CN113628235A - Self-adaptive threshold segmentation signature image binary processing method based on PDE - Google Patents

Self-adaptive threshold segmentation signature image binary processing method based on PDE Download PDF

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CN113628235A
CN113628235A CN202110505908.8A CN202110505908A CN113628235A CN 113628235 A CN113628235 A CN 113628235A CN 202110505908 A CN202110505908 A CN 202110505908A CN 113628235 A CN113628235 A CN 113628235A
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郭志昌
姚文娟
陈佳奇
温莹
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Harbin Institute of Technology
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Abstract

The invention discloses a self-adaptive threshold segmentation signature image binary processing method based on PDE. Step 1: denoising the given signature image to obtain a smooth image; step 2: processing the denoised image by using Gamma correction to increase the image contrast; and step 3: changing the image with the increased contrast in the step 2 into a binary image by using a self-adaptive threshold fast segmentation algorithm again; and 4, step 4: and (3) dividing the binary image in the step (3) into a signature font and a background, wherein the signature font corresponds to a black area, and the background corresponds to a white area. The invention aims to solve the problems that the existing signature image segmentation method is low in calculation efficiency, poor in image segmentation effect on noise and required to manually adjust parameters in the processing process.

Description

Self-adaptive threshold segmentation signature image binary processing method based on PDE
Technical Field
The invention belongs to the field of image processing; in particular to a self-adaptive threshold segmentation signature image binary processing method based on PDE.
Background
Image segmentation is a basic work in the fields of computer science and technology and the like, and the accuracy of tasks such as image recognition and the like in the later period is directly influenced by the segmentation effect. The difficulty in processing the image segmentation problem is that it has a "pathological" property, and it is difficult to obtain a unique segmentation result, and the image often contains very rich information, and it is difficult to extract features by a uniform method. Although some effective image segmentation algorithms have been proposed for certain specific applications or types of images. However, there is no general and reliable automatic segmentation algorithm so far. Therefore, the deep research on the image segmentation method has very important value and significance.
In recent years, image segmentation methods based on PDEs have been developed. Among them, the active contour model combined with the level set method is receiving much attention. The method is mainly characterized in that the image segmentation problem is solved by minimizing an energy functional of a closed curve, an initial contour curve is given at first, the curve continuously moves under the action of force, and finally stops at the edge of a target. A geodesic active contour model (GAC) is taken as one of the most basic active contour models, the image segmentation problem is reduced to minimize an energy functional of a closed curve, and the minimized energy functional is converted into gradient descending flow related to the closed curve by using a variational method; and then, completing curve evolution by using a PDE method, and stopping the evolution process at the edge of the object so as to complete the segmentation of the image. In the implementation process of the method, the gradient mode of the image needs to be calculated, and the actual image often has noise or false edges, so that the calculated gradient mode is relatively disordered and has a large influence on the subsequent curve evolution result, so that a real boundary is difficult to obtain.
Furthermore, in the level set approach implementation of the GAC model, to preserve the characteristics of the level set function (typically the chosen sign distance function SDF), the SDF needs to be initialized after each iteration. The SDF structure requires the calculation of the symbolic distance from each pixel point of the image to the closed curve (level set curve), and thus the amount of calculation is large. The implementation efficiency of the initialization method affects the implementation efficiency of the whole model.
Disclosure of Invention
The invention provides a self-adaptive threshold segmentation signature image binary processing method based on PDE (differential equation), aiming at solving the problems that the traditional signature image segmentation method is low in calculation efficiency, poor in image segmentation effect on noise and required to manually adjust parameters in the processing process.
The invention is realized by the following technical scheme:
a binary processing method for self-adaptive threshold segmentation of a signature image based on PDE (partial differential equation), wherein the specific steps of the segmentation process of the signature image are as follows:
step 1: denoising the given signature image to obtain a smooth image;
step 2: processing the denoised image by using Gamma correction to increase the image contrast;
and step 3: changing the image with the increased contrast in the step 2 into a binary image by using a self-adaptive threshold fast segmentation algorithm again;
and 4, step 4: and (3) dividing the binary image in the step (3) into a signature font and a background, wherein the signature font corresponds to a black area, and the background corresponds to a white area.
