CN102708555B - Method for removing defocus blur of color images - Google Patents

Abstract

A method for removing defocus blur of color images includes the steps of decomposition of a defocus blur color image, establishment of image defocus blur removal models, discretization of the image defocus blur removal models and output of the color image subjected to defocus blur removal. According to the method, the defocus blur color image is decomposed to three single-primary-color components including the red component, the green component and the blue component, three two-dimensional single-primary-color image defocus blur removal models including the two-dimensional red image defocus blur removal model, the two-dimensional green image defocus blur removal model and the two-dimensional blue image defocus blur removal model are established, and three two-dimensional single-primary-color images are combined into one color image by means of discretization. The method has the advantages of simplicity, good color image defocus blur removal effects and the like, and can be used for processing the defocus blur color images.

Description

Remove the method for coloured image defocusing blurring

Technical field

The invention belongs to image restoration technical field, be specifically related to a kind of method of utilizing partial differential equation to remove coloured image defocusing blurring.

Background technology

In physical world, object is regarded as being the set of the pointolite of Two dimensional Distribution conventionally, and image can be expressed as institute's distributed points light source within the scope of this object and spread the stack of hot spot in space by imaging system.In object imaging process, imaging device performance is limited, external environment condition is disturbed or the factors such as human operational error all can cause obtained image to produce defocusing blurring, thereby has a strong impact on the visual quality of image.Image goes the research of defocusing blurring to have exigence and wide prospect in many scenes such as intelligent transportation, astronomical sight, medical examination, remotely sensed image and criminal investigation monitoring, therefore this technology can meet the demand of different application field to image definition, becomes one of focus of picture research field in recent years.

From the end of the eighties in last century, partial differential equation is progressively penetrated into all directions of digital image processing field, as image is cut apart, decomposition, noise reduction, enhancing, repairing, deblurring, three-dimensional reconstruction, Super-resolution Reconstruction etc., and become gradually the main and effective solution in this field, therefore utilize the Partial Differential Equations computer vision problem of determining to become one of trend of picture research field in recent years.

The method of many removal coloured image defocusing blurrings has been proposed at present.As the Wiener Filter Method of early stage classics and Lucy Deconvolution Method etc., by these methods, can obtain picture rich in detail to a certain degree, but its visual effect still has larger room for improvement.Be accompanied by coloured image and remove going deep into of defocusing blurring Study on Problems, the method that coloured image based on Regularization Theory is removed defocusing blurring is progressively subject to extensive concern, as the Tikhonov model early proposing and classical total variation model have all obtained certain progress.Yet Tikhonov model supposes based on image smoothness, after the method is removed defocusing blurring, image is often too level and smooth, and in image, detailed information loss is more serious; Total variation model is based on image border architectural feature, and the method is removed in defocusing blurring process can effectively retain picture edge characteristic, but it is more responsive and robustness is poor to noise ratio; Take total variation model as basis, in conjunction with bilateral filtering thought, improve and proposed bilateral total variation model, the method has higher computation complexity, can not mate the applied environment that requirement of real-time is higher.

Still there is following shortcoming in the method for existing removal coloured image defocusing blurring: one, and more responsive and robustness is poor to noise ratio; Its two, remove in defocusing blurring process and easily cause detailed information loss, affect its effect; Its three, computation complexity is higher.

Summary of the invention

Technical matters to be solved by this invention is to overcome the shortcoming of the method for above-mentioned removal coloured image defocusing blurring, and the method for the removal coloured image defocusing blurring that a kind of method is simple, removal effect is good is provided.

Solving the problems of the technologies described above adopted technical scheme is comprised of following step:

1, the coloured image of defocusing blurring decomposes

The coloured image of one width defocusing blurring is decomposed into the two dimension list primary colour image of three width defocusing blurrings of three single primary components formations of red, green, blue, removes respectively defocusing blurring and process.

2, set up image and remove defocusing blurring model

By the single primary colors defocus blurred image of red, green, blue three width two dimension, adopt anisotropy method of diffusion to set up the single primary colour image of red, green, blue three width two dimension and remove defocusing blurring model.

3, image is removed to defocusing blurring model and carry out discretize processing

The single primary colour image of the red, green, blue of foundation three width two dimension is removed to defocusing blurring model and adopt method of finite difference to carry out discretize processing, the image that forms discretize is removed defocusing blurring model.

