CN106097268A - " Tujia " picture weaving in silk tradition remaining pattern digitlization restorative procedure - Google Patents

Abstract

This application discloses " Tujia " picture weaving in silk tradition remaining pattern digitlization restorative procedure, including damaged area is detected automatically, picture structure component and texture component are decomposed, structure components Variational PDE repairs the textures synthesis reparation with texture component, specifically includes following steps: set up detection and the location model automatically of the digital picture damaged area of " Tujia " picture weaving in silk；Building variation picture breakdown model is structure components and texture component by " Tujia " picture weaving in silk picture breakdown；" Tujia " picture weaving in silk structure components repaired by design Variational PDE model, and design repairs " Tujia " picture weaving in silk texture component based on the Texture Synthesis of sample；It is finally synthesizing the structure components after reparation and texture component, obtain the complete correction of " Tujia " picture weaving in silk digital picture." Tujia " picture weaving in silk tradition remaining pattern is repaired by the application by digital technology, can find repairing effect the most satisfied by repeatedly attempting, and without the need for destroying original picture-weaving in silk, is the approach that the repair of " Tujia " picture weaving in silk provides safe and convenient.

Description

" Tujia " picture weaving in silk tradition remaining pattern digitlization restorative procedure

Technical field

The application belongs to digital picture and repairs field, specifically, relates to a kind of " Tujia " picture weaving in silk tradition remaining pattern numeral Change restorative procedure.

Background technology

" Tujia " picture weaving in silk is a wonderful work of Tujia's national handicraft, is referred to as " flower of Tujia "." Tujia " picture weaving in silk has long History, " Later Han Dynasty book southwest is quite smooth to be passed " has just had initial record to this picture-weaving in silk of Tujia." Tujia " picture weaving in silk is at it In Emergence and Development and transition, fully demonstrate the perfect adaptation of practicality and artistry, and become succession Tujia Culture and art Important carrier.In June, 2006 " Tujia " picture weaving in silk be listed in the first batch of national non-material cultural heritage of country and lay special stress on protecting register.

But now with the quickening of modernization, affected by many factors such as nature, society and humanistic environments, soil The protection of family's picture-weaving in silk and succession are also faced with formidable challenges, and particularly some tradition " Tujia " picture weaving in silk patterns just fade away.And it is proper These tradition designs proper reflect the history culture of Tujia, hide the track of national origin, so being highly desirable to it Protect.

Local government has also set up the special class of protection specially, has formulated protective policy, and has arranged panel of expert to go deep into receipts among the people Collection arranges raw data, makes great efforts this " Tujia " picture weaving in silk of protection.Owing to the " Tujia " picture weaving in silk epoch in collection among the people are remote, and by warp Perseverance ground uses, so usually there will be damaged and staining.It is carried out by the manual mode using complexity now with picture-weaving in silk artist Repair, but owing to repair is heavy, and local experienced picture-weaving in silk artist's number is limited, so this remediation efficiency Extremely low.This direct reparation besides is to modify on original picture-weaving in silk, and this modification is usually irreversible, one Individual slight error may destroy the original picture-weaving in silk of preciousness.Digital Image Inpainting then brings great freedom, I Can search out, by trial repeatedly, the repairing effect being visually satisfied with the most, without destroying original picture-weaving in silk.Institute With in this case, Digital Image Inpainting can provide the approach of safe and convenient for the repair of " Tujia " picture weaving in silk.

Image repair refers to carry out reconstruction to the image being damaged.Image repair person needs to take side the most appropriate Method recovers the reset condition of image, ensures that image reaches optimal artistic effect simultaneously.As far back as the Renaissance, people are just Start to repair some medieval arts work, its object is to make picture recovery original appearance by filling up some cracks, this work Make just to be referred to as " Inpainting " (repairing, retouching) or " Retouching ".But repairing at that time is mainly the art work repaiies Multiple expert relies on professional knowledge to carry out by hand, and this repair mode has a disadvantage in that (1) remediation efficiency is extremely low；(2) have The art work of original preciousness may be destroyed.M.Bertalmio proposes image repair first can be reduced to a mathematical expression Formula, utilizes calculating function automatically to be realized.Image repair has been that one of computer graphics and computer vision are ground Study carefully focus, reject at historical relic's protection, video display special technology making, virtual reality, unnecessary object and (in such as video image, delete groups of people Thing, word, subhead etc.) etc. aspect have great using value.

Bertalmio etc., in the 27th SIGGRAPH meeting in 2000, propose digital picture first and repair this art Language, Digital Image Inpainting has obtained extensive research subsequently.At present, the development of Digital Image Inpainting is concentrated mainly on Two fields: (1), based on the image repair of non-grain structure, is mainly used in repairing the damaged digital picture of little yardstick, grinds at present Use of the person of studying carefully is repaired based on variation and partial differential equation of higher order (PDE) model more；(2) image mending based on texture structure Technology, is mainly used in blank map picture the information of big lost block, and current research is concentrated mainly on based on Markov random field (MRF) sample texture synthetic technology.

Digital Image Inpainting, in the development of this more than ten years, mainly still concentrates on theoretic to its research.? Application aspect, also has a small amount of achievement in research to be applied to the field such as medical science, archaeology, but in the reparation side of fabric digital picture Face, achievement in research is little.Only a small amount of research is also aimed at the very high fabric of some economic worths, such as Tangka.Soil Family's picture-weaving in silk is owing to having local region, and consumption ratio is compared with minority, and concerned degree is not very high, so being digitized it The research repaired lies substantially in blank.But " Tujia " picture weaving in silk is as first batch of national non-material cultural heritage, in order to protect and Passing on picture-weaving in silk specific to this Tujia, the research in terms of being digitized reparation to it is very important.

" Tujia " picture weaving in silk had both comprised substantial amounts of contour structure, contained again abundant color and vein, so single reparation skill The repairing effect that art is extremely difficult to, can solve this problem based on the restorative procedure of picture breakdown.Based on picture breakdown Repair and exactly the certain technology of image to be repaired employing is broken down into structure components and texture component sum, then right respectively Two kinds of components are repaired individually, are finally synthesizing and obtain repairing result.Bertalmio etc. took the lead in picture breakdown in 2003 After being applied to image repair, this recovery technique is studied by some researchers successively.But current this respect Achievement in research is still fewer comparatively speaking, and few quantifier elimination is also the improvement aspect concentrating on theoretical model and algorithm, rarely has This technology is used to study certain digital picture targetedly.

In sum, both at home and abroad a certain amount of research work has been carried out to image repair at present, but based on Variational Decomposition Repairing research less, for " Tujia " picture weaving in silk Digital repair research lie substantially in blank.

Content of the invention

In order to solve above-mentioned technical problem, this application discloses a kind of " Tujia " picture weaving in silk tradition remaining pattern Digital repair side Method, including damaged area is detected automatically, picture structure component and texture component are decomposed, and structure components Variational PDE is repaired and texture The textures synthesis reparation of component, specifically includes following steps:

(1) detection and the location model automatically of the digital picture damaged area of " Tujia " picture weaving in silk are set up；

(2) building variation picture breakdown model is structure components and texture component by " Tujia " picture weaving in silk picture breakdown；

(3) designing Variational PDE model and repairing " Tujia " picture weaving in silk structure components, design is based on the Texture Synthesis reparation of sample " Tujia " picture weaving in silk texture component；

(4) it is finally synthesizing the structure components after reparation and texture component, obtain the complete correction of " Tujia " picture weaving in silk digital picture.

Further, described step (1) method particularly includes: be analyzed " Tujia " picture weaving in silk image, selects suitable color Model, extracts color characteristic and textural characteristics, and carries out effective integration to these characteristics, obtains Efficient image characteristic According to；The Efficient image characteristic information obtaining fusion is dissolved in variation geometric active contour model, passes through image Segmentation Technology Realize that the damaged target area of " Tujia " picture weaving in silk image automatically extracts and positions.