Further, in the step 1, specifically,
step 1.1: discrete noise image fi,jF (I, J), where I ═ 1, ·, I, J ═ 1, ·, J, N ═ I × J ═ size (f (x)); constructing a semi-implicit numerical format of a diffusion equation corresponding to PDE filtering;
step 1.2: setting a boundary condition f according to the value format in step 1.1i,0＝fi,1,fi,J+1＝fi,J,f0,j＝f1,j,fI+1,j＝fi,j；
Step 1.3: according to the semi-hidden format in step 1.1, Gaussian convolution is applied to the noise image to obtain a smooth image fσAnd calculate fσGradient mode of
Figure BDA0003058374430000021
Step 1.4: calculating the gradient modulus of the noisy image according to the semi-hidden format in step 1.1
Figure BDA0003058374430000022
Step 1.5: using the results of the calculations in steps 1.3 and 1.4
Figure BDA0003058374430000023
And
Figure BDA0003058374430000024
calculating diffusion coefficient of diffusion equation
Figure BDA0003058374430000025
Step 1.6: calculating a diffusion coefficient matrix C by using the semi-hidden format in the step 1.1;
step 1.7: and (3) solving the semi-hidden format in the step 1.1 by utilizing a Gauss-Seidel iterative process to obtain a smooth image.
Further, the diffusion equation corresponding to the PDE filtering in step 1.1 is
Figure BDA0003058374430000026
Figure BDA0003058374430000027
u(x,0)＝f(x),x∈Ω
Wherein
Figure BDA0003058374430000028
T > 0, f is a noise image, K is an adjustment parameter, GσAs a gaussian function:
Figure BDA0003058374430000029
the semi-implicit numerical format of the diffusion equation is:
Figure BDA00030583744300000210
wherein tau is the time step, p ∈ { (i +1, j), (i-1, j), (i, j +1), (i, j-1) },
Figure BDA0003058374430000031
Figure BDA0003058374430000032
the above numerical format can be rewritten into matrix form Un+1＝(E-τAn)-1UnWherein
Figure BDA0003058374430000033
Figure BDA0003058374430000034
AnTo represent the symmetric sparse matrix of the diffusion portion, E is the identity matrix.
Further, in step 1.3 fσ＝GσF, wherein denotes a convolution operator, an
Figure BDA0003058374430000035
In said step 1.5
Figure BDA0003058374430000036
Further, in step 1.6, when the number of iteration steps is 1, the value format in step one can be represented as U1＝(E-τA0)-1F, where F is a vector representation of the noisy image. Definition C ═ E- τ A0＝(cm,n)IJ×IJThe concrete form is as follows:
Figure BDA0003058374430000037
wherein
α(j-1)*I+i＝1+2τgi,j+τ(gi-1,j+gi+1,j+gi,j-1+gi,j+1)/2
β(j-1)*I+i＝-τ(gi,j+gi+1,j)/2
γ(j-1)*I+i＝-τ(gi,j+gi,j+1)/2
Further, the gaussian-seidel iteration process in step 1.7 is: u. ofi,j＝fi,jWhen error < 0.001, the following cycle is performed: for I is more than or equal to 1 and less than or equal to I and J is more than or equal to 1 and less than or equal to J, calculating
Figure BDA0003058374430000038
And then calculate error ═ U1-U|∞Wherein U ═ U (U)1u2…uN)T,
Figure BDA0003058374430000039
U is the numerical solution sought.
Further, the step 2 is specifically that,
step 2.1: processing the image by using Gamma correction; namely, it is
Figure BDA0003058374430000041
Said gamma usually has a value in the range of [0.5,1.5 ]]；
Step 2.2: calculate the gray value range [ K ] of the smooth image um,KM]Traversing the smooth image u and recording the gray level KmCorresponding pixel ui,j；
Step 2.3: corresponding to a gray level of KmThe pixel point of (2) calculating the two divided sub-regions
Figure BDA0003058374430000042
And
Figure BDA0003058374430000043
corresponding parameter c1And c2Wherein K is Km；
Step 2.4: functional of energy calculation
Figure BDA0003058374430000044
Step 2.5: repeating steps 2.2 to 2.4, K for K ═ Km+1,…,KMCalculate KM-KmThe value of +1 corresponding energy functional e (K) is found, K ═ K at which e (K) reaches a maximum valuemax；
Step 2.6: determination of KmaxAfter, image u0Is divided into two sub-regions, i.e.
