CN104537371A - Fingerprint texture image denoising enhancing method and system - Google Patents

Abstract

The invention relates to a fingerprint texture image denoising enhancing method. According to the method, a non-local diffusion tensor diffusion-fluctuation partial differential equation model is provided. The method comprises the following steps that an image is preprocessed; the non-local structure tensor is calculated; the non-local diffusion tensor is calculated through the non-local structure tensor; iteration updating is carried out, and a result image is obtained. The texture characteristic can be enhanced while the noise is eliminated, a certain repairing function of the fracture texture is achieved, and the fingerprint recognition can be carried out more accurately in the later process.

Description

The denoising Enhancement Method of fingerprint texture image and system thereof

Technical field

The invention belongs to Preprocessing Technique field, field, particularly relate to a kind of denoising Enhancement Method and system thereof of fingerprint texture image.

Background technology

Fingerprint identification technology has become maturation and easily one of biological identification technology the most because it has high stability, uniqueness, high reliability, easy collection property and the difficult plurality of advantages such as decoding of forging, and is widely used in the industries such as security protection, public security, IT, finance, medical treatment.

In the fingerprint collecting process of reality, due to collecting device performance, gather the impact such as state of environment and gathered person's finger, can there is various noise in fingerprint image, this causes comparatively big error by follow-up Feature extraction and recognition usually.Therefore, the pre-service of fingerprint image is an important link in whole fingerprint recognition system.

Preprocessing process specifically comprises the denoising of fingerprint texture image and the enhancing of texture and suitably repairs the texture ruptured.The denoising of image is the processing procedure of conflict with strengthening, and image denoising is intended to the noise spot removed in image and makes image become level and smooth, but structure in image and textural characteristics also can be affected and fuzzy simultaneously; Image enhaucament, while raising structural texture contrast, may make again noise also be enhanced.Therefore, how weighing both is the pretreated keys of fingerprint image.

The method of current fingerprint image denoising and enhancing is mainly divided into two large classes: frequency domain filtering method and filter in spatial domain method.Frequency domain filtering method, as Fourier transform, wavelet transformation etc., all realizes the removal of noise by filtering image HFS, but has the edge of high frequency characteristics in image equally and texture information also must be lost; In spatial domain, sampling local template convolution or employing nonlinear diffusion model filtering method, can realize strengthening according to image local feature self-adaptation, but be subject to noise.

Summary of the invention

Based on this, for above-mentioned technical matters, provide a kind of denoising Enhancement Method and system thereof of texture image.

For solving the problems of the technologies described above, the present invention adopts following technical scheme:

A denoising Enhancement Method for fingerprint texture image, the method provides the diffuse-wave of a non local diffusion tensor to move PDE model:

$\left\{\begin{array}{c}\frac{{\∂}^{2}u}{{\∂t}^2}+\mathrm{\λ}\frac{\∂u}{\∂t}-{\mathrm{div}}_{\mathrm{NL}}\left(D_{\mathrm{NL}}\left(J_{\mathrm{\ρ}}\left({\▿}_{\mathrm{NL}}{u}_{\mathrm{\σ}}\right)\right){\▿}_{\mathrm{NL}}u\right)=0\\ u(x,0)=u_0\left(x\right),\frac{\∂u}{\∂t}(x,0)=0\end{array}\right.$

, this model representation is Ω is X-Y scheme image field, and T is positive time constant; λ >0 is weighting parameter; represent gradient and divergence operator respectively with div, NL represents corresponding non local operator; J _ρ() represents structure tensor; D _nLfor non local diffusion tensor; u _σrepresent through standard deviation be the gaussian kernel of σ level and smooth after image; u ₀x () is the image of initial strip noise;

And comprise the following steps:

Image semantic classification: carry out Gaussian smoothing to initial pictures, obtains the image u smoothly _σ=G _σ* u, G _σfor standard deviation is the gaussian kernel function of σ, * is convolution operation;

Calculate non local structure tensor

$J_{\mathrm{\ρ}}\left({\▿}_{\mathrm{NL}}{u}_{\mathrm{\σ}}\right):=G_{\mathrm{\ρ}}*({\▿}_{\mathrm{NL}}{u}_{\mathrm{\σ}}\⊗{\▿}_{\mathrm{NL}}{u}_{\mathrm{\σ}})=G_{\mathrm{\ρ}}*\left({\▿}_{\mathrm{NL}}{\mathrm{\μ}}_{\mathrm{\σ}}{\▿}_{\mathrm{NL}}^T{u}_{\mathrm{\σ}}\right)$

, for tensor product, T is the transposition of vector, G _ρthe gaussian kernel function of to be standard deviation be ρ, for non local gradient operator;

Non local diffusion tensor D is calculated by described non local structure tensor _nL;

Iteration upgrades and obtains result images: described in discretize, the diffuse-wave of non local diffusion tensor moves PDE model, and by the model after following formula iterative discretize:

$U^{k+1}=\frac{1}{1+\mathrm{\λ\τ}}((2+\mathrm{\λ\τ})U^k-U^{k-1}+{\mathrm{\τ}}^2{\mathrm{LU}}^k)$

, U represents a column vector of all row of two dimensional image (from left to right) splicing synthesis, subscript k=1,2 ... represent iterations, τ is time step, and L is right the difference approximation of operator, initial value arranges U ⁰=U ¹, it is the column vector of initial pictures; After iteration terminates, iteration result U is reduced into two dimensional image, is and obtains result images.