4, the coloured image after defocusing blurring is removed in output

Adopt the method for iteration to process the single primary colors defocus blurred image of red, green, blue three width two dimension, obtain red, green, blue three width and remove after defocusing blurrings two-dimentional single primary colour image clearly, by the synthetic width coloured image of the red, green, blue single primary colour image of three width two dimensions, output.

At the image of setting up of the present invention, remove in defocusing blurring model step 2, employing anisotropy method of diffusion is set up the single primary colour image removal of red, green, blue three width two dimension defocusing blurring model and is:

$g_t=\mathrm{div}(s\left(\right|(\frac{{\∂G}_{\mathrm{\σ}}}{\∂x}+\frac{\∂G_{\mathrm{\σ}}}{\∂y})\×g\left|\right)\×(\frac{\∂g}{\∂x}+\frac{\∂g}{\∂y}))+f\left(g\right)$

g(x,y,0)＝g ₀(x,y)，(x,y)∈R ²

In formula, g _tfor setting up image, remove defocusing blurring model, g ₀(x, y) is initial input image, and g is processed image, and div is divergence operator; X, y is respectively the position coordinates of each pixel in image; G _σfor Gaussian smoothing kernel function, the σ filter scale factor is 1 or 2; R ²presentation video region; F (g) is reaction; for diffusion term, represent a non-negative monotonic decreasing function, the s that satisfies condition (0)=1, is defined as:

$s\left(\right|(\frac{{\∂G}_{\mathrm{\σ}}}{\∂x}+\frac{{\∂G}_{\mathrm{\σ}}}{\∂y})\×g\left|\right)=1+|\frac{{\∂G}_{\mathrm{\σ}}}{\∂x}+\frac{{\∂G}_{\mathrm{\σ}}}{\∂y}|\×{((\frac{\∂G_{\mathrm{\σ}}}{\∂x}+\frac{{\∂G}_{\mathrm{\σ}}}{\∂y})\×g)}^2$

Above-mentioned Gaussian smoothing kernel function is:

$G_{\mathrm{\σ}}(x,y)=\frac{1}{2\mathrm{\π}{\mathrm{\σ}}^2}\exp (-\frac{(x^2+y^2)}{2{\mathrm{\σ}}^2})$

Above-mentioned reaction item function is:

$f\left(g\right)=\left\{\begin{array}{cc}-(u-g),& g\≤u_1\\ -\frac{\log \left((g-u_k)(g-v_k)\right)}{v_k-u_k},& g\∈[u_k,v_k)\\ \frac{\log \left((g-u_{k+1})(g-v_k)\right)}{u_{k+1}-v_k},& g\∈[v_k,u_{k+1})\\ -(g-u_{k+1}),& g\≥u_{q+1}\end{array}\right.$

In above formula, k is that 1, q is 2; u ₁be 15 or 37, v ₁be 43 or 49, u ₂be 67 or 167, v ₂be 123 or 195, u ₃be 203 or 215.

Of the present invention, image removal defocusing blurring model is carried out in discretize treatment step 3, adopts method of finite difference to carry out discretize and be treated to:

$\frac{(g_{i,j}^{n+1}-g_{i,j}^n)}{\mathrm{\τ}}=\frac{{\left(\right|\▿G_{\mathrm{\σ}}\×g^n\left|\right)}_{i,j}^n}{h}\{2\×[(g_{i+1,j}^n+g_{i-1,j}^n)+(g_{i,j+1}^n+g_{i,j-1}^n)]+(g_{i+1,j+1}^n+g_{i-1,j-1}^n)+(g_{i+1,j-1}^n+$

$g_{i-1,j+1}^n)-12g_{i,j}^n\}+{\left(\frac{\∂\left(\right|\▿G_{\mathrm{\σ}}\×g^n\left|\right)}{\∂x}\right)}_{i,j}^n{\left(g_x\right)}_{i,j}^n+{\left(\frac{\∂\left(\right|\▿G_{\mathrm{\σ}}\×g^n\left|\right)}{\∂y}\right)}_{i,j}^n{\left(g_y\right)}_{i,j}^n+f\left(g_{i,j}^n\right)$

This difference scheme is two layers of explicit form, i, and j is respectively the position coordinates of image slices vegetarian refreshments, and truncation error is O (τ+h ²), in above formula, time discrete step-length τ is 5～10, spatial spreading step-length h is 400; Wherein:

