1. A method for rapidly repairing a damaged fingerprint image is characterized by comprising the following steps:

1) acquiring a two-dimensional fingerprint image, wherein a partial area of the two-dimensional fingerprint image is damaged and has noise points; edge detection preprocessing is carried out on the two-dimensional fingerprint image, and the standard domain x belonging to omega/omega in the image domain is determined_inAnd damaged domainAnd damaged boundaries

2) Describing pixel information of the image after edge detection preprocessing as a local monomer density difference phi (x, t) of the diblock copolymer at a two-dimensional space point x and time t;

3) and repairing the fingerprint image by using a phase separation evolution equation of the diblock copolymer according to the local monomer density difference.

2. The method for rapidly repairing a damaged fingerprint image according to claim 1, wherein the two-dimensional fingerprint image is obtained by a fingerprint acquisition device.

3. The method for rapidly repairing damaged fingerprint image according to claim 1The method is characterized in that the local monomer density difference phi at the time t equal to 0 is phi (x,0) and is recorded as

Wherein f (x) represents a two-dimensional fingerprint image, f_maxAnd f_minRespectively representing a maximum value and a minimum value of a fingerprint image pixel.

4. The method for rapidly repairing damaged fingerprint image as claimed in claim 1, wherein the phase separation evolution equation of the diblock copolymer is:

wherein ε represents the interface thickness; alpha is a non-local term coefficient; x and t are space and time variables respectively, and delta is a Laplace operator; f (phi) is F' (phi) is phi³-φ，Calculate a boundary of

5. The method for rapidly repairing damaged fingerprint image as claimed in claim 4, wherein the formula (1) is obtained from total free energy and two-dimensional non-local CH evolution equation; wherein, the total free energy is:

E_total(φ)＝E_short(φ)+E_long(φ)

wherein G (x-y) is a Green function, and x and y are both image domains_ΩA point on;

the two-dimensional non-local CH evolution equation is as follows:

wherein ε represents the interface thickness; alpha is a non-local term coefficient; x ═ x, y, and t are space and time variables, respectively, where x, y represent the abscissa and ordinate, respectively, of a space point x; Δ is laplace operator; f (phi) is F' (phi) is phi³-φ，Calculate a boundary of

Let the total free energy be represented by the short range term free energy and the long range term free energy as:

E_total(φ)＝E_short(φ)+E_long(phi), where G (x-y) is a Green's function and x, y are both image domains_ΩA point on; from the total free energy E according to the law of energy dissipation and the gradient descent method_total(φ) the following governing equation is found:

6. the method for rapidly repairing a damaged fingerprint image according to claim 5, wherein the specific process of step 3) is as follows:

3.1) assuming that the evolution of the local monomer density difference phi along with time is controlled by a non-local Cahn-Hillard system, and establishing a two-dimensional non-local CH evolution model;

3.2) carrying out two-dimensional grid discretization on the calculation domain and the boundary of the two-dimensional non-local CH evolution model to establish a discretization grid domain;

3.3) on the established discretization grid domain, performing discretization solution on the two-dimensional non-local CH evolution model by using a discretization linear convex splitting algorithm; wherein the Laplace operator Δ and biharmonic operator Δ for the equations²Using standard 5-point difference and 13-point difference representations;

3.4) in calculating the damaged field omega_inThe local monomer density difference phi is calculated, and the purpose that x ∈ omega is set for a two-dimensional space point in a damaged area is achieved_inAnd (4) repairing.

7. The method for rapidly repairing damaged fingerprint image as claimed in claim 6, wherein in step 3.1), the two-dimensional non-local CH evolution model is as follows:

wherein ε represents the interface thickness; alpha is a non-local term coefficient; x ═ x, y, and t are space and time variables, respectively, where x, y represent the abscissa and ordinate, respectively, of a space point x; Δ is laplace operator; f (phi) is F' (phi) is phi³-φ，Calculate a boundary of

8. The method for rapidly repairing a damaged fingerprint image as claimed in claim 7, wherein in step 3.3), on the established discretization grid domain, the discretization solution is performed on the two-dimensional non-local CH evolution model by using a discretization linear convex splitting algorithm, and the two-dimensional non-local CH evolution model is transformed into a discrete form of linear convex splitting:

wherein, for Laplace operator delta and biharmonic operator delta²Discrete by standard 5-point and 13-point respectively as:

