CN103778604A - Image restoration method based on texture direction - Google Patents

Abstract

The invention discloses an image restoration method based on the texture direction. According to the image restoration method, a local texture coordinate system is constructed according to the local texture direction of a region to be restored, an energy functional based on the local texture coordinate system is constructed, the restoration equation of the region to be restored is obtained according to the energy functional, and then the restoration equation is discretized, and the image restoration equation is solved by the use of the Gauss-Seidel iterative method so as to obtain the pixel values of pixels in the region to be restored and complete restoration. According to the image restoration method, an image does not need to be pre-processed in advance and can be directly processed, the texture information and structure information of the region to be restored can be simultaneously restored, the restoration effect is greatly improved, and meanwhile, the amount of calculation is small, the restoration rate is effectively improved, and the restoration time is reduced.

Description

Based on the image repair method of grain direction

Technical field

The present invention relates to Computer Image Processing field, relate in particular to a kind of image repair method based on grain direction.

Background technology

Image repair problem is mainly repaired the part of losing in image or damage, and specifically comprises and repairs incomplete image, the dirt in removal image etc.In computer picture field, the original coordinate system of image is generally initial point take the upper left corner, and level is to the right directions X, is Y-direction straight down.

At present, repair by Texture Synthesis for texture information, use PDE algorithm repair structure information, this two classes algorithm has all been obtained certain breakthrough.But texture information and the structural information of repairing due to need are in itself not identical, so current a lot of algorithms are all difficult to repair texture information and structural information simultaneously.Just particularly, by Texture Synthesis, structural information is repaired to easy generation artificial trace, and use the algorithm of partial differential equation only effective to structural information, seem helpless for the reparation of texture information.The reasonable algorithm of another kind of repairing effect, first the image of need reparation to be analyzed, it is divided into texture information part and structural information part, then these two parts is repaired it with texture reparation algorithm and structure repair algorithm respectively, finally two-part result is merged.By image is carried out to predecomposition, then repair the result of algorithm in conjunction with two classes, the effect of this reparation is better than only using a kind of reparation algorithm (texture is repaired algorithm or structure repair algorithm), and complicated but this algorithm is implemented, the execution efficiency of algorithm is not high yet.

In addition, the reparation based on overall variation (Total Variation, TV) model is classical reparation algorithm, but the algorithm of repairing with many use partial differential equation is the same, poor effect for texture reparation; Reparation algorithm based on OABE (Oriented Anisotropic Brightness Equation) can be repaired simple texture, this algorithm is that the image repair based on partial differential equation is expanded, although this algorithm will be got well but can only repair some simple structural textures (as square mosaic) than TV algorithm, for complicated texture processing poor effect.

Summary of the invention

For the deficiencies in the prior art, the invention provides a kind of image repair method based on grain direction, this image repair method is mainly repaired from texture information and structural information two aspects of image, improve the repairing effect of image, calculated amount is little simultaneously, effectively improve reparation shrinkage, reduced the time of repairing.

Based on an image repair method for grain direction, comprising:

(1) specify the area to be repaired in image to be repaired with mark, and the minimum rectangle of definite area to be repaired covers box;

(2) area to be repaired in image to be repaired is expanded outwardly to several pixels obtain the borderline region of area to be repaired, according to the position of each pixel in borderline region, determine the local grain direction of area to be repaired, be designated as V _ρ=(m, n);

(3) cover He center as true origin, with described local grain direction V take minimum rectangle _ρand with local grain direction V _ρorthogonal vectorial V _γfor the positive dirction of coordinate axis, set up the local grain coordinate system of this area to be repaired, wherein V _γ=(n, m);

(4) in local grain coordinate system, set up the energy functional formula of this area to be repaired;

(5) according to Euler-Lagrange equation, energy functional formula is carried out to minimization operation, the Euler-Lagrange that obtains area to be repaired is repaired equation;

(6) for each pixel to be repaired in area to be repaired, determine that the pixel that is h/2 with the distance of current pixel to be repaired in local grain coordinate axis is as neighborhood territory pixel point, according to neighborhood territory pixel point, described Euler-Lagrange is repaired to equation and carry out discretize processing, obtain the discrete reparation equation of current pixel to be repaired, h is local grain direction V _ρmould;

(7) described discrete reparation equation distortion is simplified and obtained iterative equation;

(8) adopt Gauss-Seidel iteration method to carry out iteration to iterative equation, each iteration obtains a pixel value, when:

$|u_O^{\left(n\right)}-u_O^{(n-1)}|\≤\mathrm{\μ}$

Or

n=N

Time, stop iteration, and the pixel value obtaining using last iteration is as the pixel value of current pixel to be repaired, and with this pixel value, current pixel to be repaired repaired, wherein, μ is the threshold value of setting, N is the maximum iteration time of setting, wherein with

be respectively the n time and the pixel value of the current pixel to be repaired that the n-1 time iteration obtains.