Select 2 color model to be combined into composite coloured passage, this passage passes through integral image colouring information and line Reason feature construction is combined variation level set model, utilizes the minimum of energy functional to realize the accurate extraction to image damaged area And positioning.Numerical computations use the Euler-Lagrange equation in Theory of Variational Principles and gradient descent method solve functional minimum. It is implemented as follows:

Choose HSI color space and CIE LAB color space.First rgb color space is transformed into HSI color space, Change as follows:

$\left\{\begin{array}{c}H=arccos\left(\frac{\frac{1}{2}\left(\right(R-G)+(R-B))}{({\left(R-G\right)}^2+\frac{1}{2}(R-B)(G-B))}\right),\\ S=1-\frac{3}{R+G+B}\min \{R,G,B\},\\ I=\frac{R+G+B}{3},\end{array}\right.$

Rgb color space is converted to Lab color space again, and formula is as follows

$\left\{\begin{array}{c}L=116f\left(Y\right)-16,\\ a=500\left(f\right(\frac{X}{0.982})-f(Y\left)\right),\\ b=200\left(f\right(Y)-f(\frac{Z}{1.183}\left)\right),\end{array}\right.$

Wherein

$\left\{\begin{array}{c}X=0.49\×R+0.31\×G+0.2\×B,\\ Y=0.177\×R+0.812\×G+0.011\×B,\\ Z=0.01\×G+0.99\×B,\end{array}\right.$

$\left\{\begin{array}{cc}f\left(X\right)=7.787X+0.138,& X\≤0.008856\\ f\left(X\right)=X^{\frac{1}{3}},& X>0.008856\end{array}\right..$

Owing to " Tujia " picture weaving in silk is textile, there is very strong uniformity texture, cutting procedure considers the feature of texture, broken Damaging region does not has texture, and other complete area have essentially identical uniformity texture.Textural characteristicsUse area grayscale altogether Raw matrix extracts.Gray level co-occurrence matrixes is a kind of effective ways analyzing textural characteristics, and the method have studied ash in image texture The space dependence of degree level.Its distribution character to gray scale is to be represented by the distribution of the pixel different to gray value, These pixels have also been obtained embodiment to spatial relation and distribution character simultaneously.Texture feature extraction mainly comprise the processes of (1) Image " Tujia " picture weaving in silk image is carried out re-quantization, is changed to 16 grades by original 256 grades；(2) ash on four direction is constructed Degree co-occurrence matrix, this four direction is level, vertical, diagonal, back-diagonal respectively, is represented mathematically as 0 °, 45 °, 90 °, 135°；(3) from this matrix, the statistic (energy, entropy, the moment of inertia, correlative) that can characterize picture material is extracted as texture Feature

Set up the variation movable contour model based on region respectively at HSI color space and LAB color space, and incorporate The textural characteristics of imageThen the segmentation result in two different colours spaces is carried out region merging technique, detect final soil Family picture-weaving in silk image damaged area.Variation movable contour model is:

$\begin{array}{c}F(\mathrm{\φ},c_1,c_2,c_3,c_4)\\ =\mathrm{\α}{\∫}_{\mathrm{\Ω}}|\▿H\left(\mathrm{\φ}\right)|dx\\ +\frac{\mathrm{\γ}}{2}{\∫}_{\mathrm{\Ω}}{\left(\right|\▿\mathrm{\φ}|-1)}^{2}dx+{\mathrm{\λ}}_1{\∫}_{\mathrm{\Ω}}{(U-c_1)}^{2}H\left(\mathrm{\φ}\right)dx\\ +{\mathrm{\λ}}_2{\∫}_{\mathrm{\Ω}}{(U-c_2)}^2(1-H(\mathrm{\φ}))dx+{\mathrm{\β}}_1{\∫}_{\mathrm{\Ω}}{(\hat{U}-c_3)}^{2}H\left(\mathrm{\φ}\right)dx\\ +{\mathrm{\β}}_2{\∫}_{\mathrm{\Ω}}{(\hat{U}-c_4)}^2(1-H(\mathrm{\φ}))dx\end{array}$

Wherein U ∈ X, Y, Z, L, a, b},For 4 statistics of area grayscale co-occurrence matrix, i.e. energy, entropy, inertia Square, correlative.Alternative iteration method is used to calculate F (φ, c₁,c₂,c₃,c₄) minimum point:

$c_1=\frac{{\∫}_{\mathrm{\Ω}}UH\left(\mathrm{\φ}\right)dx}{{\∫}_{\mathrm{\Ω}}H\left(\mathrm{\φ}\right)dx};c_2=\frac{{\∫}_{\mathrm{\Ω}}U(1-H(\mathrm{\φ}))dx}{{\∫}_{\mathrm{\Ω}}(1-H(\mathrm{\φ}))dx}$

$c_3=\frac{{\∫}_{\mathrm{\Ω}}\hat{U}H\left(\mathrm{\φ}\right)dx}{{\∫}_{\mathrm{\Ω}}H\left(\mathrm{\φ}\right)dx};c_4=\frac{{\∫}_{\mathrm{\Ω}}\hat{U}(1-H(\mathrm{\φ}))dx}{{\∫}_{\mathrm{\Ω}}(1-H(\mathrm{\φ}))dx}$

The Euler-Lagrange equation in Theory of Variational Principles and gradient descent method is used to solve functional with regard to φ minimum point:

$\begin{array}{c}\frac{\∂\mathrm{\φ}}{\∂t}=\mathrm{\δ}\left(\mathrm{\φ}\right)div\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right)+\mathrm{\δ}\left(\mathrm{\φ}\right)({\mathrm{\λ}}_2{(U-c_2)}^2-{\mathrm{\λ}}_1{(U-c_1)}^2)+\mathrm{\δ}\left(\mathrm{\φ}\right)\left({\mathrm{\β}}_2\right(\hat{U}\\ -c_4{)}^2-{\mathrm{\β}}_1{(\hat{U}-c_3)}^2)\end{array}$

Above equation uses finite difference to solve.I.e.

${\mathrm{\φ}}^{n+1}={\mathrm{\φ}}^n+\mathrm{\Δ}t\left(\begin{array}{c}\mathrm{\δ}\left({\mathrm{\φ}}^n\right)div\left(\frac{\▿{\mathrm{\φ}}^n}{|\▿{\mathrm{\φ}}^n|}\right)+\mathrm{\δ}\left({\mathrm{\φ}}^n\right)({\mathrm{\λ}}_2{\left(U-c_2\right)}^2-{\mathrm{\λ}}_1{\left(U-c_1\right)}^2)+\\ \mathrm{\δ}\left({\mathrm{\φ}}^n\right)({\mathrm{\β}}_2{\left(\hat{U}-c_4\right)}^2-{\mathrm{\β}}_1{\left(\hat{U}-c_3\right)}^2)\end{array}\right)$

The segmentation result of 6 Color Channels in two color model is respectively φ_i=0, i=1,2 ... 6；φ_i=0 The actually edge of segmentation.Segmentation result in two different colours models is carried out region merging technique, detects final soil Family picture-weaving in silk image damaged area is:

Ω=(x, y): φ_i＜ 0, i=1,2 ... 6.}

Further, described step (2) utilizes priori to divide the structure components and texture of " Tujia " picture weaving in silk image respectively Amount is modeled, and obtains Variation Model, obtains clean structural texture by functional minimization and decomposes, method particularly includes: structure Component is modeled by non-convex biregular item, comprises non-convex sparse measurement and the second dervative non-convex sparse measurement of gradient；Texture divides Amount uses rank of matrix tolerance, extracts uniformity texture by the minimization of order；Variation Model uses alternative iteration method to solve.