9. the method for rapidly repairing a damaged fingerprint image according to claim 6, wherein in step 3.4), the final discretization equation is solved by adopting a semi-implicit Gauss-Seidel type iteration, and the specific process is as follows:

wherein r is 1/delta t +8/h²+20ε²/h⁴+ α; the non-local term coefficient alpha is inversely proportional to the wavelength of the fingerprint pattern and is used for controlling phi (x, t) to the complete fingerprint patternEvolving; and obtaining a final repairing image when the calculation reaches steady convergence.

Background

Biometric identification is an automatic personal identity identification technology based on physiological measurement or behavior characteristics, and particularly, fingerprint characteristics are widely applied to the fields of electronic commerce, criminal investigation, criminal identification, information security, civil and commercial affairs and the like based on the uniqueness, invariance, reliability, low cost and the like of individual fingerprint ridge-shaped structures and detail forms. For example, judicial authorities specify fingerprint screening as an effective criminal investigation means. With the development of optical scanning and computer technologies and the appearance of low-power-consumption capacitive fingerprint acquisition chips, the fingerprint technology under the screen of a mobile device, a fingerprint access control system and an ATM terminal identification system have come into force. Under different application scenarios, the time and accuracy of image restoration recognition are extremely strict, and for example, civil access control and police systems require real-time performance and high accuracy.

In order to improve the influence of image brightness and improve the identification accuracy, a conversion device or an amplifier is generally used for iterative sampling processing in the conventional capacitive fingerprint acquisition technology on the market. However, this method of improving the quality of fingerprints is time-consuming and causes inconvenience to the user at the time of fingerprint acquisition.

Generally, in the process of collecting a fingerprint image, various complex environmental and human factors can cause damage, blurring and smudging of the collected image, and most automatic fingerprint identification systems have high rejection rate and false identification rate on poor quality images. In general, in order to ensure the reliability and stability of the identification system, the acquired fingerprint image must be evaluated by quality, which makes the integrity and high quality of the image important for accurate identification of the image.

In addition, the fingerprint acquisition elements in mobile devices and intelligent systems are more common, and the fingerprint sensor needs to be converted to a micro-scale for saving cost, and the technology can convert the fingerprint sensor into a complete image by capturing image slice information during a sliding motion, but still has the problem that the fingerprint sensor is sometimes difficult to combine.

Disclosure of Invention

In view of the above problems, the present invention is directed to a method for rapidly repairing a damaged fingerprint image.

The purpose of the invention is solved by the following technical scheme:

a quick repairing method for damaged fingerprint images comprises the following steps:

1) acquiring a two-dimensional fingerprint image, wherein a partial area of the two-dimensional fingerprint image is damaged and has noise points; edge detection preprocessing is carried out on the two-dimensional fingerprint image, and the standard domain x belonging to omega/omega in the image domain is determined_inAnd damaged domainAnd damaged boundaries

2) Describing pixel information of the image after edge detection preprocessing as a local monomer density difference phi (x, t) of the diblock copolymer at a two-dimensional space point x and time t;

3) and repairing the fingerprint image by using a phase separation evolution equation of the diblock copolymer according to the local monomer density difference.

A further improvement of the invention consists in acquiring a two-dimensional fingerprint image by means of a fingerprint acquisition device.

In a further development of the invention, the local monomer density difference phi at time t 0, which is denoted as phi (x,0)

Wherein f (x) represents a two-dimensional fingerprint image, f_maxAnd f_minRespectively representing a maximum value and a minimum value of a fingerprint image pixel.