Figure BDA0003058374430000045
Further, parameter c in step 2.21And c2Are respectively as
Figure BDA0003058374430000046
Further, as described in step 2.3
Figure BDA0003058374430000047
Respectively represent D1,D2The number of pixel points in; if the energy e (k) reaches a maximum, the area will be divided into two sub-areas, i.e. a black area representing the font and a white area representing the background.
The invention has the beneficial effects that:
1. the self-adaptive threshold segmentation signature image binary processing technology based on the PDE can change an image into a binary image, namely a signature font corresponds to a black area, and a background corresponds to a white area; the boundary line of the new model is closer to the real boundary of the image from the gray level set, so that the complete information of the signature image is effectively segmented.
2. Compared with other image segmentation methods, the self-adaptive threshold segmentation signature image binary processing technology based on the PDE does not need to initialize parameters again, the complexity of the algorithm is deduced to be O (N), N is the number of pixel points, and therefore the algorithm can remarkably improve the calculation efficiency when processing large-scale images.
3. The self-adaptive threshold segmentation signature image binary processing technology based on the PDE is easy to realize. The first step of the new algorithm is mainly to obtain smooth images without obtaining the optimal denoising result, so that the corresponding filtering processing is carried out for several times; the new algorithm step 2 only needs to traverse the image once, then calculates 256 situations, and finally finds the best gray level to achieve the segmentation purpose. Therefore, the method is simple in processing flow and easy to implement.
4. The image segmentation method based on the diffusion equation and the gray level set is different from the traditional level set method in that the level set function needs to be solved, but the image is restored firstly, and then the level set of the image is used for segmentation, so that the defect that the variational level set needs to be solved in the original level set method is overcome, and the calculation efficiency is greatly improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is an experimental original signature image.
FIG. 3 is a schematic diagram of a signature contour processed by a geodesic active contour model (GAC) according to the present invention.
FIG. 4 is a schematic diagram of a signature contour after processing by a gradient flow (GVF) active contour model according to the present invention.
FIG. 5 is a schematic diagram of a signature contour after being segmented by the signature image segmentation method of the present invention.
Fig. 6 is a schematic diagram of a signature image after being segmented by the signature image segmentation method of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
As shown in fig. 1, a method for adaptive threshold segmentation of a signature image binary processing based on PDE includes the following specific steps:
step 1: denoising the given signature image to obtain a smooth image;
step 2: processing the denoised image by using Gamma correction to increase the image contrast;
and step 3: changing the image with the increased contrast in the step 2 into a binary image by using a self-adaptive threshold fast segmentation algorithm again;
and 4, step 4: and (3) dividing the binary image in the step (3) into a signature font and a background, wherein the signature font corresponds to a black area, and the background corresponds to a white area.
Further, in the step 1, specifically,
step 1.1: discrete noise image fi,jF (I, J), where I ═ 1, ·, I, J ═ 1, ·, J, N ═ I × J ═ size (f (x)); constructing a semi-implicit numerical format of a diffusion equation corresponding to PDE filtering;
step 1.2: setting a boundary condition f according to the value format in step 1.1i,0＝fi,1,fi,J+1＝fi,J,f0,j＝f1,j,fI+1,j＝fi,j；
Step 1.3: according to the semi-hidden format in step 1.1, Gaussian convolution is applied to the noise image to obtain a smooth image fσAnd calculate fσGradient mode of
Figure BDA0003058374430000061
Step 1.4: calculating the gradient modulus of the noisy image according to the semi-hidden format in step 1.1
Figure BDA0003058374430000062
Step 1.5: using the results of the calculations in steps 1.3 and 1.4
Figure BDA0003058374430000063
And
Figure BDA0003058374430000064
calculating diffusion coefficient of diffusion equation
Figure BDA0003058374430000065
Step 1.6: calculating a diffusion coefficient matrix C by using the semi-hidden format in the step 1.1;
step 1.7: and (3) solving the semi-hidden format in the step 1.1 by utilizing a Gauss-Seidel iterative process to obtain a smooth image.
Further, the diffusion equation corresponding to the PDE filtering in step 1.1 is
Figure BDA0003058374430000066
Figure BDA0003058374430000067
Figure BDA0003058374430000068
Wherein
Figure BDA0003058374430000069
T > 0, f is a noise image, K is an adjustment parameter, GσAs a gaussian function:
Figure BDA00030583744300000610
the semi-implicit numerical format of the diffusion equation is:
Figure BDA00030583744300000611
wherein τ is the time stepLong, p ∈ { (i +1, j), (i-1, j), (i, j +1), (i, j-1) },
Figure BDA00030583744300000612
Figure BDA00030583744300000613
the above numerical format can be rewritten into matrix form Un+1＝(E-τAn)-1UnWherein
Figure BDA00030583744300000614
Figure BDA00030583744300000615
AnTo represent the symmetric sparse matrix of the diffusion portion, E is the identity matrix.