The Variational Decomposition model set up is as follows:

WhereinIt is non-convex biregular item, be used for measuring " Tujia " picture weaving in silk The structure components of digital picture；||ρv||_*It is concussion tolerance, for extracting the texture component of blue Kapp digital picture.Due to soil Family's picture-weaving in silk is textile, and its texture has very strong uniformity, so using nuclear norm (to be substantially order tolerance rank (ρ v) Minimum Convex Closure network) tolerance concussion.For potential-energy function, select non-convex Non-smooth surface function preferably to keep the limit in structure components Edge information, is chosen as:

With

Alternative iteration method is used to solve Variational Decomposition model:

Fixing v, u₂, solve u by the following Variation Model of minimization₁

This is very famous ROF model, uses single order predual algorithm to solve；

Fixing v, u₁, solve u by the following Variation Model of minimization₂

Solve with the Euler-Lagrange equation in Theory of Variational Principles and gradient descent method；

Fixing u₁, u₂, solve u by the following Variation Model of minimization₂

$\underset{u}{min}\left\{\right|\left|\mathrm{\ρ}v\right|{|}_{*}+\frac{\mathrm{\λ}}{2}\left|\right|f-u_1-u_2-v\left|{|}_2^2\right\}$

Using iteration soft-threshold algorithm to solve this optimization problem, nuclear norm therein uses matrix singular value decomposition Method.

Above-mentioned 3 optimization problems of iterative, obtain optimal solution u₁, u₂, v, then the structure of " Tujia " picture weaving in silk digital picture is divided Amount is expressed as u=u₁+u₂；Texture component is expressed as v.

Further, described step (3) method particularly includes: the " Tujia " picture weaving in silk structure components that step (2) is obtained and texture Component is repaired respectively.Structure components reparation uses Variational PDE model；Texture component reparation uses Future Opportunities of Texture Synthesis.

The Variational PDE model of structure components reparation is, combines fractional order differential with tensor diffusion, general according to fractional order The carried Variation Model of letter theory deduction corresponding Euler-Lagrange equation, and during Numerical Implementation, utilize discrete Fourier transform definition Fractional Derivative operator and its adjoint operator, the computing formula of derivation Fractional Derivative, design and carried The numerical algorithm of repairing model.Concrete Variational PDE repairing model design is as follows:

$\left\{\begin{array}{cc}J\left(u\right)={\&Integral;}_{\mathrm{\&Omega;}}\left|D^{\mathrm{\&alpha;}}u\right|dx+\frac{{\mathrm{\&lambda;}}_D}{2}\left|\right|u_0-u|{|}_2^2,& 0<\mathrm{\&alpha;}<1\\ {\mathrm{\&lambda;}}_D\left(x\right)=\mathrm{\&lambda;}\&CenterDot;{\mathrm{\&pi;}}_D\left(x\right)=\left\{\begin{array}{cc}\mathrm{\&lambda;},& x\&Element;\mathrm{\&Omega;}-D\\ 0,& x\&Element;D\end{array}\right.& \end{array}\right.$

Wherein WithIt is the α rank fraction in x and y direction for the u respectively Order derivative.u₀It is the structure components (second step uses variation picture breakdown to obtain) of " Tujia " picture weaving in silk digital picture；D is " Tujia " picture weaving in silk The damaged area (second step uses the segmentation of variation geometric active contour model to obtain) of digital picture.With in Theory of Variational Principles Euler-Lagrange equation and gradient descent method solve this optimization problem:

$\frac{\&part;u}{\&part;t}=-RE\{\stackrel{\&OverBar;}{D_x^{\mathrm{\&alpha;}}}\left(\frac{D_x^{\mathrm{\&alpha;}}u}{\left|D_x^{\mathrm{\&alpha;}}u\right|}\right)+\stackrel{\&OverBar;}{D_y^{\mathrm{\&alpha;}}}\left(\frac{D_y^{\mathrm{\&alpha;}}u}{\left|D_y^{\mathrm{\&alpha;}}u\right|}\right)+{\mathrm{\&lambda;}}_D(u_0-u)\}$

In above formulaWithIt is respectivelyWithAdjoint operator.For repairing the marginal information of image further, with Upper diffusion equation introduces tensor diffusion, i.e.

$\frac{\&part;u}{\&part;t}=-RE\{\stackrel{\&OverBar;}{D_x^{\mathrm{\&alpha;}}}\left(T\right(x\left)\frac{D_x^{\mathrm{\&alpha;}}u}{\left|D_x^{\mathrm{\&alpha;}}u\right|}\right)+\stackrel{\&OverBar;}{D_y^{\mathrm{\&alpha;}}}\left(T\right(x\left)\frac{D_y^{\mathrm{\&alpha;}}u}{\left|D_y^{\mathrm{\&alpha;}}u\right|}\right)+{\mathrm{\&lambda;}}_D(u_0-u)\}$

T (x) is diffusion tensor, adopts and calculates with the following method: the structure tensor of definition tolerance Local Structure of Image

$J_{\mathrm{\&rho;}}(\&dtri;u_{\mathrm{\&sigma;}})=G_{\mathrm{\&rho;}}*(\&dtri;u_{\mathrm{\&sigma;}}\&dtri;{u_{\mathrm{\&sigma;}}}^T)=\left(\begin{array}{cc}{G}_{\mathrm{\&rho;}}*{\left(\frac{\&part;u_{\mathrm{\&sigma;}}}{\&part;x}\right)}^2& G_{\mathrm{\&rho;}}*\left(\frac{\&part;u_{\mathrm{\&sigma;}}}{\&part;x}\frac{\&part;u_{\mathrm{\&sigma;}}}{\&part;y}\right)\\ G_{\mathrm{\&rho;}}*\left(\frac{\&part;u_{\mathrm{\&sigma;}}}{\&part;x}\frac{\&part;u_{\mathrm{\&sigma;}}}{\&part;y}\right)& G_{\mathrm{\&rho;}}*{\left(\frac{\&part;u_{\mathrm{\&sigma;}}}{\&part;y}\right)}^2\end{array}\right)$

G_ρRepresent the Gaussian kernel with ρ as parameter.Definition

$J_{\mathrm{\&rho;}}=\left(\begin{array}{cc}{j}_{11}& j_{12}\\ j_{12}& j_{22}\end{array}\right)$

J_ρTwo characteristic values be

$\left\{\begin{array}{c}{\mathrm{\&lambda;}}_1=\frac{1}{2}(j_{11}+j_{22}+\sqrt{{(j_{11}-j_{22})}^2+4j_{12}^2})\\ {\mathrm{\&lambda;}}_2=\frac{1}{2}(j_{11}+j_{22}-\sqrt{{(j_{11}-j_{22})}^2+4j_{12}^2})\end{array}\right.$

Their characteristic of correspondence vector is v₁And v₂, v_i=(cos θ_i,sinθ_i), i=1,2.

Wherein

${\mathrm{\&theta;}}_1=\frac{1}{2}arctan\frac{2j_{12}}{j_{11}-j_{22}},{\mathrm{\&theta;}}_1={\mathrm{\&theta;}}_1+\frac{\mathrm{\&pi;}}{2}$

If μ₁And μ₂It is two characteristic values of diffusion tensor matrices T (x), if

$T\left(x\right)=\left(\begin{array}{cc}a& b\\ b& c\end{array}\right)$

v₁And v₂It is corresponding characteristic vector, have v₁=(cos θ, sin θ)；v₂=(-sin θ, cos θ).

The relation of the matrix element of T (x) and eigen vector is as follows:

$\left\{\begin{array}{c}a={\mathrm{\&mu;}}_{1}co{s}^2\mathrm{\&theta;}+{\mathrm{\&mu;}}_{2}si{n}^2\mathrm{\&theta;}\\ b=({\mathrm{\&mu;}}_1-{\mathrm{\&mu;}}_2)sin\mathrm{\&theta;}cos\mathrm{\&theta;}\\ c={\mathrm{\&mu;}}_{2}co{s}^2\mathrm{\&theta;}+{\mathrm{\&mu;}}_1{\sin }^2\mathrm{\&theta;}\end{array}\right.$

Use edge enhanced diffustion tensor: μ₁=g (λ₁), μ₂=1；Wherein g is edge function.