Describedly calculate non local diffusion tensor D by described non local structure tensor _nLstep comprises:

Described non local structure tensor is carried out feature decomposition, i.e. J _ρ=V Σ V ^t, Σ=diag (η _i), i=1 ..., m is for comprising J _ρthe diagonal matrix of eigenwert, and be η by eigenwert sequence ₁>=η ₂>=...>=η _m, V=(v ₁, v ₂..., v _m) contain the orthogonal matrix of character pair vector;

Non local diffusion tensor D is calculated by following formula _nL:

D _NL＝VΛV ^T

, Λ=diag (μ _i), i=1 ... m is diagonal matrix.

Described λ=4, σ=0.5, ρ=5, τ=0.5.

The denoising that this programme also relates to a kind of fingerprint texture image strengthens system, and this system provides the diffuse-wave of a non local diffusion tensor to move PDE model:

$\left\{\begin{array}{c}\frac{{\∂}^{2}u}{{\∂t}^2}+\mathrm{\λ}\frac{\∂u}{\∂t}-{\mathrm{div}}_{\mathrm{NL}}\left(D_{\mathrm{NL}}\left(J_{\mathrm{\ρ}}\left({\▿}_{\mathrm{NL}}{u}_{\mathrm{\σ}}\right)\right){\▿}_{\mathrm{NL}}u\right)=0\\ u(x,0)=u_0\left(x\right),\frac{\∂u}{\∂t}(x,0)=0\end{array}\right.$

, this model representation is Ω is X-Y scheme image field, and T is positive time constant; λ >0 is weighting parameter; represent gradient and divergence operator respectively with div, NL represents corresponding non local operator; J _ρ() represents structure tensor; D _nLfor non local diffusion tensor; u _σrepresent through standard deviation be the gaussian kernel of σ level and smooth after image; u ₀x () is the image of initial strip noise;

And comprise:

Image pre-processing unit, for carrying out Gaussian smoothing to initial pictures, obtains the image u smoothly _σ=G _σ* u, G _σfor standard deviation is the gaussian kernel function of σ, * is convolution operation;

Non local structure tensor computing unit, for calculating non local structure tensor

$J_{\mathrm{\ρ}}\left({\▿}_{\mathrm{NL}}{u}_{\mathrm{\σ}}\right):=G_{\mathrm{\ρ}}*({\▿}_{\mathrm{NL}}{u}_{\mathrm{\σ}}\⊗{\▿}_{\mathrm{NL}}{u}_{\mathrm{\σ}})=G_{\mathrm{\ρ}}*\left({\▿}_{\mathrm{NL}}{\mathrm{\μ}}_{\mathrm{\σ}}{\▿}_{\mathrm{NL}}^T{u}_{\mathrm{\σ}}\right)$

for tensor product, T is the transposition of vector, G _ρthe gaussian kernel function of to be standard deviation be ρ, for non local gradient operator;

Non local diffusion tensor computing unit, for calculating non local diffusion tensor D by described non local structure tensor _nL;

Iteration upgrades and obtains result images unit, and the diffuse-wave for diffusion tensor non local described in discretize moves PDE model, and by the model after following formula iterative discretize:

$U^{k+1}=\frac{1}{1+\mathrm{\λ\τ}}((2+\mathrm{\λ\τ})U^k-U^{k-1}+{\mathrm{\τ}}^2{\mathrm{LU}}^k)$

U represents a column vector of all row of two dimensional image (from left to right) splicing synthesis, subscript k=1,2 ... represent iterations, τ is time step, and L is right the difference approximation of operator, initial value arranges U ⁰=U ¹, it is the column vector of initial pictures; After iteration terminates, iteration result U is reduced into two dimensional image, is and obtains result images.

Describedly calculate non local diffusion tensor D by described non local structure tensor _nLcomprise:

Described non local structure tensor is carried out feature decomposition, i.e. J _ρ=V Σ V ^t, Σ=diag (η _i), i=1 ..., m is for comprising J _ρthe diagonal matrix of eigenwert, and be η by eigenwert sequence ₁>=η ₂>=...>=η _m, V=(v ₁, v ₂..., v _m) contain the orthogonal matrix of character pair vector;

Non local diffusion tensor D is calculated by following formula _nL:

D _NL＝VΛV ^T

Λ=diag (μ _i), i=1 ... m is diagonal matrix.

Described λ=4, σ=0.5, ρ=5, τ=0.5.

The present invention was adding wave characteristic item based on the basis of diffusion equation in the past, make model between diffusion and wave equation characteristic, therefore diffusion equation and the performance advantage of wave equation respectively on denoising and structural texture strengthen can be taken into account, denoising and enhancing while realizing image; Adopt structure tensor to describe the architectural feature of parallel stream-like texture in fingerprint image more accurately, and instruct dispersal direction and intensity by diffusion tensor, realize anisotropy parameter truly; Utilize non local technology, more effectively utilize the redundancy of image, fully excavate global information, improve the noise robustness of model; Use the fingerprint image of this inventive method process can strengthen textural characteristics while removal noise, and have certain repair to the texture of fracture, make follow-up can following carry out fingerprint recognition exactly.