The present invention builds local grain coordinate system according to the local grain direction of area to be repaired, set up the energy functional formula based on this local grain coordinate system, can repair texture information and structural information simultaneously, energy functional formula is carried out to minimization operation, and then obtain the reparation equation of this area to be repaired, a continuous problem owing to solving the reparation equation of texture structure, for convenience of calculating, we are first to repairing equation according to the definition of the gradient of equation and divergence and in conjunction with the position relationship between pixel, carry out difference discrete operation to repairing equation, then by Gauss-Seidel iteration method, image repair equation is solved.

Image repair method based on grain direction of the present invention is applicable to the image repair of the small area structure texture disappearance of arbitrary shape.This image repair method not only can be repaired the texture information of image and can repair structural information, and does not need in advance image to be carried out to resolution process, thereby this algorithm is higher to the remediation efficiency of local structural texture.The image of the small area structure texture disappearance of new algorithm of the present invention to arbitrary shape is all very effective simultaneously, and this algorithm can guarantee to repair preferably border equally, avoids artificial trace.

In described step (1), the area to be repaired in image to be repaired being expanded outwardly to several pixels obtains borderline region and does not comprise the borderline pixel in area to be repaired, the pixel only obtaining for extension, the pixel number expanding outwardly is determined according to the size of area to be repaired.Area to be repaired is less, and the pixel number expanding outwardly is larger, and the reparation precision obtaining is higher, can reduce reparation speed when simultaneously.As preferably, 3～6 pixels that expand outwardly.

Described step is determined local grain direction by following steps in (2):

(2-1) for any two pixels in borderline region, if:

|(x ₁，y ₁)-(x ₂，y ₂)|<ε，

And vector (x ₂-x ₁, y ₂-y ₁) meet MAD condition, by vector (x ₂-x ₁, y ₂-y ₁) as candidate direction vector, and the vector set using all candidate direction vectors as candidate direction, wherein, (x ₁, y ₁) and (x ₂, y ₂) being respectively the coordinate of any two pixels in borderline region, ε is the threshold value of setting;

(2-2) set of candidate direction vector is made to absolute difference function:

$\mathrm{\&sigma;}=\frac{1}{\left|Q\right|}\underset{(i^{\&prime;},j^{\&prime;})\&Element;\mathrm{\&Omega;}\backslash D}{\underset{(i,j)\&Element;Q}{\mathrm{\&Sigma;}}}\mathrm{Abs}(P(i,j)-P(i^{\&prime;},j^{\&prime;}))$

Get the candidate direction vector of minimum value as the local grain direction vector of this area to be repaired, be designated as V _ρ=(m, n), wherein,

Wherein, σ is absolute difference function,

D represents the area to be repaired in image to be repaired,

Ω represents whole image-region, Ω D represent to remove in image to be repaired region outside the D of area to be repaired,

Q is the set of the pixel of a pixel of extension on the border of area to be repaired D, | Q| represents the number of the pixel of gathering Q,

Abs () represents to ask the function of absolute value,

P (i, j) represents the pixel value of any one pixel of set Q,

P (i ', j ') represent region Ω in D coordinate be the pixel value of the pixel of (i ', j '), and:

As (i+x _t, j+y _t) ∈ Ω when D, (i ', j ')=(i+x _t, j+y _t),

As (i-x _t, j-y _t) ∈ Ω when D, (i ', j ')=(i-x _t, j-y _t),

(x _t, y _t) be any one the candidate direction vector in the set of candidate direction vector.

The threshold epsilon of setting in described step (2-1) is 5～20.The local grain direction obtaining in the present invention is approximate grain direction, and ε represents two distances between pixel, and setting value is less, the local grain direction obtaining approaches actual grain direction, considers reparation speed simultaneously, and the scope of setting in the present invention is 5～20, as preferably, ε is 8.

In described step (2-1), the threshold value of MAD condition is 10～30, if this threshold value is too large, the approximate local grain direction finally obtaining that can make and real grain direction differ too large.