Further, in step 1.3 fσ＝GσF, wherein denotes a convolution operator, an
Figure BDA00030583744300000616
In said step 1.5
Figure BDA00030583744300000617
Further, in step 1.6, when the number of iteration steps is 1, the value format in step one can be represented as U1＝(E-τA0)-1F, where F is a vector representation of the noisy image. Definition C ═ E- τ A0＝(cm,n)IJ×IJThe concrete form is as follows:
Figure BDA0003058374430000071
wherein
α(j-1)*I+i＝1+2τgi,j+τ(gi-1,j+gi+1,j+gi,j-1+gi,j+1)/2
β(j-1)*I+i＝-τ(gi,j+gi+1,j)/2
γ(j-1)*I+i＝-τ(gi,j+gi,j+1)/2
Further, the gaussian-seidel iteration process in step 1.7 is: u. ofi,j＝fi,jWhen error < 0.001, the following cycle is performed: for I is more than or equal to 1 and less than or equal to I and J is more than or equal to 1 and less than or equal to J, calculating
Figure BDA0003058374430000072
And then calculate error ═ U1-U|∞Wherein U ═ U (U)1u2…uN)T,
Figure BDA0003058374430000073
U is the numerical solution sought.
Further, the step 2 is specifically that,
step 2.1: processing the image by using Gamma correction; namely, it is
Figure BDA0003058374430000074
Said gamma usually has a value in the range of [0.5,1.5 ]](ii) a There is no optimum value for this value and the user needs to choose a smaller gamma when the processed image is dark and vice versa.
Step 2.2: calculate the gray value range [ K ] of the smooth image um,KM]Traversing the smooth image u and recording the gray level KmCorresponding pixel ui,j；
Step 2.3: corresponding to a gray level of KmThe pixel point of (2) calculating the two divided sub-regions
Figure BDA0003058374430000075
And
Figure BDA0003058374430000076
corresponding parameter c1And c2Wherein K is Km；
Step (ii) of2.4: functional of energy calculation
Figure BDA0003058374430000077
Step 2.5: repeating steps 2.2 to 2.4, K for K ═ Km+1,…,KMCalculate KM-KmThe value of +1 corresponding energy functional e (K) is found, K ═ K at which e (K) reaches a maximum valuemax；
Step 2.6: determination of KmaxAfter, image u0Is divided into two sub-regions, i.e.
Figure BDA0003058374430000081
Further, parameter c in step 2.21And c2Are respectively as
Figure BDA0003058374430000082
Further, as described in step 2.3
Figure BDA0003058374430000083
Respectively represent D1,D2The number of pixel points in; if the energy e (k) reaches a maximum, the area will be divided into two sub-areas, i.e. a black area representing the font and a white area representing the background.

Claims (9)

1. A binary processing method for signature images based on self-adaptive threshold segmentation of a PDE (differential equation), which is characterized in that the specific steps of the signature image segmentation process are as follows:
step 1: denoising the given signature image to obtain a smooth image;
step 2: processing the denoised image by using Gamma correction to increase the image contrast;
and step 3: changing the image with the increased contrast in the step 2 into a binary image by using a self-adaptive threshold fast segmentation algorithm again;
and 4, step 4: and (3) dividing the binary image in the step (3) into a signature font and a background, wherein the signature font corresponds to a black area, and the background corresponds to a white area.
2. The method according to claim 1, wherein the step 1 is specifically,
step 1.1: discrete noise image fi,jF (I, J), where I1, …, I, J1, …, J, N I × J size (f (x)); constructing a semi-implicit numerical format of a diffusion equation corresponding to PDE filtering;
step 1.2: setting a boundary condition f according to the value format in step 1.1i,0＝fi,1,fi,J+1＝fi,J,f0,j＝f1,j,fI+1,j＝fi,j；
Step 1.3: according to the semi-hidden format in step 1.1, Gaussian convolution is applied to the noise image to obtain a smooth image fσAnd calculate fσIs | vσ|i,j；
Step 1.4: calculating gradient modulo | (f) of the noise image according to the semi-hidden format in step 1.1i,j；
Step 1.5: utilizing the result | (f) calculated in steps 1.3 and 1.4σ|i,jAnd |. f | +i,jCalculating the diffusion coefficient of the diffusion equation
Figure FDA0003058374420000014
Step 1.6: calculating a diffusion coefficient matrix C by using the semi-hidden format in the step 1.1;
step 1.7: and (3) solving the semi-hidden format in the step 1.1 by utilizing a Gauss-Seidel iterative process to obtain a smooth image.