Accompanying drawing explanation

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail:

Fig. 1 is the process flow diagram of the denoising Enhancement Method of a kind of fingerprint texture image of the present invention;

Fig. 2 is the structural representation of the denoising enhancing system of a kind of fingerprint texture image of the present invention;

Fig. 3 (a) is the amplification of original fingerprint image local, Fig. 3 (b) is for adopting the enhancing result schematic diagram of CED model, Fig. 3 (c) is not for adopt the diffuse-wave based on diffusion tensor of non local technology to move the enhancing result schematic diagram of equation model, and Fig. 3 (d) is the enhancing result schematic diagram adopting the inventive method.

Embodiment

A denoising Enhancement Method for fingerprint texture image, the method provides the diffuse-wave of a non local diffusion tensor to move PDE model:

$\left\{\begin{array}{c}\frac{{\∂}^{2}u}{{\∂t}^2}+\mathrm{\λ}\frac{\∂u}{\∂t}-{\mathrm{div}}_{\mathrm{NL}}\left(D_{\mathrm{NL}}\left(J_{\mathrm{\ρ}}\left({\▿}_{\mathrm{NL}}{u}_{\mathrm{\σ}}\right)\right){\▿}_{\mathrm{NL}}u\right)=0\\ u(x,0)=u_0\left(x\right),\frac{\∂u}{\∂t}(x,0)=0\end{array}\right.$

This model representation is Ω is X-Y scheme image field, and T is positive time constant; λ >0 is weighting parameter; represent gradient and divergence operator respectively with div, NL represents corresponding non local operator; J _ρ() represents structure tensor; D _nLfor non local diffusion tensor; u _σrepresent through standard deviation be the gaussian kernel of σ level and smooth after image; u ₀x () is the image of initial strip noise.

This model has following feature:

(1) diffuse-wave is adopted to move PDE model: existing based in the image de-noising method of partial differential equation, nearly all based on diffusion equation, form is as follows:

$\frac{\∂u}{\∂t}=F(u,\▿u,{\▿}^{2}u,...)$

The advantage of diffusion equation be it by the brightness of thermal diffusion analogy image spatially smoothly reach denoising object, but inferior position is to be unfavorable for that marginal texture keeps and strengthens.Have document prove form as shown in the formula wave equation be conducive to the enhancing of image edge structure: (document: A.Averbuch, B.Epstein, N.Rabin, E.Turkel, Edge-enhancement postprocessing using artificialdissipation, IEEE Trans.Image Process.15 (2006), 1486 – 1498.):

$\frac{{\∂}^{2}u}{\∂t^2}=F(u,\▿u,{\▿}^{2}u,...)$

Therefore, the inventive method model adopts mixed type diffuse-wave to move equation, can take into account denoising and structural texture strengthens.

(2) structure tensor can reflect the local feature direction of image better than gradient, diffusion tensor according to structure tensor design can truly realize anisotropic diffusion property, the diffusion strength that namely not only can control spatially diverse location can also control dispersal direction according to local feature direction, thus realizes enhancing and the reparation of stream-like texture in image.

(3) non local technology is no longer confined to only process image based on local message in the past, but makes full use of redundancy or the self-similarity of image self, make use of more non-local information to improve the rejection ability of noise.The inventive method is used for reference non local technology and the Local Operators such as derivative, gradient, divergence is generalized to non local operator raising denoising performance.

As shown in Figure 1, denoising enhancing process of the present invention is as follows:

S110, Image semantic classification: carry out Gaussian smoothing to initial pictures, obtain the image u smoothly _σ=G _σ* u, G _σfor standard deviation is the gaussian kernel function of σ, * is convolution operation, and employing window size is the template approximate Gaussian filtering core function G of 3 × 3 _σ.

S120, calculate non local structure tensor

By the non local popularization to derivative, gradient, divergence operator, generate a series of non local operator, and then calculate non local structure tensor.Non local structure tensor is defined by the tensor product of non local gradient, namely

$J_{\mathrm{\ρ}}\left({\▿}_{\mathrm{NL}}{u}_{\mathrm{\σ}}\right):=G_{\mathrm{\ρ}}*({\▿}_{\mathrm{NL}}{u}_{\mathrm{\σ}}\⊗{\▿}_{\mathrm{NL}}{u}_{\mathrm{\σ}})=G_{\mathrm{\ρ}}*\left({\▿}_{\mathrm{NL}}{u}_{\mathrm{\σ}}{\▿}_{\mathrm{NL}}^T{u}_{\mathrm{\σ}}\right)$

for tensor product, T is the transposition of vector, G _ρthe gaussian kernel function of to be standard deviation be ρ, for non local gradient operator.

