, be easy to constantly propagate, thereby produce wrong reparation result along the direction of mistake.

Actual texture image is because the influence of factors such as illumination, geometric distortion; show features heterogeneous such as asymptotic variation through regular meeting; because existing method is in the synthetic process of texture; can not effectively control the texture synthetic direction of propagation and progress; therefore utilize the traditional texture synthetic method that the mistake coupling very easily takes place, be difficult to obtain desirable effect.

Summary of the invention

In order to address the above problem, the present invention proposes the non-homogeneous texture synthesis method in a kind of big zone.The present invention has the characteristics of asymptotic variation according to actual texture image, plan is started with from improving reparation right of priority index, by introducing the Kansa algorithm energy distribution of area to be repaired is carried out modeling from inside to outside, and then acquisition directivity texture is repaired index, the direction of propagation and the progress synthetic for texture provide index, to guarantee the synthetic effect of actual big regional non-homogeneous texture.The present invention adopts following technical scheme.

The non-homogeneous texture synthesis method in a kind of big zone comprises the following steps:

(1) determines area to be repaired Ω, extract the border, area to be repaired

Determine the central point of area to be repaired Ω, the energy value g at image area to be repaired central point and frontier point place is set at 1 and 0 respectively, the energy value of regional exterior point is made as-1;

(2) image area to be repaired Ω is divided into a plurality of subregion Ω _i, i=1,2, L Np, wherein Np represents the number of subregion, with subregion Ω _iBe adjacent subregion Ω _I+1Boundary definition be Γ _i=Ω _iI Ω _I+1

(3) at each sub regions border Γ _iOn get one and comprise N _iIndividual set of joining a little

And all join a set

The central point that should comprise area to be repaired Ω; Choose a kind of radial basis function, establish

In each join a little

Corresponding radial basis function value is

K=1,2, L N _i

(4) to each subregion Ω _i(1≤i≤Np) finds the solution each respectively and joins a little energy value: establish

Be the border Γ of i and i-1 sub regions _i=Ω _iI Ω _I+1Last k joins the energy value at a place, gets when joining a little not on the border in district to be repaired for k

Otherwise get 0;

Be that i and the borderline k of i-1 sub regions join energy value a little, get when joining a little not on the border in district to be repaired when k is individual

Otherwise get 0;

Be the borderline energy value g that joins a little of friendship in i sub regions and district to be repaired;

(5) find the solution each subregion Ω _i(1≤i≤Np) goes up the energy value u at each point place _i: definition u _iBe i sub regions Ω _iAll join the weighted sum of an energy on the border all around, and its solution formula is:

$u_i=u_i^{*}+\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}{C}_k^i{U}_k^{i,i}+\underset{k=1}{\overset{N_{i-1}}{\mathrm{\Σ}}}{C}_k^{i-1}{U}_k^{i,i-1},$

Wherein, Λ,

Λ,

With

Λ,

Λ,

Be respectively N _iAnd N _I-1Individual undetermined coefficient, satisfy relational expression between each variable:

$[\underset{k=1}{\overset{N_{i-1}}{\mathrm{\Σ}}}{C}_k^{i-1}\frac{{\∂U}_k^{i,i-1}}{{\∂n}_i}+\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}{C}_k^i(\frac{{\∂U}_k^{i,i}}{{\∂n}_i}-\frac{{\∂U}_k^{i+1,i}}{{\∂n}_i})-\underset{k=1}{\overset{N_{i+1}}{\mathrm{\Σ}}}{C}_k^{i+1}\frac{{\∂U}_k^{i+1,i+1}}{{\∂n}_i}]{|}_{{\mathrm{\Γ}}_i}=(\frac{{\∂u}_{i+1}^{*}}{{\∂n}_i}-\frac{{\∂u}_i^{*}}{{\∂n}_i}){|}_{{\mathrm{\Γ}}_i}{u}_i$ Method for solving be: at Γ _iOn get one and comprise M _iThe set of individual point

M _i〉=N _i, will

In M _iIndividual point is brought in the relational expression, forms a system of equations, and separating this system of equations can obtain

With

The gained coefficient is brought the energy value that formula can be tried to achieve the inner each point of i sub regions into;

(6) according to each the subregion Ω that is tried to achieve _iOn the energy value formula, set up the energy distribution model of area to be repaired Ω, establish p and be in the area to be repaired a bit, its energy value is V (p);

(7) determine directivity priority coefficient S (p)=1-V (p) according to energy distribution V (p);

(8) directivity priority coefficient S (p) is combined by weight coefficient with quantity of information and structural FACTOR P (p), define new priority coefficient T (p);

(9) determine the fill order of borderline each pixel in image district to be repaired according to the priority coefficient T (p) of redetermination,

It is synthetic and repair successively each with the corresponding pixel points to be that the piece to be repaired at center carries out texture, till finishing, obtains final texture composograph.