The energy functional formula that described step (4) obtains is as follows:

$J_{\mathrm{\&lambda;}}^t\left[u\right]=\underset{G\&cup;D}{\&Integral;}\left|{\&dtri;}_u\right|\mathrm{d\&rho;d\&gamma;}+\frac{\mathrm{\&lambda;}}{2}\underset{G}{\&Integral;}{|u-u^0|}^2\mathrm{d\&rho;d\&gamma;},$

Wherein,

represent energy functional formula,

G is the borderline region of area to be repaired,

D is the area to be repaired of repairing in image,

G ∪ D is the combination of area to be repaired and borderline region,

ρ, γ represents respectively horizontal ordinate and the ordinate of local grain coordinate system,

U is the pixel value of any one pixel to be repaired in area to be repaired, u ⁰for original pixel values corresponding to this pixel to be repaired,

for the gradient of any one pixel to be repaired in area to be repaired,

λ is constant.

All there is an original pixel values in each pixel to be repaired, can be directly from Image Acquisition to be repaired, and the pixel value of pixel to be repaired is unknown quantity.λ is constant, rule of thumb sets λ=15 in the present invention.

It is as follows that the Euler-Lagrange of described area to be repaired is repaired equation:

$-\&dtri;\&CenterDot;\left(\frac{{\&dtri;}_u}{\left|{\&dtri;}_u\right|}\right)+\mathrm{\&gamma;}(u-u^0)=0,$

Wherein,

for asking divergence symbol.

for the divergence of the content in bracket under local coordinate system, this reparation equation is applicable to all pixels in area to be repaired.

In described step (6), the discrete reparation equation of current pixel to be repaired is as follows:

${\mathrm{\&Sigma;}}_{P\&Element;\mathrm{\&Lambda;}}\frac{1}{|\&dtri;u_p|}(u_0-u_p)+\mathrm{\&gamma;}(u_O-u_O^0)=0,$

Wherein, Λ represents the set of neighborhood territory pixel point,

P is any one neighborhood territory pixel point,

O is current pixel to be repaired,

U _ofor the pixel value of current pixel O to be repaired,

for the original pixel values of current pixel O to be repaired,

U _pfor the pixel value of neighborhood territory pixel point P,

for the gradient of neighborhood territory pixel point P point under local grain coordinate system.

Comprising the following steps of difference discrete processing in described step (6):

(6-1) Euler to current pixel to be repaired-Lagrange is repaired the divergence of equation and is carried out discretize operation, order:

$\&dtri;\&CenterDot;\mathrm{\&upsi;}=\frac{{\&PartialD;\mathrm{\&upsi;}}^1}{\&PartialD;\mathrm{\&rho;}}+\frac{{\&PartialD;\mathrm{\&upsi;}}^2}{\&PartialD;\mathrm{\&gamma;}}\&ap;\frac{{\mathrm{\&upsi;}}_r^1-{\mathrm{\&upsi;}}_l^1}{h}+\frac{{\mathrm{\&upsi;}}_u^2-{\mathrm{\&upsi;}}_d^2}{h},$

Wherein,

represent vector v to ask divergence,

U, d, l, r is respectively neighbours territory pixel, and corresponding coordinate is respectively: (x+n/2, y-m/2), (x-n/2, y+m/2), (x-m/2, y-n/2), (x+m/2, y+n/2),

be illustrated respectively in r, the component value of (X direction in local grain coordinate system) in first dimension of l neighborhood territory pixel point vector,

be illustrated respectively in u, the component value of (X direction in local grain coordinate system) in second dimension of d neighborhood territory pixel point vector;

(6-2) according to formula:

$v_r^1=\frac{1}{|\&dtri;u_r|}\frac{u_R-u_O}{h}$

Calculate

wherein:

$|\&dtri;u_r|\&ap;{\{{\left(\frac{u_R-u_O}{h}\right)}^2+{\left[\frac{1}{2}(\frac{u_{\mathrm{RU}}-u_{\mathrm{RD}}}{2h}+\frac{u_U-u_D}{2h})\right]}^2\}}^{1/2},$

According to formula:

$v_l^1=\frac{1}{|\&dtri;u_l|}\frac{u_L-u_O}{h}$

Calculate

wherein:

$|\&dtri;u_l|\&ap;{\{{\left(\frac{u_L-u_O}{h}\right)}^2+{\left[\frac{1}{2}(\frac{u_{\mathrm{LU}}-u_{\mathrm{LD}}}{2h}+\frac{u_U-u_D}{2h})\right]}^2\}}^{1/2},$

According to formula:

$v_u^2=\frac{1}{|\&dtri;u_u|}\frac{u_U-u_O}{h}$

Calculate

wherein:

$|\&dtri;u_u|\&ap;{\{{\left(\frac{u_U-u_O}{h}\right)}^2+{\left[\frac{1}{2}(\frac{u_{\mathrm{UR}}-u_{\mathrm{UL}}}{2h}+\frac{u_R-u_L}{2h})\right]}^2\}}^{1/2},$