Particularly:

(1) popularization of non local operator: for two dimensional image, the gradient of image is a bivector, and its component adopts the difference of horizontal direction and vertical direction adjacent pixel values to be similar to respectively.General Difference Calculation only make use of limited local message, as 4 neighborhood territory pixels.And for general natural image, image itself has very high redundancy and self-similarity, make full use of the noise that these redundancies can remove image.For this reason, first the gradient operator of local is generalized to non local gradient operator by the present invention, the form of its continuous situation as shown in the formula:

${\▿}_{\mathrm{NL}}u(x,y)=(u\left(y\right)-u\left(x\right))\sqrt{\mathrm{\ω}(x,y)}$

Wherein x, y are two-dimensional coordinate, and weight function is defined as follows:

$\mathrm{\ω}(x,y)=\exp (-\frac{1}{h^2}{|u^p\left(x\right)-u^p\left(y\right)|}^2)$

Wherein h is positive constant, u ^p(x) and u ^py () represents the image block centered by x and y respectively.Be the image of m+1 for sum of all pixels, non local gradient above discretely can turn to the column vector of m × 1, namely for image u at x place along y _ithe non local partial derivative in direction, namely $u_{y_i}\left(x\right)=(u\left(y_i\right)-u\left(x\right))\sqrt{\mathrm{\ω}(x,y_i)}.$

(2) non local structure tensor is calculated: the non local gradient calculated is asked tensor product to self, namely above namely obtain the matrix of a m × m, then by element, Gaussian smoothing is carried out to it, obtain non local structure tensor.Can verify, non local structure tensor is a positive semidefinite symmetrical matrix.

S130, the non local structure tensor obtained by S120 step calculate non local diffusion tensor D _nL:

(1) feature decomposition of non local structure tensor: non local structure tensor is carried out feature decomposition, i.e. J _ρ=V Σ V ^t, wherein Σ=diag (η _i), i=1 ..., m is for comprising J _ρthe diagonal matrix of eigenwert, and be η by eigenwert sequence ₁>=η ₂>=...>=η _m, V=(v ₁, v ₂..., v _m) contain the orthogonal matrix of character pair vector.

(2) degree of coherence is calculated according to eigenwert: degree of coherence computing formula is as follows:

$\mathrm{\κ}=\underset{i=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=i+1}{\overset{m}{\mathrm{\Σ}}}{({\mathrm{\η}}_i-{\mathrm{\η}}_j)}^2$

Each eigenwert of structure tensor reflects the intensity on each characteristic direction of correspondence, therefore in edge or corner location, on certain characteristic direction, eigenwert is obviously greater than the eigenwert of other characteristic directions, and then can reach a conclusion: become large at edge or corner location degree of coherence, and go to zero at flat site degree of coherence.

(3) non local diffusion tensor is constructed: because structure tensor proper vector reflects image spatial feature direction, character pair value reflects intensity, therefore in order to regulate diffusion strength adaptively according to characteristics of image, can realize by regulating the eigenwert size of each characteristic direction.Therefore the structure principle of non local diffusion tensor is for keeping proper vector constant, and namely matrix V is constant, and eigenwert adjusts as required, and concrete adjustment is as follows:

μ _i＝α,α∈(0,1),α<<1,i＝1,...,m-1,

Wherein ε is threshold value, and generally getting less value can as 0.1.Non local diffusion tensor is D thus _nL=V Λ V ^t, wherein Λ=diag (μ _i), i=1 ... m is diagonal matrix.Can verify, non local diffusion tensor is positive definite symmetrical matrix.

S140, iteration upgrade and obtain result images: described in discretize, the diffuse-wave of non local diffusion tensor moves PDE model, and by the model after following formula iterative discretize:

$U^{k+1}=\frac{1}{1+\mathrm{\&lambda;\&tau;}}((2+\mathrm{\&lambda;\&tau;})U^k-U^{k-1}+{\mathrm{\&tau;}}^2{\mathrm{LU}}^k)---\left(1\right)$

U represents a column vector of all row of two dimensional image (from left to right) splicing synthesis, subscript k=1,2 ... represent iterations, τ is time step, and L is right the difference approximation of operator, initial value arranges U ⁰=U ¹, it is the column vector of initial pictures; After iteration terminates, iteration result U is reduced into two dimensional image, is and obtains result images.

Detailed process is as follows:

(1) grandfather tape noise image u is inputted ₀, it is pulled into a column vector by row, namely each is arranged the formation column vector U that is stitched together ⁰, and make U ¹=U ⁰; Setting-up time step-length τ, weighting parameter λ.

(2) difference approximation is adopted to calculate operator be designated as matrix L=(l _ij(U)) _ij, wherein each element l _ijare all functions of U, are specifically calculated as follows:

, wherein, i, j are pixel two-dimensional coordinate point, N _ni () represents the neighborhood territory pixel set of pixel i along the n-th coordinate axis (for two dimensional image, n=1 represents horizontal axis, and n=2 represents vertical coordinate axis), d _ijfor non local diffusion tensor D _nLin element, ω _ijfor the value of the weight function ω (i, j) of discretize.In order to improve operation efficiency, when calculating non local operator, do not adopt the image overall information of ideal situation, but the contiguous range that setting one is larger, compared with only utilizing 4 neighborhoods with Local Operators such as common differential, the non local operator calculated like this make use of more image redundancy information equally.

(3) utilize formula (1) to carry out iterative computation, stop iteration when iterations equals to set the number of times stopped.