A further improvement of the present invention is that the phase separation evolution equation using diblock copolymers is:

wherein ε represents the interface thickness; alpha is a non-local term coefficient; x and t are spaces respectivelyAnd a time variable, Δ being the laplace operator; f (phi) is F' (phi) is phi³-φ，Calculate a boundary of

The invention is further improved in that formula (1) is obtained from total free energy and a two-dimensional non-local CH evolution equation; wherein, the total free energy is:

E_total(φ)＝E_short(φ)+E_long(φ)

wherein G (x-y) is a Green function, and x and y are both image domains_ΩA point on;

the two-dimensional non-local CH evolution equation is as follows:

wherein ε represents the interface thickness; alpha is a non-local term coefficient; x ═ x, y, and t are space and time variables, respectively, where x, y represent the abscissa and ordinate, respectively, of a space point x; Δ is laplace operator; f (phi) is F' (phi) is phi³-φ，Calculate a boundary of

Let the total free energy be represented by the short range term free energy and the long range term free energy as:

E_total(φ)＝E_short(φ)+E_long(phi), wherein G (x-y) is a Green function, and x and y are both points in the image domain omega; from the total free energy E according to the law of energy dissipation and the gradient descent method_total(φ) the following governing equation is found:

the further improvement of the invention is that the specific process of the step 3) is as follows:

3.1) assuming that the evolution of the local monomer density difference phi along with time is controlled by a non-local Cahn-Hillard system, and establishing a two-dimensional non-local CH evolution model;

3.2) carrying out two-dimensional grid discretization on the calculation domain and the boundary of the two-dimensional non-local CH evolution model to establish a discretization grid domain;

3.3) on the established discretization grid domain, performing discretization solution on the two-dimensional non-local CH evolution model by using a discretization linear convex splitting algorithm; wherein the Laplace operator Δ and biharmonic operator Δ for the equations²Using standard 5-point difference and 13-point difference representations;

3.4) in calculating the damaged field omega_inThe local monomer density difference phi is calculated, and the purpose that x ∈ omega is set for a two-dimensional space point in a damaged area is achieved_inAnd (4) repairing.

The further improvement of the invention is that in step 3.1), the two-dimensional non-local CH evolution model is as follows:

wherein ε represents the interface thickness; alpha is a non-local term coefficient; x ═ x, y, and t are space and time variables, respectively, where x, y represent the abscissa and ordinate, respectively, of a space point x; Δ is laplace operator; f (phi) is F' (phi) is phi³-φ，Calculate a boundary of

The further improvement of the invention is that in the step 3.3), on the established discretization grid domain, the discretization linear convex splitting algorithm is used for discretization solving on the two-dimensional non-local CH evolution model, and the linear convex splitting discrete format is adopted to transform the two-dimensional non-local CH evolution model into:

wherein, for Laplace operator delta and biharmonic operator delta²Discrete by standard 5-point and 13-point respectively as:

the further improvement of the invention is that in step 3.4), the final discretization equation is solved by adopting semi-implicit Gauss-Seidel type iteration, and the specific process is as follows:

wherein r is 1/delta t +8/h²+20ε²/h⁴+ α; the non-local term coefficient alpha and the fingerprintThe wavelength of the pattern is inversely proportional and is used for controlling phi (x, t) to the complete fingerprint patternEvolving; and obtaining a final repairing image when the calculation reaches steady convergence.

Compared with the prior art, the invention has the following beneficial effects: the method can obtain the pixel value of the damaged fingerprint domain by utilizing the image information outside the damaged fingerprint domain, and is suitable for repairing different types of fingerprint features and multiple damaged area images. The pixel values outside the damaged fingerprint area are the same as the pixel values in the original input image, and the pixel values outside the damaged fingerprint area are not calculated, so that the calculation efficiency of the method is high. The method converts the image processing problem into an optimization problem which can theoretically prove that the solution has uniqueness. The method can be quickly converged, is simple and easy to implement, and has the characteristic of real-time restoration. Therefore, the method can realize quick repair aiming at the incomplete image and reduce the acquisition cost.

Drawings

FIG. 1 is a repair evolution process for a single-region incomplete fingerprint image; (a) is an original incomplete fingerprint image, (b) is an example graph of an incomplete fingerprint, (c) is a finally repaired fingerprint image by using the method; (d) - (g) is a detail repair evolution process diagram.

FIG. 2 is a restored image obtained using the present invention for both arcuate and circular fingerprint images; wherein, (a) is the damaged original fingerprint image, (b) is the fingerprint calculation domain boundary after edge detection, and (c) is the final fingerprint image repaired by the invention.