Desirable texture is synthetic should to be distribution situation by texture around the area to be repaired, by progressively spreading to the center around the damage zone of rational progress by image, takes into account quantity of information and structural information simultaneously.The great advantage of the inventive method is can be according to texture situation around the image area to be repaired, automatically obtain its energy distribution at different directions, and definite on this basis directivity is repaired the right of priority index, for the texture building-up process provides index, thereby guarantee that image in the synthetic process of texture, can remain rational direction and progress.The present invention is incorporated into the Kansa algorithm of art of mathematics in the middle of the big area image texture synthetic technology, according to texture distribution situation around the area to be repaired, self-adaptation is chosen relevant joining a little, according to different texture distribution situation on every side, energy distribution to the area to be repaired is carried out three-dimensional modeling, and then obtain its energy distribution, and determine directivity texture reparation index based on this, progress and the direction synthetic for each point texture provide index; By combining with the legacy priority index, form new reparation priority coefficient, thereby guarantee in the synthetic process of big zone-texture, can remain correct direction and progress, reduce the mistake coupling, satisfy the synthetic requirement of the big zone-texture of actual non-homogeneous texture image.

Description of drawings

Fig. 1 utilizes the modeling effect of Kansa algorithm to three kinds of common zones, wherein figure (a) be by around to the modeling effect of center diffusion, figure (b) be by about to the effect of center diffusion, figure (c) is the effect by the diffusion of upward and downward center.

Fig. 2 is based on the synthetic synoptic diagram of repairing of the texture block of right of priority;

Fig. 3 contrasts the big regional synthetic effect of the non-homogeneous texture of reality with the present invention and classical texture composition algorithm, wherein, figure (a) is original non-homogeneous texture image, figure (b) is the area to be repaired image, figure (c) is for utilizing the repairing effect of traditional texture composition algorithm, and figure (d) has increased directivity to repair the texture synthetic effect of priority coefficient.

Embodiment

The Kansa method promptly based on the asymmetric point collocation of radial basis function, is a kind of numerical method that is used to find the solution the differential equation that grew up in recent years, and it all has a wide range of applications in Computational Mechanics, calculating electromagnetics and field of engineering technology.The Kansa method belongs to a kind of of no grid method, and not only computation process is simple for it, and precision is higher.The Kansa algorithm only is used for level and smooth curved surface is carried out modeling at present, or is used to analyze field distribution situations such as light stream, electromotive force, energy, and the present invention is incorporated into image processing field with this method, with the modeling that realizes that big region energy distributes.

The step of carrying out image modeling based on the Kansa algorithm of Region Decomposition is as follows:

Step 1: image area to be repaired Ω is divided into a plurality of subregion Ω _i, i=1,2, L Np, wherein Np represents the number of subregion; The boundary definition of all subregion is Γ _i=Ω _iI Ω _I+1If the energy value g of area to be repaired Ω central point and boundary equals 1 and 0 respectively, the energy value of regional exterior point is made as-1.

Step 2: at all subregion border Γ _iOn get and comprise N _iIndividual set of joining a little

And all join a set The central point that should comprise area to be repaired Ω;

In each join a little

Corresponding radial basis function

K=1,2, L N _i

Step 3: to each subregion Ω _i(1≤i≤Np) finds the solution each respectively and joins a little energy value

$U_k^{i,i}=\left\{\begin{array}{ccc}0& {\∂\mathrm{\Ω}}_{i}I\∂\mathrm{\Ω}& \\ 0& {\mathrm{\Γ}}_{i-1}\backslash ({\mathrm{\Γ}}_{i-1}I\∂\mathrm{\Ω})& \\ {\mathrm{\φ}}_k^i& {\mathrm{\Γ}}_i\backslash ({\mathrm{\Γ}}_{i}I\∂\mathrm{\Ω})& (1\≤k\≤N_i)\end{array}\right.---\left(1\right)$