(4) iteration result U is reverted to original two dimensional image array u and be final process result.

In order to make assessment to effect of the present invention, invention has been following experiment:

Real fingerprint image (being of a size of 72 × 72 pixels) is adopted to test, as shown in Fig. 3 (a).

Image block size during weight function ω calculates is 7 × 7, the Size of Neighborhood that non local operator calculates is set as 21 × 21, weighting parameter λ=4, gaussian kernel function standard deviation sigma=0.5 of initial Gaussian filtering, gaussian kernel function standard deviation ρ=5 during structure tensor calculates, time step τ=0.5.

Coherence enhancing diffusion (the Coherenceenhancing diffusion that Fig. 3 (b) proposes for adopting the people such as Weickert, CED) the enhancing result of model, Fig. 3 (c) for not adopt the diffuse-wave based on diffusion tensor of non local technology to move the enhancing result of equation model, the enhancing result that Fig. 3 (d) is the inventive method.

From result images, because CED model proposes based on diffusion equation, the hold facility therefore for some high-frequency region is more weak, may cause the fuzzy of texture; Do not adopt the diffuse-wave of non local technology to move equation model owing to only make use of image local information, therefore affected by noise comparatively large and Acacia crassicarpaA ability is more weak, some grain details made is lost; And the inventive method is better than the above two in the maintenance and enhancing ability of grain details, and there is stronger restraint speckle ability.

The denoising that the invention still further relates to a kind of fingerprint texture image strengthens system.

This system provides the diffuse-wave of a non local diffusion tensor to move PDE model:

$\left\{\begin{array}{c}\frac{{\&PartialD;}^{2}u}{{\&PartialD;t}^2}+\mathrm{\&lambda;}\frac{\&PartialD;u}{\&PartialD;t}-{\mathrm{div}}_{\mathrm{NL}}\left(D_{\mathrm{NL}}\left(J_{\mathrm{\&rho;}}\left({\&dtri;}_{\mathrm{NL}}{u}_{\mathrm{\&sigma;}}\right)\right){\&dtri;}_{\mathrm{NL}}u\right)=0\\ u(x,0)=u_0\left(x\right),\frac{\&PartialD;u}{\&PartialD;t}(x,0)=0\end{array}\right.$

This model representation is Ω is X-Y scheme image field, and T is positive time constant; λ >0 is weighting parameter; represent gradient and divergence operator respectively with div, NL represents corresponding non local operator; J _ρ() represents structure tensor; D _nLfor non local diffusion tensor; u _σrepresent through standard deviation be the gaussian kernel of σ level and smooth after image; u ₀x () is the image of initial strip noise.

This model has following feature:

(1) diffuse-wave is adopted to move PDE model: existing based in the image de-noising method of partial differential equation, nearly all based on diffusion equation, form is as follows:

$\frac{\&PartialD;u}{\&PartialD;t}=F(u,\&dtri;u,{\&dtri;}^{2}u,...)$

The advantage of diffusion equation be it by the brightness of thermal diffusion analogy image spatially smoothly reach denoising object, but inferior position is to be unfavorable for that marginal texture keeps and strengthens.Have document prove form as shown in the formula wave equation be conducive to the enhancing of image edge structure: (document: A.Averbuch, B.Epstein, N.Rabin, E.Turkel, Edge-enhancement postprocessing using artificialdissipation, IEEE Trans.Image Process.15 (2006), 1486 – 1498.):

$\frac{{\&PartialD;}^{2}u}{\&PartialD;t^2}=F(u,\&dtri;u,{\&dtri;}^{2}u,...)$

Therefore, the inventive method model adopts mixed type diffuse-wave to move equation, can take into account denoising and structural texture strengthens.

(2) structure tensor can reflect the local feature direction of image better than gradient, diffusion tensor according to structure tensor design can truly realize anisotropic diffusion property, the diffusion strength that namely not only can control spatially diverse location can also control dispersal direction according to local feature direction, thus realizes enhancing and the reparation of stream-like texture in image.

(3) non local technology is no longer confined to only process image based on local message in the past, but makes full use of redundancy or the self-similarity of image self, make use of more non-local information to improve the rejection ability of noise.The inventive method is used for reference non local technology and the Local Operators such as derivative, gradient, divergence is generalized to non local operator raising denoising performance.

And present system also comprises the renewal of image pre-processing unit 11, non local structure tensor computing unit 12, non local diffusion tensor computing unit 13 and iteration obtains result images unit 14.

Image pre-processing unit 11, for carrying out Gaussian smoothing to initial pictures, obtains the image u smoothly _σ=G _σ* u, G _σfor standard deviation is the gaussian kernel function of σ, * is convolution operation;

Non local structure tensor computing unit 12, for calculating non local structure tensor

$J_{\mathrm{\&rho;}}\left({\&dtri;}_{\mathrm{NL}}{u}_{\mathrm{\&sigma;}}\right):=G_{\mathrm{\&rho;}}*({\&dtri;}_{\mathrm{NL}}{u}_{\mathrm{\&sigma;}}\&CircleTimes;{\&dtri;}_{\mathrm{NL}}{u}_{\mathrm{\&sigma;}})=G_{\mathrm{\&rho;}}*\left({\&dtri;}_{\mathrm{NL}}{\mathrm{\&mu;}}_{\mathrm{\&sigma;}}{\&dtri;}_{\mathrm{NL}}^T{u}_{\mathrm{\&sigma;}}\right)$

for tensor product, T is the transposition of vector, G _ρthe gaussian kernel function of to be standard deviation be ρ, for non local gradient operator.