Detailed Description

The present invention will be described in detail below with reference to the accompanying drawings.

The invention provides an effective and steady image restoration algorithm aiming at the problem of restoring incomplete fingerprint images. The algorithm innovatively uses the non-local CH equation of the phase field model to reconstruct the image and has good applicability to multi-region damaged images and different types of fingerprint images. And performing efficient and stable restoration on the damaged area information according to the image information outside the damaged fingerprint area.

A quick repairing method for damaged fingerprint images comprises the following steps:

1) acquiring a two-dimensional fingerprint image f (x) by fingerprint acquisition equipment, wherein a partial area of the two-dimensional fingerprint image is damaged and has noise points; edge detection preprocessing is carried out on the fingerprint image, and a standard domain x in an image domain omega belongs to omega/omega_inAnd damaged domainAnd damaged boundaries

2) The pixel information of the image after the edge detection preprocessing is described as a local monomer density difference phi (x,0) of the diblock copolymer at a two-dimensional spatial point x and a time t of 0, that is, the local monomer density difference phi (x, t) is a variable with respect to the space x (x, y) and the time t;

wherein the local monomer density difference φ ═ φ (x,0) is recorded as

Wherein f is_maxAnd f_minRespectively representing the maximum value and the minimum value of the fingerprint image pixel;

for the point x in the damaged area to be equal to omega_inAnd (5) repairing.

3) Repairing the fingerprint image by using a phase separation evolution equation of the diblock copolymer;

assuming that the evolution of the local monomer density difference phi along with time is controlled by a non-local Cahn-Hillard (CH) system, and establishing a two-dimensional non-local CH evolution model;

wherein, the constructed non-local Cahn-Hillard (CH) evolution model for controlling the local monomer density difference phi change is as follows:

wherein ε represents a boundaryFace thickness; alpha is a non-local term coefficient; x ═ x, y, and t are space and time variables, respectively, where x, y represent the abscissa and ordinate, respectively, of a space point x; Δ is laplace operator; f (phi) is F' (phi) is phi³-φ，Calculate a boundary of

Adding non-local terms to non-local CH equationsThe non-local CH free energy is minimized based on a monomer density functional theory to ensure that the equilibrium state of a phase field tends to be a complete fingerprint image.

Wherein the model for controlling the evolution of the local monomer density difference phi along with time is derived from the decrease of the total free energy dissipation of the system; let the total free energy be represented by the sum of the short-range free energy and the long-range free energy

E_total(φ)＝E_short(φ)+E_long(φ)，

Wherein G (x-y) is a Green function, and x and y are points on an omega domain.

According to the law of energy dissipation and the gradient descent method, from E_total(φ) the following governing equation can be found:

4) since the two-dimensional non-local CH evolution model contains two Laplacian operators and has high calculation complexity, the two-dimensional non-local CH evolution model in the step 3) is simplified by using the linear convex splitting algorithm and the 5-point and 13-point difference method, and since the two-dimensional non-local CH evolution model contains two Laplacian operators and has high calculation complexity.

Performing two-dimensional grid discretization on the calculation domain and the boundary of the two-dimensional non-local CH evolution model in the step 3);

wherein it is assumed that N is given_x×N_yTwo-dimensional fingerprint image domain omega, N of each pixel point_xNumber of pixels representing the direction of the abscissa, N_yExpressing the number of pixel points in the vertical coordinate direction; damaged fingerprint areaWherein (a, b), (c, d) are respectively omega_inThe horizontal and vertical coordinates of the top point of the lower left corner and the horizontal and vertical coordinates of the top point of the upper right corner; then carrying out grid discretization representation on the image domain; defining discrete computational domains for fingerprint imagesWherein (x)_i,y_j) For grid point coordinates, i and j are grid point indices, n_xAnd n_yThe grid interval number of the horizontal coordinate direction and the vertical coordinate direction is represented; in addition, noteDenotes phi (x)_i,y_j,nΔt)；

5) And 4) on the discretization grid domain established in the step 4), performing discretization solution on the two-dimensional non-local CH evolution model by using a discretization linear convex splitting algorithm. Wherein the Laplace operator Δ and biharmonic operator Δ for the equations²Using standard 5-point difference and 13-point difference representations;

wherein, a linear convex splitting discrete format is adopted to transform a two-dimensional non-local CH evolution model into

Wherein, for Laplace operator delta and biharmonic operator delta²Discrete by standard 5-point and 13-point respectively as:

6) in the computational domain omega_inThe local monomer density difference phi is calculated, and the purpose that x ∈ omega is set for a two-dimensional space point in a damaged area is achieved_inAnd (4) repairing.