According to formula:

$v_d^2=\frac{1}{|\&dtri;u_d|}\frac{u_D-u_O}{h}$

Calculate

wherein:

$|\&dtri;u_d|\&ap;{\{{\left(\frac{u_D-u_O}{h}\right)}^2+{\left[\frac{1}{2}(\frac{u_{\mathrm{DR}}-u_{\mathrm{DL}}}{2h}+\frac{u_R-u_L}{2h})\right]}^2\}}^{1/2},$

The coordinate of U, D, L, R, LU, LD, RU and RD is respectively: (x+n, _y-m), (x-n, y+m), (x-m, y-n), (x+m, y+n), (x-m+n, y-m-n), (x-m-n, y+m-n), (x+m+n, y-m+n) and (x+m-n, y+m+n),

U _tfor the pixel value of pixel t, wherein t is u, d, l, r, U, D, L, R, LU, LD, RU and RD;

(6-3) above each public affairs successively substitution Euler-Lagrange repaired to equation obtain the discrete reparation equation of current pixel to be repaired.

Iterative equation in described step (7) is as follows:

$u_O={\mathrm{\&Sigma;}}_{P\&Element;\mathrm{\&Delta;}}{h}_{\mathrm{OP}}{u}_p+h_{\mathrm{OO}}{u}_O^0,$

Wherein, $w_p=1/|\&dtri;u_p|,h_{\mathrm{OP}}=w_p/(\underset{P\&Element;\mathrm{\&Lambda;}}{\mathrm{\&Sigma;}}{w}_p+\mathrm{\&lambda;}),\mathrm{\&lambda;}/(\underset{P\&Element;\mathrm{\&Lambda;}}{\mathrm{\&Sigma;}}{w}_p+\mathrm{\&lambda;})=h_{\mathrm{OO}}.$

Can obtain according to iterative equation the pixel value that the n time iteration obtains

for:

$u_O^{\left(n\right)}=\underset{P\&Element;\mathrm{\&Lambda;}}{\mathrm{\&Sigma;}}{h}_{\mathrm{OP}}^{(n-1)}{u}_P^{(n-1)}+h_{\mathrm{OO}}^{(n-1)}{u}_O^{(n-1)}$

Wherein,

it is the pixel value that the n-1 time iteration obtains.

The threshold value μ setting in described step (8) is 1～5, selects less threshold value to obtain repairing preferably result.If the threshold value arranging is larger, although can improve the speed of algorithm, last repairing effect reduces greatly.

The maximum iteration time N setting in described step (8) is 50～150, sets maximum iteration time and is for fear of the poor absolute value of result of adjacent twice iteration after iteration many times to be still greater than threshold value μ, thus the speed of the algorithm reducing.

In the present invention, be not specifically noted, the position coordinates of all vector sum pixels is the value under original coordinate system.

Compared with prior art, advantage of the present invention is as follows:

(a) the present invention does not need in advance image to anticipate work, can directly process image, not only can repair the texture information of image but also the structural information that can repair image, has shortened widely the time loss of algorithm;

(b) image of the small area structure texture disappearance of algorithm of the present invention to arbitrary shape is all effective, and versatility is high, and this algorithm can guarantee good repairing effect simultaneously, avoids artificial trace;

(c) algorithm of the present invention can automanually be repaired image, only given image-region and the initial parameter (threshold value) that needs reparation, and the enforcement of algorithm is simple and convenient.

Embodiment

Based on an image repair method for grain direction, comprise the following steps:

(1) specify the area to be repaired in image to be repaired with mark, and the minimum rectangle of definite area to be repaired covers box;

(2) area to be repaired in image to be repaired is expanded outwardly to several (being 3 pixels in the present embodiment) pixels and obtain the borderline region of area to be repaired, according to the position of each pixel in borderline region, the local grain direction of determining area to be repaired, comprises the following steps:

Described step is determined local grain direction by following steps in (2):

(2-1) for any two pixels in borderline region, if:

|(x ₁，y ₁)-(x ₂，y ₂)|<ε， （1）

And vector (x ₂-x ₁, y ₂-y ₁) meet MAD condition, by vector (x ₂-x ₁, y ₂-y ₁) as candidate direction vector, and the vector set using all candidate direction vectors as candidate direction, be designated as T, wherein, (x ₁, y ₁) and (x ₂, y ₂) being respectively the coordinate of any two pixels in borderline region, ε is the threshold value (ε=8 in the present embodiment) of setting;

(2-2) will in candidate direction vector set T, make absolute difference function:

$\mathrm{\&sigma;}=\frac{1}{\left|Q\right|}\underset{(i^{\&prime;},j^{\&prime;})\&Element;\mathrm{\&Omega;}\backslash D}{\underset{(i,j)\&Element;Q}{\mathrm{\&Sigma;}}}\mathrm{Abs}(P(i,j)-P(i^{\&prime;},j^{\&prime;}))---\left(2\right)$

Get the local grain direction vector of minimum candidate direction vector as this area to be repaired, be designated as V _ρ=(m, n), wherein,

Wherein, σ is absolute difference function,

D represents the area to be repaired in image to be repaired,

Ω represents whole image-region, Ω D represent to remove in image to be repaired region outside the D of area to be repaired,

Q is the set of the pixel of a pixel of extension on the border of area to be repaired D, | Q| represents the number of the pixel of gathering Q,

Abs () represents to ask the function of absolute value,

P (i, j) represents the pixel value of any one pixel of set Q,

P (i ', j ') represent region Ω in D coordinate be the pixel value of the pixel of (i ', j '), and:

As (i+x _t, j+y _t) ∈ Ω when D, (i ', j ')=(i+x _t, j+y _t);

As (i-x _t, j-y _t) ∈ Ω when D, (i ', j ')=(i-x _t, j-y _t),

(x _t, y _t) be any one candidate direction vector in candidate direction vector set T.

Wherein, if vector (x ₂-x ₁, y ₂-y ₁) meet following condition:

, vector (x ₂-x ₁, y ₂-y ₁) meet MAD (Mean Absolute Difference) condition, wherein,

S={(Δx,Δy)|Δx∈[-1,1]，Δy[-1,1]，(x ₁+Δx,y ₁+Δy),(x ₂+Δx,y ₂+Δy)∈Ω\D}，

| S| represents element number in S;

represent to think that the MAD condition threshold value of setting is (in the present embodiment );

Δ x, Δ y represents respectively the side-play amount of horizontal direction and vertical direction, and is integer;

X ₁, x ₂, y ₁, y ₂horizontal ordinate and the ordinate of pixel in presentation video respectively.

(3) cover He center as true origin, with the local grain direction V of this area to be repaired take minimum rectangle _ρand with local grain direction V _ρorthogonal vector V _γfor the direction of coordinate axis, set up the local grain coordinate system of this area to be repaired, wherein V _γ=(n, m);

(4) in local grain coordinate system, set up the energy functional formula of this area to be repaired:

$J_{\mathrm{\&lambda;}}^t\left[u\right]=\underset{G\&cup;D}{\&Integral;}\left|{\&dtri;}_u\right|\mathrm{d\&rho;d\&gamma;}+\frac{\mathrm{\&lambda;}}{2}\underset{G}{\&Integral;}{|u-u^0|}^2\mathrm{d\&rho;d\&gamma;},---\left(4\right)$

represent energy functional formula,

G is the borderline region of area to be repaired,

D is the area to be repaired of repairing in image,

G ∪ D is the combination of area to be repaired and borderline region,

ρ, γ represents respectively horizontal ordinate and the ordinate of local grain coordinate system,

U is that the pixel value of any one pixel to be repaired in area to be repaired (is unknown quantity, needs

The desired value solving), u ⁰for original pixel values corresponding to this pixel to be repaired,

for the gradient of any one pixel to be repaired in area to be repaired,

λ is constant (λ=15 in the present embodiment);

(5) according to Euler-Lagrange equation, energy functional formula is carried out to minimization operation, when this energy functional minimalization, meets equation:

$-\&dtri;\&CenterDot;\left(\frac{{\&dtri;}_u}{\left|{\&dtri;}_u\right|}\right)+\mathrm{\&lambda;}(u-u^0)=0,---\left(5\right)$

This equation is the Euler-Lagrange of area to be repaired and repairs equation,

Wherein,

for ask divergence symbol (

for the divergence of the content in bracket under local coordinate system);

(6), for each pixel to be repaired in area to be repaired, determine that the pixel that is h/2 along the distance of local grain change in coordinate axis direction and current pixel to be repaired is as neighbours territory pixel, the discrete reparation equation of pixel to be repaired:

$\underset{P\&Element;\mathrm{\&Lambda;}}{\mathrm{\&Sigma;}}\frac{1}{|\&dtri;u_p|}(u_0-u_p)+\mathrm{\&lambda;}(u_O-u_O^0)=0,---\left(6\right)$

Wherein, h is local grain direction V _ρmould,

Λ represents the set of neighborhood territory pixel point,

P is any one neighborhood territory pixel point,

O is current pixel to be repaired.