Particularly:

(1) popularization of non local operator: for two dimensional image, the gradient of image is a bivector, and its component adopts the difference of horizontal direction and vertical direction adjacent pixel values to be similar to respectively.General Difference Calculation only make use of limited local message, as 4 neighborhood territory pixels.And for general natural image, image itself has very high redundancy and self-similarity, make full use of the noise that these redundancies can remove image.For this reason, first the gradient operator of local is generalized to non local gradient operator by the present invention, the form of its continuous situation as shown in the formula:

${\&dtri;}_{\mathrm{NL}}u(x,y)=(u\left(y\right)-u\left(x\right))\sqrt{\mathrm{\&omega;}(x,y)}$

Wherein x, y are two-dimensional coordinate, and weight function is defined as follows:

$\mathrm{\&omega;}(x,y)=\exp (-\frac{1}{h^2}{|u^p\left(x\right)-u^p\left(y\right)|}^2)$

Wherein h is positive constant, u ^p(x) and u ^py () represents the image block centered by x and y respectively.Be the image of m+1 for sum of all pixels, non local gradient above discretely can turn to the column vector of m × 1, namely for image u at x place along y _ithe non local partial derivative in direction, namely $u_{y_i}\left(x\right)=(u\left(y_i\right)-u\left(x\right))\sqrt{\mathrm{\&omega;}(x,y_i)}.$

Non local diffusion tensor computing unit 13, for calculating non local diffusion tensor D by described non local structure tensor _nL, process is as follows particularly:

(1) feature decomposition of non local structure tensor: non local structure tensor is carried out feature decomposition, i.e. J _ρ=V Σ V ^t, wherein Σ=diag (η _i), i=1 ..., m is for comprising J _ρthe diagonal matrix of eigenwert, and be η by eigenwert sequence ₁>=η ₂>=...>=η _m, V=(v ₁, v ₂..., v _m) contain the orthogonal matrix of character pair vector.

(2) degree of coherence is calculated according to eigenwert: degree of coherence computing formula is as follows:

Each eigenwert of structure tensor reflects the intensity on each characteristic direction of correspondence, therefore on limit

$\mathrm{\&kappa;}=\underset{i=1}{\overset{m-1}{\mathrm{\&Sigma;}}}\underset{j=i+1}{\overset{m}{\mathrm{\&Sigma;}}}{({\mathrm{\&eta;}}_i-{\mathrm{\&eta;}}_j)}^2$

Edge or corner location, on certain characteristic direction, eigenwert is obviously greater than the eigenwert of other characteristic directions, and then can reach a conclusion: become large at edge or corner location degree of coherence, and go to zero at flat site degree of coherence.

(3) non local diffusion tensor is constructed: because structure tensor proper vector reflects image spatial feature direction, character pair value reflects intensity, therefore in order to regulate diffusion strength adaptively according to characteristics of image, can realize by regulating the eigenwert size of each characteristic direction.Therefore the structure principle of non local diffusion tensor is for keeping proper vector constant, and namely matrix V is constant, and eigenwert adjusts as required, and concrete adjustment is as follows:

μ _i＝α,α∈(0,1),α<<1,i＝1,...,m-1,

Wherein ε is threshold value, and generally getting less value can as 0.1.Non local diffusion tensor is D thus _nL=V Λ V ^t, wherein Λ=diag (μ _i), i=1 ... m is diagonal matrix.Can verify, non local diffusion tensor is positive definite symmetrical matrix.

Iteration upgrades and obtains result images unit 14, and the diffuse-wave for diffusion tensor non local described in discretize moves PDE model, and by the model after following formula iterative discretize:

$U^{k+1}=\frac{1}{1+\mathrm{\&lambda;\&tau;}}((2+\mathrm{\&lambda;\&tau;})U^k-U^{k-1}+{\mathrm{\&tau;}}^2{\mathrm{LU}}^k)$

, U represents a column vector of all row of two dimensional image (from left to right) splicing synthesis, subscript k=1,2 ... represent iterations, τ is time step, and L is right the difference approximation of operator, initial value arranges U ⁰=U ¹, it is the column vector of initial pictures; After iteration terminates, iteration result U is reduced into two dimensional image, is and obtains result images.Detailed process is as follows:

(1) grandfather tape noise image u is inputted ₀, it is pulled into a column vector by row, namely each is arranged the formation column vector U that is stitched together ⁰, and make U ¹=U ⁰; Setting-up time step-length τ, weighting parameter λ.