And 6) solving the final discretization equation by adopting semi-implicit Gauss-Seidel type iteration:

wherein r is 1/delta t +8/h²+20ε²/h⁴+ α; the non-local term coefficient alpha is inversely proportional to the wavelength of the fingerprint pattern and is used for controlling phi (x, t) to the complete fingerprint patternEvolving; when the calculation reaches steady state convergence, the final repair image can be obtained.

The method not only can realize the efficient and rapid repair of the damaged fingerprint image (figure 1), but also can extract a self-adaptive and steady algorithm from the aspect of the mathematical theory of a non-local phase field model, and realize the repair of the damaged part of the fingerprint image only by utilizing the image information of an undamaged area. The method also supports image inpainting for different fingerprint types (fig. 2) and can perform multi-region simultaneous inpainting for multi-region damaged fingerprint images.

Example 1

First, the main symbol definitions of the present invention are shown in table 1:

TABLE 1 Primary symbol convention in the present invention

A 2D fingerprint image considering repair defects is shown in fig. 1 (a). The fingerprint image restoration is firstly proposed by using a non-local CH equation. Phi is the local monomer density difference of the fingerprint. Derivation of evolution equation for φ:

wherein ψ satisfiesDetermining the rhythm according to energy dissipationThe control equation can be obtained:

(boundary)Upper)

Wherein the content of the first and second substances,

f(φ)＝F′(φ)＝φ³-φ，

F(φ)＝0.25(φ²-1)²，

in the above equationFor non-local terms, the coefficient α may ensure that φ tends towardsAnd (5) evolving.

The following is a solution using a robust, fast and accurate numerical method.

Suppose given N_x×N_yTwo-dimensional fingerprint image domain omega of each pixel point, as shown in fig. 2 (a), n is considered to be on omega_x×n_yDamaged fingerprint area of individual pixelLet grid size h ═ b-a)/n_x＝(d-c)/n_yLet x_i＝a+(i-0.5)h，y_j＝c+(j-0.5)h，0≤i≤n_x，0≤j≤n_y(ii) a Defining discrete calculation domain and discrete boundary of fingerprint image as:

and

as shown in fig. 2 (b);

lower markDenotes phi (x)_i,y_jN Δ t), Δ t representing a time step;

using a linear stationary convex splitting algorithm for the non-local CH equations:

the above equation is then discretized as:

wherein, standard 5-point difference of Laplace operator delta and biharmonic operator delta²The standard 13 point difference of (d) is:

and using Dirichlet boundary conditions:

finally, a simplified solution form of the equation is obtained:

wherein r is 1/delta t +8/h²+20ε²/h⁴+ α and

thereby completing the restoration of the image.

The method is used for efficiently restoring the fingerprint image and solves the problem that the traditional fingerprint image identification lacks of mathematical theory support. The fingerprint modeling is carried out by using a non-local CH equation of a phase field model for the first time, and a non-local term is added into the CH equation to ensure that the obtained phase field equilibrium state is close to a complete fingerprint image. The non-local CH equation solved by the Dirichlet boundary conditions can be used for directly utilizing the image information outside the damaged domain to realize high-precision and quick repair on multi-region fingerprint images of different fingerprint types. The numerical method uses a linear convex splitting scheme and a standard 5-point and 13-point difference mode, and solves the non-local CH equation of the Dirichlet boundary condition by adopting semi-implicit Gauss-Seidel type iteration. The fingerprint restoration technology is simple and easy to implement, efficient and stable, can be widely used for biological identity recognition in the fields of civil use, medical treatment and commercial use, and provides a mathematical basis for ridge restoration of fingerprint images based on a reaction diffusion system.