U _ofor the pixel value (being unknown quantity, the desired value that need to solve) of current pixel O to be repaired,

for the original pixel values of current pixel O to be repaired,

U _pfor the pixel value of neighborhood territory pixel point P,

for the gradient of neighborhood territory pixel point P point under local grain coordinate system, the comprising the following steps of difference discrete processing:

(6-1) Euler to current pixel to be repaired-Lagrange is repaired the divergence of equation and is carried out discretize operation, order:

$\&dtri;\&CenterDot;v=\frac{\&PartialD;v^1}{\&PartialD;\mathrm{\&rho;}}+\frac{\&PartialD;v^2}{\&PartialD;\mathrm{\&gamma;}}\&ap;\frac{v_r^1-v_l^1}{h}+\frac{v_u^2-v_d^2}{h},---\left(7\right)$

Wherein, represent vector v to ask divergence,

$v=(v^1,v^2)=\frac{{\&dtri;}_u}{\left|{\&dtri;}_u\right|},$

U, d, l, r is respectively neighbours territory pixel, and corresponding coordinate is respectively: (x+n/2, y-m/2), (x-n/2, y+m/2), (x-m/2, y-n/2), (x+m/2, y+n/2),

be illustrated respectively in r, the component value in first dimension of l neighborhood territory pixel point vector,

be illustrated respectively in u, the component value in second dimension of d neighborhood territory pixel point vector;

(6-2) according to formula:

$v_r^1=\frac{1}{|\&dtri;u_r|}\frac{u_R-u_O}{h}---\left(8\right)$

Calculate

wherein:

$|\&dtri;u_r|\&ap;{\{{\left(\frac{u_R-u_O}{h}\right)}^2+{\left[\frac{1}{2}(\frac{u_{\mathrm{RU}}-u_{\mathrm{RD}}}{2h}+\frac{u_U-u_D}{2h})\right]}^2\}}^{1/2},---\left(9\right)$

According to formula:

$v_l^1=\frac{1}{|\&dtri;u_l|}\frac{u_L-u_O}{h}---\left(10\right)$

Calculate wherein:

$|\&dtri;u_l|\&ap;{\{{\left(\frac{u_L-u_O}{h}\right)}^2+{\left[\frac{1}{2}(\frac{u_{\mathrm{LU}}-u_{\mathrm{LD}}}{2h}+\frac{u_U-u_D}{2h})\right]}^2\}}^{1/2},---\left(11\right)$

According to formula:

$v_u^2=\frac{1}{|\&dtri;u_u|}\frac{u_U-u_O}{h}---\left(12\right)$

Calculate

wherein:

$|\&dtri;u_u|\&ap;{\{{\left(\frac{u_U-u_O}{h}\right)}^2+{\left[\frac{1}{2}(\frac{u_{\mathrm{UR}}-u_{\mathrm{UL}}}{2h}+\frac{u_R-u_L}{2h})\right]}^2\}}^{1/2},---\left(13\right)$

According to formula:

$v_d^1=\frac{1}{|\&dtri;u_d|}\frac{u_D-u_O}{h}---\left(14\right)$

Calculate wherein:

$|\&dtri;u_d|\&ap;{\{{\left(\frac{u_D-u_O}{h}\right)}^2+{\left[\frac{1}{2}(\frac{u_{\mathrm{DR}}-u_{\mathrm{DL}}}{2h}+\frac{u_R-u_L}{2h})\right]}^2\}}^{1/2},---\left(15\right)$

The coordinate of U, D, L, R, LU, LD, RU and RD is respectively: (x+n, y-m), (x-n, y+m), (x-m, y-n), (x+m, y+n), (x-m+n, y-m-n), (x-m-n, y+m-n), (x+m+n, and (x+m-n, y+m+n) y-m+n)

U _tfor the pixel value of pixel t, wherein t is u, d, l, r, U, D, L, R, LU, LD, RU and RD;

(6-3) formula (7)～formula (15) substitution formula (5) is obtained to the discrete reparation equation (being formula (6)) of current pixel to be repaired.