(2) difference approximation is adopted to calculate operator be designated as matrix L=(l _ij(U)) _ij, wherein each element l _ijare all functions of U, are specifically calculated as follows:

, wherein, i, j are pixel two-dimensional coordinate point, N _ni () represents the neighborhood territory pixel set of pixel i along the n-th coordinate axis (for two dimensional image, n=1 represents horizontal axis, and n=2 represents vertical coordinate axis),

D _ijfor non local diffusion tensor D _nLin element, ω _ijfor the value of the weight function ω (i, j) of discretize.In order to improve operation efficiency, when calculating non local operator, do not adopt the image overall information of ideal situation, but the contiguous range that setting one is larger, compared with only utilizing 4 neighborhoods with Local Operators such as common differential, the non local operator calculated like this make use of more image redundancy information equally.

(3) utilize formula (1) to carry out iterative computation, stop iteration when iterations equals to set the number of times stopped.

(4) iteration result U is reverted to original two dimensional image array u and be final process result.

In order to make assessment to effect of the present invention, invention has been following experiment:

Real fingerprint image (being of a size of 72 × 72 pixels) is adopted to test, as shown in Fig. 3 (a).

Image block size during weight function ω calculates is 7 × 7, the Size of Neighborhood that non local operator calculates is set as 21 × 21, weighting parameter λ=4, gaussian kernel function standard deviation sigma=0.5 of initial Gaussian filtering, gaussian kernel function standard deviation ρ=5 during structure tensor calculates, time step τ=0.5.

Coherence enhancing diffusion (the Coherenceenhancing diffusion that Fig. 3 (b) proposes for adopting the people such as Weickert, CED) the enhancing result of model, Fig. 3 (c) for not adopt the diffuse-wave based on diffusion tensor of non local technology to move the enhancing result of equation model, the enhancing result that Fig. 3 (d) is the inventive method.

From result images, because CED model proposes based on diffusion equation, the hold facility therefore for some high-frequency region is more weak, may cause the fuzzy of texture; Do not adopt the diffuse-wave of non local technology to move equation model owing to only make use of image local information, therefore affected by noise comparatively large and Acacia crassicarpaA ability is more weak, some grain details made is lost; And the inventive method is better than the above two in the maintenance and enhancing ability of grain details, and there is stronger restraint speckle ability.

But, those of ordinary skill in the art will be appreciated that, above embodiment is only used to the present invention is described, and be not used as limitation of the invention, as long as in spirit of the present invention, all will drop in Claims scope of the present invention the change of the above embodiment, modification.

Claims (6)

1. a denoising Enhancement Method for fingerprint texture image, is characterized in that, the method provides the diffuse-wave of a non local diffusion tensor to move PDE model:

$\left\{\begin{array}{c}\frac{{\&PartialD;}^{2}u}{{\&PartialD;t}^2}+\mathrm{\&lambda;}\frac{\&PartialD;u}{\&PartialD;t}-{\mathrm{div}}_{\mathrm{NL}}\left(D_{\mathrm{NL}}\left(J_{\mathrm{\&rho;}}\left({\&dtri;}_{\mathrm{NL}}{u}_{\mathrm{\&sigma;}}\right)\right){\&dtri;}_{\mathrm{NL}}u\right)=0\\ u(x,0)=u_0\left(x\right),\frac{\&PartialD;u}{\&PartialD;t}(x,0)=0\end{array}\right.$

, this model representation is u (x, t), t ∈ T, Ω are X-Y scheme image field, and T is positive time constant; λ >0 is weighting parameter; represent gradient and divergence operator respectively with div, NL represents corresponding non local operator; J _ρ() represents structure tensor; D _nLfor non local diffusion tensor; u _σrepresent through standard deviation be the gaussian kernel of σ level and smooth after image; u ₀x () is the image of initial strip noise;

And comprise the following steps:

Image semantic classification: carry out Gaussian smoothing to initial pictures, obtains the image u smoothly _σ=G _σ* u, G _σfor standard deviation is the gaussian kernel function of σ, * is convolution operation;

Calculate non local structure tensor

$J_{\mathrm{\&rho;}}\left({\&dtri;}_{\mathrm{NL}}{u}_{\mathrm{\&sigma;}}\right):=G_p*({\&dtri;}_{\mathrm{NL}}{u}_{\mathrm{\&sigma;}}\&CircleTimes;{\&dtri;}_{\mathrm{NL}}{u}_{\mathrm{\&sigma;}})=G_{\mathrm{\&rho;}}*\left({\&dtri;}_{\mathrm{NL}}{u}_{\mathrm{\&sigma;}}{\&dtri;}_{\mathrm{NL}}^T{u}_{\mathrm{\&sigma;}}\right)$

for tensor product, T is the transposition of vector, G _ρthe gaussian kernel function of to be standard deviation be ρ, for non local gradient operator;

Non local diffusion tensor D is calculated by described non local structure tensor _nL;

Iteration upgrades and obtains result images: described in discretize, the diffuse-wave of non local diffusion tensor moves PDE model, and by the model after following formula iterative discretize:

$U^{k+1}=\frac{1}{1+\mathrm{\&lambda;\&tau;}}((2+\mathrm{\&lambda;\&tau;})U^k-U^{k-1}+{\mathrm{\&tau;}}^2{\mathrm{LU}}^k)$

, U represents a column vector of all row of two dimensional image (from left to right) splicing synthesis, subscript k=1,2 ... represent iterations, τ is time step, and L is right the difference approximation of operator, initial value arranges U ⁰=U ¹, it is the column vector of initial pictures; After iteration terminates, iteration result U is reduced into two dimensional image, is and obtains result images.