Finite difference is used to solve above-mentioned PDE:

$u^{n+1}=u^n+\mathrm{\&Delta;}t(-RE\{\stackrel{\&OverBar;}{D_x^{\mathrm{\&alpha;}}}\left(T\frac{D_x^{\mathrm{\&alpha;}}{u}^n}{\left|D_x^{\mathrm{\&alpha;}}{u}^n\right|}\right)+\stackrel{\&OverBar;}{D_y^{\mathrm{\&alpha;}}}\left(T\frac{D_y^{\mathrm{\&alpha;}}{u}^n}{\left|D_y^{\mathrm{\&alpha;}}{u}^n\right|}\right)+{\mathrm{\&lambda;}}_D\left(u_0-u^n\right)\})$

Fractional Derivative can be calculated by using efficient Discrete Fourier Transform:

$U({\mathrm{\&omega;}}_1,{\mathrm{\&omega;}}_2)=\frac{1}{N}{\mathrm{\&Sigma;}}_{m,n=1}^{N}u(m,n)\exp (-j2\mathrm{\&pi;}({\mathrm{m\&omega;}}_1+{\mathrm{n\&omega;}}_2)/N)$

Integer order derivative is generalized to Fractional Derivative, obtains based on the fractional order difference under discrete Fouier conversion meaningWithThey at the corresponding relation of spatial domain and frequency domain are:

$D_x^{\mathrm{\&alpha;}}u=(1-\exp (-j2\mathrm{\&pi;}\left({\mathrm{m\&omega;}}_1\right)/N\left)\right)U({\mathrm{\&omega;}}_1,{\mathrm{\&omega;}}_2)$

$D_y^{\mathrm{\&alpha;}}u=(1-\exp (-j2\mathrm{\&pi;}\left({\mathrm{m\&omega;}}_2\right)/N\left)\right)U({\mathrm{\&omega;}}_1,{\mathrm{\&omega;}}_2)$

Fractional order difference operatorWithAdjoint operatorWithSpatial domain and the corresponding relation of frequency domain For:

$\stackrel{\&OverBar;}{D_x^{\mathrm{\&alpha;}}}u=\stackrel{\&OverBar;}{(1-\exp (-j2\mathrm{\&pi;}\left({\mathrm{m\&omega;}}_1\right)/N\left)\right)}U({\mathrm{\&omega;}}_1,{\mathrm{\&omega;}}_2)$

$\stackrel{\&OverBar;}{D_y^{\mathrm{\&alpha;}}}u=\stackrel{\&OverBar;}{(1-\exp (-j2\mathrm{\&pi;}\left({\mathrm{m\&omega;}}_2\right)/N\left)\right)}U({\mathrm{\&omega;}}_1,{\mathrm{\&omega;}}_2)$

Using sample texture synthetic technology to repair texture component, the complexity utilizing image block is adaptive as standard Region of search should be changed to improve reparation speed in ground；The complexity utilizing image block determines repairs order to obtain preferably reparation Effect.Detailed process is as follows: uses fractal dimension and the complexity of comentropy tolerance image block, utilizes complexity to determine the field of search Territory and reparation order.Empirically determined entropy and the Weighted Threshold of fractal dimension, at the multiblock to be repaired more than threshold value, select relatively Big region of search completes to mate padding；At the multiblock to be repaired less than threshold value then contrary.And the big image of complexity Block is preferentially repaired.In numerical computations, in conjunction with differential box method of counting and fractal Brown motion self-similarity method calculating figure As the fractal dimension of block, at utmost to distinguish different roughness texture.

Comentropy is used to measure the complexity of block of pixels.Comentropy is the statistical form of a kind of feature, and it reflects figure The number of average information in Xiang.The comentropy of image represents the information content that the aggregation characteristic of intensity profile in image is comprised, Make P_iRepresent block of pixels Ψ_pMiddle gray value is the ratio shared by the pixel of i, i.e.

$P_i=\frac{\#\{n:n\&Element;{\mathrm{\&Psi;}}_p\&cap;\mathrm{\&Phi;},n=i\}}{|{\mathrm{\&Psi;}}_p\&cap;\mathrm{\&Phi;}|},i=0,1,...,255$

The unitary comentropy then defining gray level image is:

$H\left(p\right)=\frac{-{\mathrm{\&Sigma;}}_{i=0}^{255}{P}_{i}log\left(P_i\right)}{b}$

Wherein b is normalized parameter, selects b=5 in an experiment.Above formula only defines a metamessage of gray level image Entropy, for coloured image, uses the average of unitary comentropy under tri-Color Channels of RGB, i.e.

$H\left(p\right)=\frac{H_R\left(p\right)+H_G\left(p\right)+H_B\left(p\right)}{3}$

Carrying out based in the image mending of the textures synthesis of sample block, the big repairing block of comentropy H (p) will first be repaiied Multiple.

Fractal box is used to measure block of pixels Ψ further_pComplexity.The fractal box of image is a kind of special The statistical form levied, reflect average information in block of pixels number, value is normally between interval 2-3.Fractal dimension Closer to dimension 2, show more smooth (under normal circumstances, constant value block of pixels Ψ of image_pThe fractal box of=C is 2)；Closer to Dimension 3, shows that grey scale change is more violent, and image is more complicated.The unitary fractal box then defining gray level image is:

F (p)=aD (Ψ_p)-b

Wherein a, b are normalized parameter, select a=1 in an experiment；B=-2.It is apparent that F (p) ∈ [0,1].If picture In element block, intensity profile is more uniform, and fractal box F (p) is closer to 0；Whereas if grey scale change is more violent in block of pixels, Containing a lot of image informations, fractal box F (p) is closer to 1.For coloured image, use under tri-Color Channels of RGB The average of unitary fractal box, i.e.

$F\left(p\right)=\frac{F_R\left(p\right)+F_G\left(p\right)+F_B\left(p\right)}{3}$

It is attached to fractal box and the comentropy of block of pixels in prioritization functions, carrying out the texture based on sample block During the image repair of synthesis, fractal box and the big reparation block of comentropy will first be repaired.

Prioritization functions is defined as:

P (p)=α C (p) D (p)+β F (p)+γ H (p)

Wherein α ＞ 0, β ＞ 0 and γ ＞ 0 be weight factor, and meet alpha+beta+γ=1.

Match block search uses following process: by match block Ψ_qBy complexity, (fractal box adds with comentropy in set Power, i.e. β F (p)+γ H (p)) size imparting liter sequence structure, then use binary search, compose sequence match block Ψ_qIn set right With input multiblock Ψ to be repaired under complexity meaning_pImmediate match block Ψ_qK neighborhood in again carry out coupling search, find The minimum match block of SSD.I.e.

Ψ_q=argmin{d (Ψ_p,Ψ_q):Ψ_q∈K}

Wherein K is match block Ψ_qIn set under fractal box meaning with input multiblock Ψ to be repaired_pImmediate Join block Ψ_qK neighborhood.The size of k is chosen as k=32.

Further, the structure components after described step (4) synthesis is repaired and texture component method particularly includes: to reparation After structure components and texture component be weighted averagely.

If the structure components after Xiu Fuing and texture component are respectively u and v, then complete correction is expressed as

F=2 × (a × u+ (1-a) × v)

Wherein a ∈ (0,1) is weight factor.Adjust this parameter and can obtain different visual effects.Ordinary circumstance is divided into Determine a=0.5.

Compared with prior art, the application can obtain and include techniques below effect:

1) the application by digital technology to " Tujia " picture weaving in silk tradition remaining pattern repair, can be by repeatedly tasting Examination, finds repairing effect the most satisfied, without the need for destroying original picture-weaving in silk, is that the repair of " Tujia " picture weaving in silk provides peace Full approach easily.

2) the present processes has for the texture-rich such as " Tujia " picture weaving in silk, beautiful in colour and textile and well repairs effect Really, the vision requirement of people can be met well.

3) the automatic of " Tujia " picture weaving in silk digital picture damaged area detects and positioning, by optimum knot manual with expert Really comparison, accuracy is up to more than 98%.

4) the present processes has reparation speed faster, the image to be repaired of less than 1024 × 1024 sizes, repairs Region, below 50 × 50, about can complete whole repair process in 100 seconds to 600 seconds.

5) technical scheme of the application, step is simple, it is easy to operation, and reproducible, technical staff is easy to learn, easily grasp.

Certainly, the arbitrary product implementing the application must be not necessarily required to reach all the above technique effect simultaneously.