$U_k^{i,i-1}=\left\{\begin{array}{ccc}0& {\∂\mathrm{\Ω}}_{i}I\∂\mathrm{\Ω}& \\ {\mathrm{\φ}}_k^{i-1}& {\mathrm{\Γ}}_{i-1}\backslash ({\mathrm{\Γ}}_{i-1}I\∂\mathrm{\Ω})& \\ 0& {\mathrm{\Γ}}_i\backslash ({\mathrm{\Γ}}_{i}I\∂\mathrm{\Ω})& (1\≤k\≤N_i)\end{array}\right.---\left(2\right)$

$u_i^{*}=\left\{\begin{array}{cc}g& {\∂\mathrm{\Ω}}_{i}I\∂\mathrm{\Ω}\\ 0& \left({\mathrm{\Γ}}_{i}U{\mathrm{\Γ}}_{i-1}\right)\backslash \left(({\mathrm{\Γ}}_{i}I\∂\mathrm{\Ω})U({\mathrm{\Γ}}_{i-1}I\∂\mathrm{\Ω})\right)\end{array}\right.---\left(3\right)$

Wherein,

Represent the border of district to be repaired and i subregion respectively,

Represent the friendship border in i subregion and district to be repaired. Representative removes that the friendship in i sub regions and district to be repaired is borderline joining a little, i is individual and the borderline position of respectively joining a little of the friendship of i-1 sub regions.In like manner, Represent respectively to join on the friendship border of i sub regions and i+1 sub regions position a little, do not comprise borderline the joining a little of friendship in it and district to be repaired;

Represent subregion border Γ respectively _I-1And Γ _iOn respectively join a position.

Step 4: find the solution Ω _iOn energy value u _i

$u_i=u_i^{*}+\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}{C}_k^i{U}_k^{i,i}+\underset{k=1}{\overset{N_{i-1}}{\mathrm{\Σ}}}{C}_k^{i-1}{U}_k^{i,i-1}---\left(4\right)$

Wherein

Λ,

Λ,

With

Λ, Λ,

Be respectively N _iAnd N _I-1Individual undetermined coefficient, satisfy relation between each variable:

$[\underset{k=1}{\overset{N_{i-1}}{\mathrm{\Σ}}}{C}_k^{i-1}\frac{{\∂U}_k^{i,i-1}}{{\∂n}_i}+\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}{C}_k^i(\frac{{\∂U}_k^{i,i}}{{\∂n}_i}-\frac{{\∂U}_k^{i+1,i}}{{\∂n}_i})-\underset{k=1}{\overset{N_{i+1}}{\mathrm{\Σ}}}{C}_k^{i+1}\frac{{\∂U}_k^{i+1,i+1}}{{\∂n}_i}]{|}_{{\mathrm{\Γ}}_i}=(\frac{{\∂u}_{i+1}^{*}}{{\∂n}_i}-\frac{{\∂u}_i^{*}}{{\∂n}_i}){|}_{{\mathrm{\Γ}}_i}---\left(5\right)$

At Γ _iOn get one and comprise M _iThe set of individual point M satisfies condition _i〉=N _i, will In M _iIndividual point is brought equation (5) into, forms a system of equations, and separating this system of equations can obtain With

Step 5: will With

Bring (4) into, can be in the hope of district to be repaired at Ω _iOn energy values separate.

$u=u_i=u_i^{*}+\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}{C}_k^i{U}_k^{i,i}+\underset{k=1}{\overset{N_{i-1}}{\mathrm{\Σ}}}{C}_k^{i-1}{U}_k^{i,i-1}---\left(6\right)$

U satisfies u=1 at central point, on the border On satisfy boundary condition u=0, then be approximate smooth on Ω, therefore can be used as Ω _iOn the energy distribution model.(the present invention selects radial basis function φ (r)=r ⁵As the interpolation basis function).