2. the denoising Enhancement Method of a kind of fingerprint texture image according to claim 1, is characterized in that, describedly calculates non local diffusion tensor D by described non local structure tensor _nLstep comprises:

Described non local structure tensor is carried out feature decomposition, i.e. J _ρ=V Σ V ^t, Σ=diag (η _i), i=1 ..., m is for comprising J _ρthe diagonal matrix of eigenwert, and be η by eigenwert sequence ₁>=η ₂>=...>=η _m, V=(v ₁, v ₂..., v _m) contain the orthogonal matrix of character pair vector;

Non local diffusion tensor D is calculated by following formula _nL:

D _NL＝VΛV ^T

, Λ=diag (μ _i), i=1 ... m is diagonal matrix.

3. the denoising Enhancement Method of a kind of fingerprint texture image according to claim 1 and 2, is characterized in that, described λ=4, σ=0.5, ρ=5, τ=0.5.

4. the denoising of fingerprint texture image strengthens a system, and it is characterized in that, this system provides the diffuse-wave of a non local diffusion tensor to move PDE model:

$\left\{\begin{array}{c}\frac{{\&PartialD;}^{2}u}{{\&PartialD;t}^2}+\mathrm{\&lambda;}\frac{\&PartialD;u}{\&PartialD;t}-{\mathrm{div}}_{\mathrm{NL}}\left(D_{\mathrm{NL}}\left(J_{\mathrm{\&rho;}}\left({\&dtri;}_{\mathrm{NL}}{u}_{\mathrm{\&sigma;}}\right)\right){\&dtri;}_{\mathrm{NL}}u\right)=0\\ u(x,0)=u_0\left(x\right),\frac{\&PartialD;u}{\&PartialD;t}(x,0)=0\end{array}\right.$

, this model representation is u (x, t), t ∈ T, Ω are X-Y scheme image field, and T is positive time constant; λ >0 is weighting parameter; represent gradient and divergence operator respectively with div, NL represents corresponding non local operator; J _ρ() represents structure tensor; D _nLfor non local diffusion tensor; u _σrepresent through standard deviation be the gaussian kernel of σ level and smooth after image; u ₀x () is the image of initial strip noise;

And comprise:

Image pre-processing unit, for carrying out Gaussian smoothing to initial pictures, obtains the image u smoothly _σ=G _σ* u, G _σfor standard deviation is the gaussian kernel function of σ, * is convolution operation;

Non local structure tensor computing unit, for calculating non local structure tensor

$J_{\mathrm{\&rho;}}\left({\&dtri;}_{\mathrm{NL}}{u}_{\mathrm{\&sigma;}}\right):=G_p*({\&dtri;}_{\mathrm{NL}}{u}_{\mathrm{\&sigma;}}\&CircleTimes;{\&dtri;}_{\mathrm{NL}}{u}_{\mathrm{\&sigma;}})=G_{\mathrm{\&rho;}}*\left({\&dtri;}_{\mathrm{NL}}{u}_{\mathrm{\&sigma;}}{\&dtri;}_{\mathrm{NL}}^T{u}_{\mathrm{\&sigma;}}\right)$

for tensor product, T is the transposition of vector, G _ρthe gaussian kernel function of to be standard deviation be ρ, for non local gradient operator;

Non local diffusion tensor computing unit, for calculating non local diffusion tensor D by described non local structure tensor _nL;

Iteration upgrades and obtains result images unit, and the diffuse-wave for diffusion tensor non local described in discretize moves PDE model, and by the model after following formula iterative discretize:

$U^{k+1}=\frac{1}{1+\mathrm{\&lambda;\&tau;}}((2+\mathrm{\&lambda;\&tau;})U^k-U^{k-1}+{\mathrm{\&tau;}}^2{\mathrm{LU}}^k)$

, U represents a column vector of all row of two dimensional image (from left to right) splicing synthesis, subscript k=1,2 ... represent iterations, τ is time step, and L is right the difference approximation of operator, initial value arranges U ⁰=U ¹, it is the column vector of initial pictures; After iteration terminates, iteration result U is reduced into two dimensional image, is and obtains result images.

5. the denoising of a kind of fingerprint texture image according to claim 4 strengthens system, it is characterized in that, describedly calculates non local diffusion tensor D by described non local structure tensor _nLcomprise:

Described non local structure tensor is carried out feature decomposition, i.e. J _ρ=V Σ V ^t, Σ=diag (η _i), i=1 ..., m is for comprising J _ρthe diagonal matrix of eigenwert, and be η by eigenwert sequence ₁>=η ₂>=...>=η _m, V=(v ₁, v ₂..., v _m) contain the orthogonal matrix of character pair vector;

Non local diffusion tensor D is calculated by following formula _nL:

D _NL＝VΛV ^T

, Λ=diag (μ _i), i=1 ... m is diagonal matrix.

6. the denoising of a kind of fingerprint texture image according to claim 4 or 5 strengthens system, it is characterized in that, described λ=4, σ=0.5, ρ=5, τ=0.5.