Brief description

Accompanying drawing described herein is used for providing further understanding of the present application, constitutes the part of the application, this Shen Schematic description and description please is used for explaining the application, is not intended that the improper restriction to the application.In the accompanying drawings:

Fig. 1 is damaged " Tujia " picture weaving in silk image in the embodiment of the present application；

Fig. 2 is damaged " Tujia " picture weaving in silk image segmentation result figure in the embodiment of the present application；

Fig. 3 is damaged " Tujia " picture weaving in silk image damaged area figure in the embodiment of the present application；

Fig. 4 is damaged " Tujia " picture weaving in silk image repair mask figure in the embodiment of the present application；

Fig. 5 is damaged " Tujia " picture weaving in silk picture structure component map in the embodiment of the present application；

Fig. 6 is damaged " Tujia " picture weaving in silk image texture component map in the embodiment of the present application；

Fig. 7 is the reparation result figure of the damaged structure components of damaged " Tujia " picture weaving in silk image in the embodiment of the present application；

Fig. 8 is the reparation result figure of the damaged texture component of damaged " Tujia " picture weaving in silk image in the embodiment of the present application；

Fig. 9 is that in the embodiment of the present application, damaged " Tujia " picture weaving in silk image finally repairs result figure.

Detailed description of the invention

Describe presently filed embodiment in detail below in conjunction with drawings and Examples, thereby how the application is applied Technological means solve technical problem and reach technology effect realize that process can fully understand and implement according to this.

Embodiment " Tujia " picture weaving in silk tradition remaining pattern digitlization restorative procedure

(1) detection and the location model automatically of the digital picture damaged area of " Tujia " picture weaving in silk are set up

As Figure 1-4, Fig. 1 is the local sectional drawing of the damaged " Tujia " picture weaving in silk of a width, and wherein white portion is damaged area.Figure Damaged area is carried out splitting the damaged " Tujia " picture weaving in silk image segmentation result figure obtaining by 2 for using variation geometric active contour.Fig. 3 For damaged " Tujia " picture weaving in silk image damaged area figure, the interior zone of closed curve is damaged area.Damaged area gray value is fixed Justice is 1, and other regions are defined as 0, obtains repairing mask, as shown in Figure 4.

" Tujia " picture weaving in silk image is analyzed, selects suitable color model, extract color characteristic and textural characteristics, and right These characteristics carry out effective integration, obtain Efficient image characteristic；The Efficient image characteristic information obtaining fusion melts Enter in variation geometric active contour model, realize that the damaged target area of " Tujia " picture weaving in silk image carries automatically by image Segmentation Technology Take and position.

Select 2 color model to be combined into composite coloured passage, this passage passes through integral image colouring information and line Reason feature construction is combined variation level set model, utilizes the minimum of energy functional to realize the accurate extraction to image damaged area And positioning.

Choose HSI color space and CIE LAB color space.First rgb color space is transformed into HSI color space, Change as follows:

$\left\{\begin{array}{c}H=\arccos \left(\frac{\frac{1}{2}\left(\right(R-G)+(R-B))}{({(R-G)}^2+\frac{1}{2}(R-B\left)\right(G-B\left)\right)}\right),\\ S=1-\frac{3}{R+G+B}\min \{R,G,B\},\\ I=\frac{R+G+B}{3},\end{array}\right.$

Rgb color space is converted to Lab color space again, and formula is as follows

$\left\{\begin{array}{c}L=116f\left(Y\right)-16,\\ a=500\left(f\right(\frac{X}{0.982})-f(Y\left)\right),\\ b=200\left(f\right(Y)-f(\frac{Z}{1.183}\left)\right),\end{array}\right.$

Wherein

$\left\{\begin{array}{c}X=0.49\&times;R+0.31\&times;G+0.2\&times;B,\\ Y=0.177\&times;R+0.812\&times;G+0.011\&times;B,\\ Z=0.01\&times;G+0.99\&times;B,\end{array}\right.$

$\left\{\begin{array}{c}f\left(X\right)=7.787X+0.138,X\&le;0.008856\\ f\left(X\right)=X^{\frac{1}{3}},X>0.008856\end{array}\right.$

Owing to " Tujia " picture weaving in silk is textile, there is very strong uniformity texture, cutting procedure considers the feature of texture, broken Damaging region does not has texture, and other complete area have essentially identical uniformity texture.Textural characteristicsUse area grayscale altogether Raw matrix extracts.Gray level co-occurrence matrixes is a kind of effective ways analyzing textural characteristics, and the method have studied ash in image texture The space dependence of degree level.Its distribution character to gray scale is to be represented by the distribution of the pixel different to gray value, These pixels have also been obtained embodiment to spatial relation and distribution character simultaneously.Texture feature extraction mainly comprise the processes of (1) Image " Tujia " picture weaving in silk image is carried out re-quantization, is changed to 16 grades by original 256 grades；(2) ash on four direction is constructed Degree co-occurrence matrix, this four direction is level, vertical, diagonal, back-diagonal respectively, is represented mathematically as 0 °, 45 °, 90 °, 135°；(3) from this matrix, the statistic (energy, entropy, the moment of inertia, correlative) that can characterize picture material is extracted as texture Feature

Set up the variation movable contour model based on region at HSI color space and LAB color space respectively

$\begin{array}{c}F(\mathrm{\&phi;},c_1,c_2,c_3,c_4)\\ =\mathrm{\&alpha;}{\&Integral;}_{\mathrm{\&Omega;}}|\&dtri;H\left(\mathrm{\&phi;}\right)|dx\\ +\frac{\mathrm{\&gamma;}}{2}{\&Integral;}_{\mathrm{\&Omega;}}{\left(\right|\&dtri;\mathrm{\&phi;}|-1)}^{2}dx+{\mathrm{\&lambda;}}_1{\&Integral;}_{\mathrm{\&Omega;}}{(U-c_1)}^{2}H\left(\mathrm{\&phi;}\right)dx\\ +{\mathrm{\&lambda;}}_2{\&Integral;}_{\mathrm{\&Omega;}}{(U-c_2)}^2(1-H(\mathrm{\&phi;}))dx+{\mathrm{\&beta;}}_1{\&Integral;}_{\mathrm{\&Omega;}}{(\hat{U}-c_3)}^{2}H\left(\mathrm{\&phi;}\right)dx\\ +{\mathrm{\&beta;}}_2{\&Integral;}_{\mathrm{\&Omega;}}{(\hat{U}-c_4)}^2(1-H(\mathrm{\&phi;}))dx\end{array}$

Incorporate the textural characteristics of imageWherein U ∈ X, Y, Z, L, a, b},4 systems for area grayscale co-occurrence matrix Metering, i.e. energy, entropy, the moment of inertia, correlative.Alternative iteration method is used to calculate F (φ, c₁,c₂,c₃,c₄) minimum point:

$c_1=\frac{{\&Integral;}_{\mathrm{\&Omega;}}UH\left(\mathrm{\&phi;}\right)dx}{{\&Integral;}_{\mathrm{\&Omega;}}H\left(\mathrm{\&phi;}\right)dx};c_2=\frac{{\&Integral;}_{\mathrm{\&Omega;}}U(1-H(\mathrm{\&phi;}))dx}{{\&Integral;}_{\mathrm{\&Omega;}}(1-H(\mathrm{\&phi;}))dx}$

$c_3=\frac{{\&Integral;}_{\mathrm{\&Omega;}}\hat{U}H\left(\mathrm{\&phi;}\right)dx}{{\&Integral;}_{\mathrm{\&Omega;}}H\left(\mathrm{\&phi;}\right)dx};c_4=\frac{{\&Integral;}_{\mathrm{\&Omega;}}\hat{U}(1-H(\mathrm{\&phi;}))dx}{{\&Integral;}_{\mathrm{\&Omega;}}(1-H(\mathrm{\&phi;}))dx}$

The Euler-Lagrange equation in Theory of Variational Principles and gradient descent method is used to solve functional with regard to φ minimum point:

$\begin{array}{c}\frac{\&part;\mathrm{\&phi;}}{\&part;t}=\mathrm{\&delta;}\left(\mathrm{\&phi;}\right)div\left(\frac{\&dtri;\mathrm{\&phi;}}{|\&dtri;\mathrm{\&phi;}|}\right)+\mathrm{\&delta;}\left(\mathrm{\&phi;}\right)({\mathrm{\&lambda;}}_2{(U-c_2)}^2-{\mathrm{\&lambda;}}_1{(U-c_1)}^2)+\mathrm{\&delta;}\left(\mathrm{\&phi;}\right)\left({\mathrm{\&beta;}}_2\right(\hat{U}\\ -c_4{)}^2-{\mathrm{\&beta;}}_1{(\hat{U}-c_3)}^2)\end{array}$

Above equation uses finite difference to solve.I.e.