3. The method as claimed in claim 1, wherein the PDE filtering in step 1.1 corresponds to a diffusion equation of
Figure FDA0003058374420000011
Figure FDA0003058374420000012
u(x,0)＝f(x),x∈Ω
Wherein
Figure FDA0003058374420000013
T > 0, f is a noise image, K is an adjustment parameter, GσAs a gaussian function:
Figure FDA0003058374420000021
the semi-implicit numerical format of the diffusion equation is:
Figure FDA0003058374420000022
wherein tau is the time step, p ∈ { (i +1, j), (i-1, j), (i, j +1), (i, j-1) },
Figure FDA0003058374420000023
Figure FDA0003058374420000024
the above numerical format can be rewritten into matrix form Un+1＝(E-τAn)-1UnWherein
Figure FDA0003058374420000025
Figure FDA0003058374420000026
AnTo represent the symmetric sparse matrix of the diffusion portion, E is the identity matrix.
4. The method of claim 1, wherein f is step 1.3σ＝GσF, wherein denotes a convolution operator, an
Figure FDA0003058374420000027
In said step 1.5
Figure FDA0003058374420000028
5. The method of claim 1, wherein in step 1.6, when the number of iteration steps is 1, the numerical format in step 1.1 is represented as U1＝(E-τA0)-1F, where F is a vector representation of the noisy image. Definition C ═ E- τ A0＝(cm,n)IJ×IJThe concrete form is as follows:
Figure FDA0003058374420000029
wherein
α(j-1)*I+i＝1+2τgi,j+τ(gi-1,j+gi+1,j+gi,j-1+gi,j+1)/2
β(j-1)*I+i＝-τ(gi,j+gi+1,j)/2
γ(j-1)*I+i＝-τ(gi,j+gi,j+1)/2。
6. The method of claim 1, wherein the gaussian-seidel iteration process in step 1.7 is as follows: u. ofi,j＝fi,jWhen error < 0.001, the following cycle is performed: for I is more than or equal to 1 and less than or equal to I and J is more than or equal to 1 and less than or equal to J, calculating
Figure FDA0003058374420000031
And then calculate error ═ U1-U|∞Wherein U ═ U (U)1u2…uN)T,
Figure FDA0003058374420000032
U is the numerical solution sought.
7. The method according to claim 1, wherein the step 2 is specifically,
step 2.1: processing the image by using Gamma correction; namely, it is
Figure FDA0003058374420000033
Said gamma usually has a value in the range of [0.5,1.5 ]]；
Step 2.2: calculate the gray value range [ K ] of the smooth image um,KM]Traversing the smooth image u and recording the gray level KmCorresponding pixel ui,j；
Step 2.3: corresponding to a gray level of KmThe pixel point of (2) calculating the two divided sub-regions
Figure FDA0003058374420000034
And
Figure FDA0003058374420000035
corresponding parameter c1And c2Wherein K is Km；
Step 2.4: functional of energy calculation
Figure FDA0003058374420000036
Step 2.5: repeating steps 2.2 to 2.4, K for K ═ Km+1,…,KMCalculate KM-KmThe value of +1 corresponding energy functional e (K) is found, K ═ K at which e (K) reaches a maximum valuemax；
Step 2.6: determination of KmaxAfter, image u0Is divided into two sub-regions, i.e.
Figure FDA0003058374420000037
8. The method of claim 1, wherein the parameter c in step 2.2 is used in the adaptive threshold segmentation signature image binary processing method based on PDE1And c2Are respectively as
Figure FDA0003058374420000038
9. The method according to claim 1, wherein the step 2.3 is performed by using a PDE-based adaptive threshold segmentation signature image binary processing method
Figure FDA0003058374420000039
Respectively represent D1,D2The number of pixel points in; if the energy e (k) reaches a maximum, the area will be divided into two sub-areas, i.e. a black area representing the font and a white area representing the background.
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