Utilize the Kansa algorithm that big zone-texture is synthesized, concrete steps are as follows:

---determine area to be repaired Ω, extract the border, area to be repaired

The central point of zoning Ω; The energy value at image area to be repaired central point and frontier point place is set at 1 and 0 respectively, and the energy value of regional exterior point is made as-1, is distributed in [0,1] scope to guarantee the modeling region energy;

---utilize the Kansa algorithm that above-mentioned model is carried out modeling, uniformly-spaced choose relevant joining a little, calculate whole parameter values, modeling is carried out in the area to be repaired, obtain the energy profile of inside, area to be repaired at central point and boundary;

---determine orientation preferentially weight coefficient S (p) according to energy distribution, p be in the district to be repaired a bit;

---equidistant priority coefficient S (p) is combined with quantity of information C (p) and structural coefficient D (p) in the classic method, define new priority coefficient T (p);

---determine the image fill order according to the priority coefficient of redetermination, successively each piece is carried out the synthetic and reparation of texture, till finishing, obtain final texture composograph.

Said method is used for curved surface's modeling, need chooses relevant joining a little by the homogeneity principle in known region, each joins parameter value of a correspondence, by solving equation group and then acquisition correlation parameter; Select suitable radial basis function as the interpolation basis function, utilize the linear combination of the two, just can realize mathematical modeling and reconstruction to curved surface, the modeling rear curved surface distributes and satisfies the condition of whole flatness.

The present invention to the improvements of traditional texture composition algorithm is, improve algorithm with Kansa image is carried out pre-service, thereby obtain the energy distribution of image, and right of priority index is in the past made amendment determine directivity reparation right of priority index on this basis, progress and the direction synthetic for each point texture provide index, adopt the damaged piece that piece mates each different priorities to mate one by one then.Concrete enforcement is as follows:

1) utilize improvement Kansa algorithm that image is carried out three-dimensional modeling

Because the fluctuation of real image curved surface is violent, do not satisfy the requirement of flatness usually, be difficult to the direct modeling of Kansa algorithm, therefore project is before to the real image modeling, at first it is carried out medium filtering,, in the protection edge, reduce noise to satisfy the condition of whole flatness; Inventor early stage studies show that this measure can effectively reduce the conditional number of finding the solution matrix, improve the accuracy of modeling.The present invention selects radial basis function φ (r)=r for use ⁵As the interpolation basis function, realize the three-dimensional modeling of image.

The present invention adopts on the border, area to be repaired and central point is evenly chosen the method for joining a little, realizes the automatic modeling of image area to be repaired energy distribution.Join a little what and need determine that according to inventor's result of study in early stage, joining counts just can satisfy the requirement of modeling accuracy basically between 60～90 according to actual conditions.

The inventor utilizes the Kansa algorithm respectively three kinds of common regional situations to be carried out modeling in earlier stage, according to the distribution situation of texture around the area to be repaired, as shown in Figure 1, it is repaired direction and should be respectively: by spreading to the center all around, by about to center diffusion, and spread by the upward and downward center.For three kinds of different situations, utilize Kansa to improve algorithm and can both obtain the energy needed distribution, also as can be seen,, choose different joining a little in the while modeling process even for the identical texture region of shape, the energy distribution of acquisition also has very big difference.

2) determine to be matched right of priority

After finishing energy profile, can determine new directivity reparation right of priority index.As shown in Figure 2, Ω is the area to be repaired,

Be the border, area to be repaired, Φ is source region (effective information zone), ψ _pIt is target area piece to be filled.The point p be in the district to be repaired a bit, its linear coordinate is that (i, j), (i, j), then the directivity priority coefficient of this point is defined as for V to utilize the Kansa modeling to obtain its energy distribution

S(i，j)＝1-V(i，j) (7)

The reparation right of priority that is frontier point is for the highest by 1, and the reparation right of priority of central point is 0.

S (p) is combined with quantity of information and structural FACTOR P (p) in the classic method, thereby define new priority coefficient T (p), the reparation that is used for determining each point in the image area to be repaired is (descending) in proper order.

T(p)＝λ ₁·P(p)+λ ₂·S(p) (8)

Wherein, λ ₁, λ ₂Be weight coefficient, they satisfy relation: 0≤λ ₁≤ 1,0≤λ ₂≤ 1, λ ₁+ λ ₂=1.λ ₁, λ ₂Can choose according to concrete image, the directivity of texture image is strong more, λ ₂Value corresponding also should be big more.P (p) is conventional information amount and structural reparation coefficient.