${\mathrm{\&phi;}}^{n+1}={\mathrm{\&phi;}}^n+\mathrm{\&Delta;}t\left(\begin{array}{c}\mathrm{\&delta;}\left({\mathrm{\&phi;}}^n\right)div\left(\frac{\&dtri;{\mathrm{\&phi;}}^n}{|\&dtri;{\mathrm{\&phi;}}^n|}\right)+\mathrm{\&delta;}\left({\mathrm{\&phi;}}^n\right)({\mathrm{\&lambda;}}_2{\left(U-c_2\right)}^2-{\mathrm{\&lambda;}}_1{\left(U-c_1\right)}^2)+\\ \mathrm{\&delta;}\left({\mathrm{\&phi;}}^n\right)({\mathrm{\&beta;}}_2{\left(\hat{U}-c_4\right)}^2-{\mathrm{\&beta;}}_1{\left(\hat{U}-c_3\right)}^2)\end{array}\right)$

The segmentation result of 6 Color Channels in two color model is respectively φ_i=0, i=1,2 ... 6；φ_i=0 The actually edge of segmentation.Segmentation result in two different colours models is carried out region merging technique, detects final soil Family picture-weaving in silk image damaged area is:

Ω=(x, y): φ_i＜ 0, i=1,2 ... 6.}

(2) use Variational Decomposition model that " Tujia " picture weaving in silk digital picture is decomposed into structure components and texture component

As seen in figs. 5-6, use non-convex biregular to be modeled structure components, obtain Tujia by variation minimization and knit Brocade picture structure component；Use nuclear norm to be modeled texture component, obtain " Tujia " picture weaving in silk image line by variation minimization Reason component.

Utilize priori to be modeled the structure components and texture component of " Tujia " picture weaving in silk image respectively, obtain variation mould Type, obtains clean structural texture by functional minimization and decomposes, method particularly includes: structure components is built by non-convex biregular item Mould, comprises non-convex sparse measurement and the second dervative non-convex sparse measurement of gradient；Texture component uses rank of matrix tolerance, passes through order Minimization extract uniformity texture；Variation Model uses alternative iteration method to solve.

The Variational Decomposition model set up is as follows:

WhereinIt is non-convex biregular item, be used for measuring " Tujia " picture weaving in silk The structure components of digital picture；||ρv||_*It is concussion tolerance, for extracting the texture component of blue Kapp digital picture.Due to soil Family's picture-weaving in silk is textile, and its texture has very strong uniformity, so using nuclear norm (to be substantially order tolerance rank (ρ v) Minimum Convex Closure network) tolerance concussion.For potential-energy function, select non-convex Non-smooth surface function preferably to keep the limit in structure components Edge information, is chosen as:

With

Alternative iteration method is used to solve Variational Decomposition model:

Fixing v, u₂, solve u by the following Variation Model of minimization₁

This is very famous ROF model, uses single order predual algorithm to solve；

Fixing v, u₁, solve u by the following Variation Model of minimization₂

Solve with the Euler-Lagrange equation in Theory of Variational Principles and gradient descent method；

Fixing u₁, u₂, solve u by the following Variation Model of minimization₂

$\underset{u}{min}\left\{\right|\left|\mathrm{\&rho;}v\right|{|}_{*}+\frac{\mathrm{\&lambda;}}{2}\left|\right|f-u_1-u_2-v\left|{|}_2^2\right\}$

Using iteration soft-threshold algorithm to solve this optimization problem, nuclear norm therein uses matrix singular value decomposition Method.

Above-mentioned 3 optimization problems of iterative, obtain optimal solution u₁, u₂, v, then the structure of " Tujia " picture weaving in silk digital picture is divided Amount is expressed as u=u₁+u₂；Texture component is expressed as v.

(3) designing Variational PDE model and repairing " Tujia " picture weaving in silk structure components, design is based on the Texture Synthesis reparation of sample " Tujia " picture weaving in silk texture component

As Figure 7-8, Variational PDE model is used to repair structure components；Use the textures synthesis based on sample Texture component is repaired by algorithm.

The " Tujia " picture weaving in silk structure components and the texture component that obtain to step (2) are repaired respectively.Structure components reparation is adopted Use Variational PDE model；Texture component reparation uses Future Opportunities of Texture Synthesis.

The Variational PDE model of structure components reparation is, combines fractional order differential with tensor diffusion, general according to fractional order The carried Variation Model of letter theory deduction corresponding Euler-Lagrange equation, and during Numerical Implementation, utilize discrete Fourier transform definition Fractional Derivative operator and its adjoint operator, the computing formula of derivation Fractional Derivative, design and carried The numerical algorithm of repairing model.Concrete Variational PDE repairing model design is as follows:

$\left\{\begin{array}{cc}J\left(u\right)={\&Integral;}_{\mathrm{\&Omega;}}\left|D^{\mathrm{\&alpha;}}u\right|dx+\frac{{\mathrm{\&lambda;}}_D}{2}\left|\right|u_0-u|{|}_2^2,& 0<\mathrm{\&alpha;}<1\\ {\mathrm{\&lambda;}}_D\left(x\right)=\mathrm{\&lambda;}\&CenterDot;{\mathrm{\&pi;}}_D\left(x\right)=\left\{\begin{array}{cc}\mathrm{\&lambda;},& x\&Element;\mathrm{\&Omega;}-D\\ 0,& x\&Element;D\end{array}\right.& \end{array}\right.$

Wherein WithIt is the α rank fraction in x and y direction for the u respectively Order derivative.u₀It is the structure components (second step uses variation picture breakdown to obtain) of " Tujia " picture weaving in silk digital picture；D is " Tujia " picture weaving in silk The damaged area (second step uses the segmentation of variation geometric active contour model to obtain) of digital picture.With in Theory of Variational Principles Euler-Lagrange equation and gradient descent method solve this optimization problem:

$\frac{\&part;u}{\&part;t}=-RE\{\stackrel{\&OverBar;}{D_x^{\mathrm{\&alpha;}}}\left(\frac{D_x^{\mathrm{\&alpha;}}u}{\left|D_x^{\mathrm{\&alpha;}}u\right|}\right)+\stackrel{\&OverBar;}{D_y^{\mathrm{\&alpha;}}}\left(\frac{D_y^{\mathrm{\&alpha;}}u}{\left|D_y^{\mathrm{\&alpha;}}u\right|}\right)+{\mathrm{\&lambda;}}_D(u_0-u)\}$

In above formulaWithIt is respectivelyWithAdjoint operator.For repairing the marginal information of image further, with Upper diffusion equation introduces tensor diffusion, i.e.