(7) order:

$\left\{\begin{array}{c}1/|\&dtri;u_p|=w_p\\ w_p/(\underset{P\&Element;\mathrm{\&Lambda;}}{\mathrm{\&Sigma;}}{w}_p+\mathrm{\&lambda;})=h_{\mathrm{OP}}\\ \mathrm{\&lambda;}/(\underset{P\&Element;\mathrm{\&Lambda;}}{\mathrm{\&Sigma;}}{w}_p+\mathrm{\&lambda;})=h_{\mathrm{OO}}\end{array}\right.,---\left(16\right)$

By in formula (16) substitution formula (6), obtain iterative equation:

$u_O=\underset{P\&Element;\mathrm{\&Lambda;}}{\mathrm{\&Sigma;}}{h}_{\mathrm{OP}}{u}_p+h_{\mathrm{OO}}{u}_O^0;---\left(17\right)$

(8) setting maximum iteration time is N, adopts Gauss-Seidel iteration method to carry out iteration to iterative equation, and each iteration obtains a pixel value, the pixel value that wherein the n time iteration obtains

for:

$u_O^{\left(n\right)}=\underset{P\&Element;\mathrm{\&Lambda;}}{\mathrm{\&Sigma;}}{h}_{\mathrm{OP}}^{(n-1)}{u}_P^{(n-1)}+h_{\mathrm{OO}}^{(n-1)}{u}_O^{(n-1)},---\left(18\right)$

Wherein,

be the pixel value that the n-1 time iteration obtains, when:

$|u_O^{\left(n\right)}-u_O^{(n-1)}|\&le;\mathrm{\&mu;}$

Or

n=N

Time, stop iteration, and the pixel value obtaining using last iteration is as the pixel value of current pixel O to be repaired, and with this pixel value, current pixel to be repaired repaired to (μ=4 in the present embodiment, N=100).

Claims (10)

1. the image repair method based on grain direction, is characterized in that, comprising:

(1) specify the area to be repaired in image to be repaired with mark, and the minimum rectangle of definite area to be repaired covers box;

(2) area to be repaired in image to be repaired is expanded outwardly to several pixels obtain the borderline region of area to be repaired, according to the position of each pixel in borderline region, determine the local grain direction of area to be repaired, be designated as V _ρ=(m, n);

(3) cover He center as true origin, with described local grain direction V take minimum rectangle _ρand with local grain direction V _ρorthogonal vectorial V _γfor the positive dirction of coordinate axis, set up the local grain coordinate system of this area to be repaired, wherein V _γ=(n, m);

(4) in local grain coordinate system, set up the energy functional formula of this area to be repaired;

(5) according to Euler-Lagrange equation, energy functional formula is carried out to minimization operation, the Euler-Lagrange that obtains area to be repaired is repaired equation;

(6) for each pixel to be repaired in area to be repaired, determine that the pixel that is h/2 with the distance of current pixel to be repaired in local grain coordinate axis is as neighborhood territory pixel point, according to neighborhood territory pixel point, described Euler-Lagrange is repaired to equation and carry out discretize processing, obtain the discrete reparation equation of current pixel to be repaired, h is local grain direction V _ρmould;

(7) described discrete reparation equation distortion is simplified and obtained iterative equation;

(8) adopt Gauss-Seidel iteration method to carry out iteration to iterative equation, each iteration obtains a pixel value, when:

$|u_O^{\left(n\right)}-u_O^{(n-1)}|\&le;\mathrm{\&mu;}$

Or

n=N

Time, stop iteration, and the pixel value obtaining using last iteration is as the pixel value of current pixel to be repaired, and with this pixel value, current pixel to be repaired repaired, wherein, μ is the threshold value of setting, N is the maximum iteration time of setting, wherein

with be respectively the n time and the pixel value of the current pixel to be repaired that the n-1 time iteration obtains.

2. the image repair method based on grain direction as claimed in claim 1, is characterized in that, described step is determined local grain direction by following steps in (2):

(2-1) for any two pixels in borderline region, if:

|(x ₁，y ₁)-(x ₂，y ₂)|<ε，

And vector (x ₂-x ₁, y ₂-y ₁) meet MAD condition, by vector (x ₂-x ₁, y ₂-y ₁) as candidate direction vector, and the vector set using all candidate direction vectors as candidate direction, wherein, (x ₁, y ₁) and (x ₂, y ₂) being respectively the coordinate of any two pixels in borderline region, ε is the threshold value of setting;

(2-2) set of candidate direction vector is made to absolute difference function:

$\mathrm{\&sigma;}=\frac{1}{\left|Q\right|}\underset{(i^{\&prime;},j^{\&prime;})\&Element;\mathrm{\&Omega;}\backslash D}{\underset{(i,j)\&Element;Q}{\mathrm{\&Sigma;}}}\mathrm{Abs}(P(i,j)-P(i^{\&prime;},j^{\&prime;}))$

Get the candidate direction vector of minimum value as the local grain direction vector of this area to be repaired, be designated as V _ρ=(m, n), wherein,

Wherein, σ is absolute difference function,

D represents the area to be repaired in image to be repaired,

Ω represents whole image-region, Ω D represent to remove in image to be repaired region outside the D of area to be repaired,

Q is the set of the pixel of a pixel of extension on the border of area to be repaired D, | Q| represents the number of the pixel of gathering Q,

Abs () represents to ask the function of absolute value,

P (i, j) represents the pixel value of any one pixel of set Q,

P (i ', j ') represent region Ω in D coordinate be the pixel value of the pixel of (i ', j '), and:

As (i+x _t, j+y _t) ∈ Ω D, (i ', j ')=(i+x _t, j+y _t),

As (i-x _t, j-y _t) ∈ Ω D, (i ', j ')=(i-x _t, j-y _t),

(x _t, y _t) be any one the candidate direction vector in the set of candidate direction vector.