P(p)＝C′(p)*D(p) (9)

Wherein C ' is expression current block ψ (p) _pThe degree of confidence item of reliability, D (p) are used for characterizing the isophote intensity that p is ordered.

$C^{\′}\left(p\right)=\frac{{\mathrm{\Σ}}_{q\∈{\mathrm{\ψ}}_p\∪\stackrel{\‾}{\mathrm{\Ω}}}C\left(q\right)}{\left|{\mathrm{\ψ}}_p\right|},$ $D_p=\frac{|\▿I_p^{\⊥}\·n_p|}{\mathrm{\α}}---\left(10\right)$

Wherein

Be intact zone, | ψ _p| the texture match block ψ of expression impact point p _pArea, α is a normalization coefficient, makes 0≤D (p)≤1.n _pFor filling the edge

The normal vector that last p is ordered,

The vertical direction of expression p point gradient direction.

The degree of confidence of C (p) expression point p.During initialization, order

$C\left(p\right)=\left\{\begin{array}{c}0,\∀p\∈\mathrm{\Ω}\\ 1,\∀p\∈\stackrel{\‾}{\mathrm{\Ω}}\end{array}\right.---\left(11\right)$

0≤C (p)≤1 in continuous mending course like this, the inside of deeply waiting to mend regional Ω, confidence value is just low more, meets universal law.Confidence value C (p) is low more, and the right of priority T that obtains at last (p) is just low more, and this has guaranteed that synthetic order is synthetic to the center from the periphery basically.

After the right of priority of being had a few on the border, district to be repaired is calculated, just can determine the piece to be repaired of highest priority.As from the foregoing, right of priority T (p) is the fundamental function of image, has reflected and has waited to repair piece ψ _pThe comprehensive characteristics of degree of confidence, isophote intensity and directivity. the image filling and repairing order by its decision can make the image sampling process in an organized way carry out, and meets " vision connection principle ", occurs after avoiding repairing that structure disconnects, phenomenon such as fuzzy.

3) determine best matching blocks

Find have the highest priority match block after, then search and its sample block of mating most in the whole effective information zone of image.Get the some p of right of priority maximum, in former figure in the complete good zone search be the square synthesis window ψ at center with p _pThe piece ψ that mates most _q, make

${\mathrm{\ψ}}_q={\arg \min }_{{\mathrm{\ψ}}_{q^{\′}}\⋐\mathrm{\Φ}}d({\mathrm{\ψ}}_p,{\mathrm{\ψ}}_{q^{\′}})---\left(12\right)$

Wherein, d (ψ _p, ψ _{Q '}) be ψ _pAnd ψ _{Q '}The variance of corresponding point color rgb value and, for gray level image then be corresponding each point gray-scale value variance and.By above range formula, calculate and compare, lowest distance value corresponding sample piece is exactly a best matching blocks.

4) information is filled

In case found to have the piece ψ of highest priority _p, and found its best matching blocks ψ _qAfter, just can use ψ _qThe pixel of middle correspondence position is filled ψ _pIn the unknown pixel point.The simple copy process of data that Here it is.Finish the structure from the source region to the target area and the propagation of texture information in this way, a part of loss of learning zone in the image is filled.

5) upgrade confidence value

When new image information is filled in ψ _pIn data disappearance place after, need to upgrade the confidence value that is replicated the data corresponding pixel points.Degree of confidence C (p) upgrades according to following formula:

C(q)＝C′(p) $\∀q\∈{\mathrm{\ψ}}_p\∩\mathrm{\Ω}---\left(13\right)$

And then upgrade the border in district to be repaired, and calculate to be repaired new right of priority, determine the optimum matching sample block that it is corresponding, structure that copy and paste is new and texture information are in the target area.So circulation, the confidence value of all pixels is non-0 in image, and whole area to be repaired was filled and was finished this moment.

Said method people validity is verified, the present invention has chosen the natural landscape (as sky, white clouds, ocean etc.) of a few width of cloth actual photographed, and emulation experimentizes, to the invention provides method and classical big zone-texture composition algorithm, contrast with the texture synthetic effect of Criminisi algorithm, experimental result respectively as shown in Figure 3.From figure, can obviously find out, utilize traditional texture synthetic method (figure c) the mistake coupling to occur, have tangible repairing mark, and the present invention increase the texture composition algorithm (figure d) of directivity reparation index, has then obtained gratifying repairing effect.