$\frac{\&part;u}{\&part;t}=-RE\{\stackrel{\&OverBar;}{D_x^{\mathrm{\&alpha;}}}\left(T\right(x\left)\frac{D_x^{\mathrm{\&alpha;}}u}{\left|D_x^{\mathrm{\&alpha;}}u\right|}\right)+\stackrel{\&OverBar;}{D_y^{\mathrm{\&alpha;}}}\left(T\right(x\left)\frac{D_y^{\mathrm{\&alpha;}}u}{\left|D_y^{\mathrm{\&alpha;}}u\right|}\right)+{\mathrm{\&lambda;}}_D(u_0-u)\}$

T (x) is diffusion tensor, adopts and calculates with the following method: the structure tensor of definition tolerance Local Structure of Image

$J_{\mathrm{\&rho;}}(\&dtri;u_{\mathrm{\&sigma;}})=G_{\mathrm{\&rho;}}*(\&dtri;u_{\mathrm{\&sigma;}}\&dtri;{u_{\mathrm{\&sigma;}}}^T)=\left(\begin{array}{cc}{G}_{\mathrm{\&rho;}}*{\left(\frac{\&part;u_{\mathrm{\&sigma;}}}{\&part;x}\right)}^2& G_{\mathrm{\&rho;}}*\left(\frac{\&part;u_{\mathrm{\&sigma;}}}{\&part;x}\frac{\&part;u_{\mathrm{\&sigma;}}}{\&part;y}\right)\\ G_{\mathrm{\&rho;}}*\left(\frac{\&part;u_{\mathrm{\&sigma;}}}{\&part;x}\frac{\&part;u_{\mathrm{\&sigma;}}}{\&part;y}\right)& G_{\mathrm{\&rho;}}*{\left(\frac{\&part;u_{\mathrm{\&sigma;}}}{\&part;y}\right)}^2\end{array}\right)$

G_ρRepresent the Gaussian kernel with ρ as parameter.Definition

$J_{\mathrm{\&rho;}}=\left(\begin{array}{cc}{j}_{11}& j_{12}\\ j_{12}& j_{22}\end{array}\right)$

J_ρTwo characteristic values be

$\left\{\begin{array}{c}{\mathrm{\&lambda;}}_1=\frac{1}{2}(j_{11}+j_{22}+\sqrt{{(j_{11}-j_{22})}^2+4j_{12}^2})\\ {\mathrm{\&lambda;}}_2=\frac{1}{2}(j_{11}+j_{22}-\sqrt{{(j_{11}-j_{22})}^2+4j_{12}^2})\end{array}\right.$

Their characteristic of correspondence vector is v₁And v₂, v_i=(cos θ_i,sinθ_i), i=1,2.

Wherein

${\mathrm{\&theta;}}_1=\frac{1}{2}arctan\frac{2j_{12}}{j_{11}-j_{22}},{\mathrm{\&theta;}}_1={\mathrm{\&theta;}}_1+\frac{\mathrm{\&pi;}}{2}$

If μ₁And μ₂It is two characteristic values of diffusion tensor matrices T (x), if

$T\left(x\right)=\left(\begin{array}{cc}a& b\\ b& c\end{array}\right)$

v₁And v₂It is corresponding characteristic vector, have v₁=(cos θ, sin θ)；v₂=(-sin θ, cos θ).

The relation of the matrix element of T (x) and eigen vector is as follows:

$\left\{\begin{array}{c}a={\mathrm{\&mu;}}_{1}co{s}^2\mathrm{\&theta;}+{\mathrm{\&mu;}}_{2}si{n}^2\mathrm{\&theta;}\\ b=({\mathrm{\&mu;}}_1-{\mathrm{\&mu;}}_2)sin\mathrm{\&theta;}cos\mathrm{\&theta;}\\ c={\mathrm{\&mu;}}_{2}co{s}^2\mathrm{\&theta;}+{\mathrm{\&mu;}}_1{\sin }^2\mathrm{\&theta;}\end{array}\right.$

Use edge enhanced diffustion tensor: μ₁=g (λ₁), μ₂=1；Wherein g is edge function.

Finite difference is used to solve above-mentioned PDE:

$u^{n+1}=u^n+\mathrm{\&Delta;}t(-RE\{\stackrel{\&OverBar;}{D_x^{\mathrm{\&alpha;}}}\left(T\frac{D_x^{\mathrm{\&alpha;}}{u}^n}{\left|D_x^{\mathrm{\&alpha;}}{u}^n\right|}\right)+\stackrel{\&OverBar;}{D_y^{\mathrm{\&alpha;}}}\left(T\frac{D_y^{\mathrm{\&alpha;}}{u}^n}{\left|D_y^{\mathrm{\&alpha;}}{u}^n\right|}\right)+{\mathrm{\&lambda;}}_D\left(u_0-u^n\right)\})$

Fractional Derivative can be calculated by using efficient Discrete Fourier Transform:

$U({\mathrm{\&omega;}}_1,{\mathrm{\&omega;}}_2)=\frac{1}{N}{\mathrm{\&Sigma;}}_{m,n=1}^{N}u(m,n)\exp (-j2\mathrm{\&pi;}({\mathrm{m\&omega;}}_1+{\mathrm{n\&omega;}}_2)/N)$

Integer order derivative is generalized to Fractional Derivative, obtains based on the fractional order difference under discrete Fouier conversion meaningWithThey at the corresponding relation of spatial domain and frequency domain are:

$D_x^{\mathrm{\&alpha;}}u=(1-\exp (-j2\mathrm{\&pi;}\left({\mathrm{m\&omega;}}_1\right)/N\left)\right)U({\mathrm{\&omega;}}_1,{\mathrm{\&omega;}}_2)$

$D_y^{\mathrm{\&alpha;}}u=(1-\exp (-j2\mathrm{\&pi;}\left({\mathrm{m\&omega;}}_2\right)/N\left)\right)U({\mathrm{\&omega;}}_1,{\mathrm{\&omega;}}_2)$

Fractional order difference operatorWithAdjoint operatorWithSpatial domain and the corresponding relation of frequency domain For:

$\stackrel{\&OverBar;}{D_x^{\mathrm{\&alpha;}}}u=\stackrel{\&OverBar;}{(1-\exp (-j2\mathrm{\&pi;}\left({\mathrm{m\&omega;}}_1\right)/N\left)\right)}U({\mathrm{\&omega;}}_1,{\mathrm{\&omega;}}_2)$

$\stackrel{\&OverBar;}{D_y^{\mathrm{\&alpha;}}}u=\stackrel{\&OverBar;}{(1-\exp (-j2\mathrm{\&pi;}\left({\mathrm{m\&omega;}}_2\right)/N\left)\right)}U({\mathrm{\&omega;}}_1,{\mathrm{\&omega;}}_2)$

Using sample texture synthetic technology to repair texture component, the complexity utilizing image block is adaptive as standard Region of search should be changed to improve reparation speed in ground；The complexity utilizing image block determines repairs order to obtain preferably reparation Effect.Detailed process is as follows: uses fractal dimension and the complexity of comentropy tolerance image block, utilizes complexity to determine the field of search Territory and reparation order.Empirically determined entropy and the Weighted Threshold of fractal dimension, at the multiblock to be repaired more than threshold value, select relatively Big region of search completes to mate padding；At the multiblock to be repaired less than threshold value then contrary.And the big image of complexity Block is preferentially repaired.In numerical computations, in conjunction with differential box method of counting and fractal Brown motion self-similarity method calculating figure As the fractal dimension of block, at utmost to distinguish different roughness texture.

Comentropy is used to measure the complexity of block of pixels.Comentropy is the statistical form of a kind of feature, and it reflects figure The number of average information in Xiang.The comentropy of image represents the information content that the aggregation characteristic of intensity profile in image is comprised, Make P_iRepresent block of pixels Ψ_pMiddle gray value is the ratio shared by the pixel of i, i.e.

$P_i=\frac{\#\{n:n\&Element;{\mathrm{\&Psi;}}_p\&cap;\mathrm{\&Phi;},n=i\}}{|{\mathrm{\&Psi;}}_p\&cap;\mathrm{\&Phi;}|},i=0,1,...,255$

The unitary comentropy then defining gray level image is:

$H\left(p\right)=\frac{-{\mathrm{\&Sigma;}}_{i=0}^{255}{P}_{i}log\left(P_i\right)}{b}$

Wherein b is normalized parameter, selects b=5 in an experiment.Above formula only defines a metamessage of gray level image Entropy, for coloured image, uses the average of unitary comentropy under tri-Color Channels of RGB, i.e.

$H\left(p\right)=\frac{H_R\left(p\right)+H_G\left(p\right)+H_B\left(p\right)}{3}$

Carrying out based in the image mending of the textures synthesis of sample block, the big repairing block of comentropy H (p) will first be repaiied Multiple.