3. the image repair method based on grain direction as claimed in claim 2, is characterized in that, the threshold epsilon of setting in described step (2-1) is 5～20.

4. the image repair method based on grain direction as claimed in claim 3, is characterized in that, in described step (2-1), the threshold value of MAD condition is 10～30.

5. the image repair method based on grain direction as claimed in claim 4, is characterized in that, the energy functional formula that described step (4) obtains is as follows:

$J_{\mathrm{\&lambda;}}^t\left[u\right]=\underset{G\&cup;D}{\&Integral;}\left|{\&dtri;}_u\right|\mathrm{d\&rho;d\&gamma;}+\frac{\mathrm{\&lambda;}}{2}\underset{G}{\&Integral;}{|u-u^0|}^2\mathrm{d\&rho;d\&gamma;},$

Wherein,

represent energy functional formula,

G is the borderline region of area to be repaired,

D is the area to be repaired of repairing in image,

G ∪ D is the combination of area to be repaired and borderline region,

for the gradient of any one pixel to be repaired in area to be repaired,

ρ, γ represents respectively horizontal ordinate and the ordinate of local grain coordinate system,

U is the pixel value of any one pixel to be repaired in area to be repaired, u ⁰for this picture to be repaired

The original pixel values that vegetarian refreshments is corresponding,

λ is constant.

6. the image repair method based on grain direction as claimed in claim 5, is characterized in that, it is as follows that the Euler-Lagrange of described area to be repaired is repaired equation:

$-\&dtri;\&CenterDot;\left(\frac{{\&dtri;}_u}{\left|{\&dtri;}_u\right|}\right)+\mathrm{\&gamma;}(u-u^0)=0,$

Wherein,

for asking divergence symbol.

7. the image repair method based on grain direction as claimed in claim 6, is characterized in that, in described step (6), the discrete reparation equation of current pixel to be repaired is as follows:

${\mathrm{\&Sigma;}}_{P\&Element;\mathrm{\&Lambda;}}\frac{1}{|\&dtri;u_p|}(u_0-u_p)+\mathrm{\&gamma;}(u_O-u_O^0)=0,$

Wherein, the set that Λ is neighborhood territory pixel point,

P is any one neighborhood territory pixel point,

O is current pixel to be repaired,

U _ofor the pixel value of current pixel O to be repaired, for the original pixel values of current pixel O to be repaired,

U _pfor the pixel value of neighborhood territory pixel point P,

for the gradient of neighborhood territory pixel point P point under local grain coordinate system.

8. the image repair method based on grain direction as claimed in claim 7, is characterized in that, the iterative equation in described step (7) is as follows:

$u_O={\mathrm{\&Sigma;}}_{P\&Element;\mathrm{\&Lambda;}}{h}_{\mathrm{OP}}{u}_p+h_{\mathrm{OO}}{u}_O^0,$

Wherein, $w_p=1/\left|{\&dtri;u}_p\right|,h_{\mathrm{OP}}=w_p/(\underset{P\&Element;\mathrm{\&Lambda;}}{\mathrm{\&Sigma;}}{w}_p+\mathrm{\&lambda;}),\mathrm{\&lambda;}/(\underset{P\&Element;\mathrm{\&Lambda;}}{\mathrm{\&Sigma;}}{w}_p+\mathrm{\&lambda;})=h_{\mathrm{OO}}.$

The pixel value that wherein the n time iteration obtains

for:

$u_O^{\left(n\right)}=\underset{P\&Element;\mathrm{\&Lambda;}}{\mathrm{\&Sigma;}}{h}_{\mathrm{OP}}^{(n-1)}{u}_P^{(n-1)}+h_{\mathrm{OO}}^{(n-1)}{u}_O^{(n-1)}$

Wherein,

it is the pixel value that the n-1 time iteration obtains.

9. the image repair method based on grain direction as claimed in claim 8, is characterized in that, the threshold value μ setting in described step (8) is 1～5.

10. the image repair method based on grain direction as claimed in claim 9, is characterized in that, the maximum iteration time N setting in described step (8) is 50～150.