Claims (1)

1. one kind big regional non-homogeneous texture synthesis method comprises the following steps:

(1) determines area to be repaired Ω, extract the border, area to be repaired

Determine the central point of area to be repaired Ω, the energy value g at image area to be repaired central point and frontier point place is set at 1 and 0 respectively, the energy value of regional exterior point is made as-1;

(2) image area to be repaired Ω is divided into a plurality of subregion Ω _i, i=1,2, L Np, wherein Np represents the number of subregion, with subregion Ω _iBe adjacent subregion Ω _I+1Boundary definition be Γ _i=Ω _iI Ω _I+1

(3) at each sub regions border Γ _iOn get one and comprise N _iIndividual set of joining a little

And all join a set The central point that should comprise area to be repaired Ω; Choose a kind of radial basis function, establish

In each join a little

Corresponding radial basis function value is

K=1,2, L N _i

(4) to each subregion Ω _i(1≤i≤Np) finds the solution each respectively and joins a little energy value: establish

Be the border Γ of i and i-1 sub regions _i=Ω _iI Ω _I+1Last k joins the energy value at a place, gets when joining a little not on the border in district to be repaired for k

Otherwise get 0;

Be that i and the borderline k of i-1 sub regions join energy value a little, get when joining a little not on the border in district to be repaired when k is individual

Otherwise get 0;

Be the borderline energy value g that joins a little of friendship in i sub regions and district to be repaired;

(5) find the solution each subregion Ω _i(1≤i≤Np) goes up the energy value u at each point place _i: definition u _iBe i sub regions Ω _iAll join the weighted sum of an energy on the border all around, and its solution formula is:

$u_i=u_i^{*}+\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}{C}_k^i{U}_k^{i,i}+\underset{k=1}{\overset{N_{i-1}}{\mathrm{\Σ}}}{C}_k^{i-1}{U}_k^{i,i-1},$

Wherein,

Λ, Λ,

With

Λ,

Λ,

Be respectively N _iAnd N _I-1Individual undetermined coefficient, satisfy relational expression between each variable:

$[\underset{k=1}{\overset{N_{i-1}}{\mathrm{\Σ}}}{C}_k^{i-1}\frac{{\∂U}_k^{i,i-1}}{{\∂n}_i}+\underset{k=1}{\overset{N_i}{\mathrm{\Σ}}}{C}_k^i(\frac{{\∂U}_k^{i,i}}{{\∂n}_i}-\frac{{\∂U}_k^{i+1,i}}{{\∂n}_i})-\underset{k=1}{\overset{N_{i+1}}{\mathrm{\Σ}}}{C}_k^{i+1}\frac{{\∂U}_k^{i+1,i+1}}{{\∂n}_i}]{|}_{{\mathrm{\Γ}}_i}=(\frac{{\∂u}_{i+1}^{*}}{{\∂n}_i}-\frac{{\∂u}_i^{*}}{{\∂n}_i}){|}_{{\mathrm{\Γ}}_i}{u}_i$ Method for solving be: at Γ _iOn get one and comprise M _iThe set of individual point

M _i〉=N _i, will

In M _iIndividual point is brought in the relational expression, forms a system of equations, and separating this system of equations can obtain

With

The gained coefficient is brought the energy value that formula can be tried to achieve the inner each point of i sub regions into;

(6) according to each the subregion Ω that is tried to achieve _iOn the energy value formula, set up the energy distribution model of area to be repaired Ω, establish p and be in the area to be repaired a bit, its energy value is V (p);

(7) determine directivity priority coefficient S (p)=1-V (p) according to energy distribution V (p);

(8) directivity priority coefficient S (p) is combined by weight coefficient with quantity of information and structural FACTOR P (p), define new priority coefficient T (p);

(9) determine the fill order of borderline each pixel in image district to be repaired according to the priority coefficient T (p) of redetermination, it is synthetic and repair successively each with the corresponding pixel points to be that the piece to be repaired at center carries out texture, till finishing, obtain final texture composograph.

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