Fractal box is used to measure block of pixels Ψ further_pComplexity.The fractal box of image is a kind of special The statistical form levied, reflect average information in block of pixels number, value is normally between interval 2-3.Fractal dimension Closer to dimension 2, show more smooth (under normal circumstances, constant value block of pixels Ψ of image_pThe fractal box of=C is 2)；Closer to Dimension 3, shows that grey scale change is more violent, and image is more complicated.The unitary fractal box then defining gray level image is:

F (p)=aD (Ψ_p)-b

Wherein a, b are normalized parameter, select a=1 in an experiment；B=-2.It is apparent that F (p) ∈ [0,1].If picture In element block, intensity profile is more uniform, and fractal box F (p) is closer to 0；Whereas if grey scale change is more violent in block of pixels, Containing a lot of image informations, fractal box F (p) is closer to 1.For coloured image, use under tri-Color Channels of RGB The average of unitary fractal box, i.e.

$F\left(p\right)=\frac{F_R\left(p\right)+F_G\left(p\right)+F_B\left(p\right)}{3}$

It is attached to fractal box and the comentropy of block of pixels in prioritization functions, carrying out the texture based on sample block During the image repair of synthesis, fractal box and the big reparation block of comentropy will first be repaired.

Prioritization functions is defined as:

P (p)=α C (p) D (p)+β F (p)+γ H (p)

Wherein α ＞ 0, β ＞ 0 and γ ＞ 0 be weight factor, and meet alpha+beta+γ=1.

Match block search uses following process: by match block Ψ_qBy complexity, (fractal box adds with comentropy in set Power, i.e. β F (p)+γ H (p)) size imparting liter sequence structure, then use binary search, compose sequence match block Ψ_qIn set right With input multiblock Ψ to be repaired under complexity meaning_pImmediate match block Ψ_qK neighborhood in again carry out coupling search, find The minimum match block of SSD.I.e.

Ψ_q=argmin{d (Ψ_p,Ψ_q):Ψ_q∈K}

Wherein K is match block Ψ_qIn set under fractal box meaning with input multiblock Ψ to be repaired_pImmediate Join block Ψ_qK neighborhood.The size of k is chosen as k=32.

(4) structure components after synthesis is repaired and texture component, obtain the complete correction of " Tujia " picture weaving in silk digital picture

As it is shown in figure 9, structure components and texture component after repairing are weighted averagely, the structure after synthesis is repaired is divided Amount and texture component, obtain the complete correction of final " Tujia " picture weaving in silk digital picture.

If the structure components after Xiu Fuing and texture component are respectively u and v, then complete correction is expressed as

F=2 × (a × u+ (1-a) × v)

Wherein a ∈ 0,1) it is weight factor.Adjust this parameter and can obtain different visual effects.Generally set A=0.5.

The application by digital technology to " Tujia " picture weaving in silk tradition remaining pattern repair, can by repeatedly attempting, Find repairing effect the most satisfied, without the need for destroying original picture-weaving in silk, be that the repair of " Tujia " picture weaving in silk provides safety Approach easily.The present processes has well reparation for the texture-rich such as " Tujia " picture weaving in silk, beautiful in colour and textile Effect, can meet the vision requirement of people well.

Automatically the detection of " Tujia " picture weaving in silk digital picture damaged area and positioning, by optimal result manual with expert Comparison, accuracy is up to more than 98%.The present processes has reparation speed faster, treating of less than 1024 × 1024 sizes Repairing image, repairing area, below 50 × 50, about can complete whole repair process in 100 seconds to 600 seconds.

The technical scheme of the application, step is simple, it is easy to operation, and reproducible, technical staff is easy to learn, easily grasp.

Censure special component or method as employed some vocabulary in the middle of specification and claim.Art technology Personnel are it is to be appreciated that same composition may be called with different nouns in different regions.This specification and claims are not In the way of the difference of title is used as distinguishing composition.As in the middle of specification and claim in the whole text, mentioned "comprising" is One open language, therefore " comprise but be not limited to " should be construed to." substantially " refer in receivable error range, this area Technical staff can solve described technical problem in the range of certain error, basically reaches described technique effect.Specification is follow-up Being described as implementing the better embodiment of the application, right described description is for the purpose of the rule that the application is described, not In order to limit scope of the present application.The protection domain of the application ought be as the criterion depending on the defined person of claims.

Also, it should be noted term " includes ", "comprising" or its any other variant are intended to nonexcludability Comprise, so that include that the commodity of a series of key element or system not only include those key elements, but also include not clearly Other key elements listed, or also include for this commodity or the intrinsic key element of system.In the feelings not having more restriction Under condition, the key element that limited by statement " including ... ", it is not excluded that in the commodity including described key element or system also There is other identical element.

Described above illustrate and describes some preferred embodiments of the application, but as previously mentioned, it should be understood that the application Be not limited to form disclosed herein, be not to be taken as the eliminating to other embodiments, and can be used for other combinations various, Modification and environment, and can be in application contemplated scope described herein, by technology or the knowledge of above-mentioned teaching or association area It is modified.And the change that those skilled in the art are carried out and change are without departing from spirit and scope, then all should be in this Shen Please be in the protection domain of claims.

Claims (5)

1. " Tujia " picture weaving in silk tradition remaining pattern digitlization restorative procedure, it is characterised in that include that damaged area is detected automatically, image Structure components and texture component are decomposed, and structure components Variational PDE is repaired and the textures synthesis reparation of texture component, specifically include with Lower step:

(1) detection and the location model automatically of the digital picture damaged area of " Tujia " picture weaving in silk are set up；

(2) building variation picture breakdown model is structure components and texture component by " Tujia " picture weaving in silk picture breakdown；

(3) designing Variational PDE model and repairing " Tujia " picture weaving in silk structure components, design repairs Tujia based on the Texture Synthesis of sample Picture-weaving in silk texture component；

(4) it is finally synthesizing the structure components after reparation and texture component, obtain the complete correction of " Tujia " picture weaving in silk digital picture.

2. " Tujia " picture weaving in silk tradition remaining pattern digitlization restorative procedure as claimed in claim 1, it is characterised in that described step (1) it is detection and the positioning utilizing the variation movable contour model of fused images much information to carry out damaged area, concrete grammar For: " Tujia " picture weaving in silk image is analyzed, selects 2 color model, extract color characteristic and textural characteristics, and to characteristic Merge, obtain Efficient image characteristic；The Efficient image characteristic information obtaining fusion is dissolved in Variation Model, real Existing image special objective extracted region and positioning.

3. " Tujia " picture weaving in silk tradition remaining pattern digitlization restorative procedure as claimed in claim 2, it is characterised in that described step (2) for utilizing priori to be modeled the structure components and texture component of " Tujia " picture weaving in silk image respectively, Variation Model is obtained, Obtain clean structural texture by functional minimization to decompose, method particularly includes: described structure components passes through non-convex biregular item Modeling, comprises non-convex sparse measurement and the second dervative non-convex sparse measurement of gradient；Described texture component uses rank of matrix tolerance, Extract uniformity texture by the minimization of order；Described Variation Model uses alternative iteration method to solve.

4. " Tujia " picture weaving in silk tradition remaining pattern digitlization restorative procedure as claimed in claim 3, it is characterised in that described step (3) repairing structure components for design Variational PDE model, texture component is repaired by design Texture Synthesis, tool Body method is: for the design of described Variational PDE repairing model, combines fractional order differential with tensor diffusion, proposes variation Model, according to the corresponding Euler-Lagrange equation of the carried Variation Model of fractional order Functional Theory derivation, utilizes discrete Fourier transform definition Fractional Derivative operator and its adjoint operator, the computing formula of derivation Fractional Derivative, design and carried The numerical algorithm of repairing model；For the design of described Texture Synthesis, fractal box is used to measure image with comentropy The complexity of block, utilizes the region of search of complexity constraint match block and the definition of priority, to improve reparation speed and to repair Multiple precision.

5. " Tujia " picture weaving in silk tradition remaining pattern digitlization restorative procedure as claimed in claim 4, it is characterised in that described step (4) structure components after synthesis is repaired and texture component method particularly includes: the structure components after repairing and texture component are entered Row weighted average.