(g _x) _i,j＝(2(g _i+1,j-g _i-1,j)+g _i+1,j+1-g _i-1,j+1+g _i+1,j-1-g _i-1,j-1)/4

(g _y) _i,j＝(2(g _i,j+1-g _i,j-1)+g _i+1,j+1-g _i+1,j-1+g _i-1,j+1-g _i-1,j-1)/4

The present invention compares with existing removal coloured image defocusing blurring method, the present invention adopts the coloured image of defocusing blurring is resolved into three single primary components of red, green, blue, set up the single primary colour image of red, green, blue three width two dimension and remove defocusing blurring model, carry out discretize processing, by the synthetic width coloured image of the red, green, blue single primary colour image of three width two dimensions, output.The present invention has the advantages such as method is simple, removal coloured image defocusing blurring is effective, can be used for the coloured image of defocusing blurring to process.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention.

Fig. 2 adopts the present invention to remove the image before colored character image defocusing blurring.

Fig. 3 (a) is that colored character image is decomposed into the red character image of two dimension.

Fig. 3 (b) is that colored character image is decomposed into the green character image of two dimension.

Fig. 3 (c) is that colored character image is decomposed into the blue character image of two dimension.

Fig. 4 adopts the present invention to remove the image after colored character image defocusing blurring.

Fig. 5 adopts Wiener Filter Method to remove the image after colored character image defocusing blurring.

Fig. 6 adopts Richadson-Lucy Deconvolution Method to remove the image after colored character image defocusing blurring.

Fig. 7 adopts the present invention to remove the fuzzy front image of colored text image defocus.

Fig. 8 (a) is that colored text picture breakdown is the red character image of two dimension.

Fig. 8 (b) is that colored text picture breakdown is the green character image of two dimension.

Fig. 8 (c) is that colored text picture breakdown is the blue character image of two dimension.

Fig. 9 adopts the present invention to remove the image of colored text image defocus after fuzzy.

Figure 10 adopts Wiener Filter Method to remove the image after defocusing blurring to colored text image.

Figure 11 adopts Richardson-Lucy Deconvolution Method to remove the image after defocusing blurring to colored text image.

Embodiment

Below in conjunction with accompanying drawing and embodiment, the present invention is described in more detail, but the invention is not restricted to these embodiment.

Embodiment 1

Adopt Matlab R2009a programming to realize method described in the invention.Experiment porch configuration is as follows: operating system is Windows Server 2003 Standard Edition, and CPU is Intel Core 2 Duo E7300, and RAM is 2G.

The method of removing colored character image defocusing blurring of take is example, and its step is as follows:

1, the coloured image of defocusing blurring decomposes

As shown in Figure 2, Fig. 2 is the colored character image that a width is affected by Gauss's defocusing blurring, is decomposed into the two dimension list primary colors character image that three kinds of colors of red, green, blue form, and is designated as respectively g _r, g _g, g _b, see Fig. 3 a,, Fig. 3 b, Fig. 3 c, the single primary colour image size of every width two dimension is 256 * 256 pixels.For convenience of description by g _r, g _g, g _bthe unified g that is designated as.The gray scale character image that affected by Gauss's defocusing blurring, does not need to carry out picture breakdown.

2, set up image and remove defocusing blurring model

To in step 1, decompose the two dimension list primary colour image of the red, green, blue three width defocusing blurrings that obtain, adopt the anisotropy method of diffusion of analog image vision, set up image removal defocusing blurring model as follows:

$g_t=\mathrm{div}(s\left(\right|(\frac{{\∂G}_{\mathrm{\σ}}}{\∂x}+\frac{\∂G_{\mathrm{\σ}}}{\∂y})\×g\left|\right)\×(\frac{\∂g}{\∂x}+\frac{\∂g}{\∂y}))+f\left(g\right)$

g(x,y,0)＝g ₀(x,y)，(x,y)∈R ²

In formula, g _tfor setting up image, remove defocusing blurring model, g ₀(x, y) is initial input image, and g is processed image, and div is divergence operator; X, y is respectively the position coordinates of each pixel in image; G _σfor Gaussian smoothing kernel function, σ is that the filter scale factor is 1; R ²presentation video region; F (g) is reaction; for diffusion term, represent a non-negative monotonic decreasing function, the s that satisfies condition (0)=1, is defined as:

$s\left(\right|(\frac{{\∂G}_{\mathrm{\σ}}}{\∂x}+\frac{{\∂G}_{\mathrm{\σ}}}{\∂y})\×g\left|\right)={(1+\left(\right|\frac{{\∂G}_{\mathrm{\σ}}}{\∂x}+\frac{\∂G_{\mathrm{\σ}}}{\∂y}\left|\right)\×(\frac{\∂G_{\mathrm{\σ}}}{\∂x}+\frac{{\∂G}_{\mathrm{\σ}}}{\∂y})\×g)}^2$

Gaussian smoothing kernel function in above formula is:

$G_{\mathrm{\σ}}(x,y)=\frac{1}{2\mathrm{\π}{\mathrm{\σ}}^2}\exp (-\frac{(x^2+y^2)}{2{\mathrm{\σ}}^2})$

Reaction item function in above formula is:

$f\left(g\right)=\left\{\begin{array}{cc}-(u-g),& g\≤u_1\\ -\frac{\log \left((g-u_k)(g-v_k)\right)}{v_k-u_k},& g\∈[u_k,v_k)\\ \frac{\log \left((g-u_{k+1})(g-v_k)\right)}{u_{k+1}-v_k},& g\∈[v_k,u_{k+1})\\ -(g-u_{k+1}),& g\≥u_{q+1}\end{array}\right.$

In above formula, k is that 1, q is 2; u ₁be 15, v ₁be 43, u ₂be 67, v ₂be 123, u ₃be 203.

Set up respectively according to the method described above the removal defocus blurred image model of the single primary colour image of red, green, blue three width two dimension.

3, image is removed to defocusing blurring model and carry out discretize processing

The single primary colour image of the red, green, blue of setting up in step 2 three width two dimension is removed to defocusing blurring model, adopts method of finite difference to carry out discretize processing:

$\frac{(g_{i,j}^{n+1}-g_{i,j}^n)}{\mathrm{\τ}}=\frac{{\left(\right|\▿G_{\mathrm{\σ}}\×g^n\left|\right)}_{i,j}^n}{h}\{2\×[(g_{i+1,j}^n+g_{i-1,j}^n)+(g_{i,j+1}^n+g_{i,j-1}^n)]+(g_{i+1,j+1}^n+g_{i-1,j-1}^n)+(g_{i+1,j-1}^n+$

$g_{i-1,j+1}^n)-12g_{i,j}^n\}+{\left(\frac{\∂\left(\right|\▿G_{\mathrm{\σ}}\×g^n\left|\right)}{\∂x}\right)}_{i,j}^n{\left(g_x\right)}_{i,j}^n+{\left(\frac{\∂\left(\right|\▿G_{\mathrm{\σ}}\×g^n\left|\right)}{\∂y}\right)}_{i,j}^n{\left(g_y\right)}_{i,j}^n+f\left(g_{i,j}^n\right)$

This difference scheme is two layers of explicit form, i, and j is respectively the position coordinates of image slices vegetarian refreshments.Truncation error is O (τ+h ²), in above formula, time discrete step-length τ is 5, and spatial spreading step-length h is 400, and iterations n is 10.Wherein:

(g _x) _i,j＝(2(g _i+1,j-g _i-1,j)+g _i+1,j+1-g _i-1,j+1+g _i+1,j-1-g _i-1,j-1)/4

(g _y) _i,j＝(2(g _i,j+1-g _i,j-1)+g _i+1,j+1-g _i+1,j-1+g _i-1,j+1-g _i-1,j-1)/4

4, the coloured image after defocusing blurring is removed in output

Adopt the method for iteration to process the single primary colour image defocus blurred image of the three width two dimension of red, green, blue in step 3, obtain red, green, blue three width and remove after defocusing blurrings two-dimentional single primary colour image clearly, by the synthetic width coloured image of the red, green, blue single primary colour image of three width two dimensions, output, is shown in Fig. 4.

For being described, coloured image of the present invention removes the beneficial effect of defocusing blurring method, inventor adopts the method for the embodiment of the present invention 1 and Wiener Filtering, Richadson-Lucy deconvolution method to carry out contrast to colored character image defocusing blurring and removes defocusing blurring experiment, the results are shown in Figure 5 and Fig. 6.Fig. 5 removes the image after defocusing blurring for Wiener Filtering, and Fig. 6 is that Richadson-Lucy deconvolution method is removed the image after defocusing blurring.Shown in comparing result, the inventive method is removed defocusing blurring and is retained original image information effect colored character image and is obviously better than other two kinds of methods.

Embodiment 2

The fuzzy method of removal colored text image defocus of take is example, and its step is as follows:

Fig. 7 adopts the present invention to remove the fuzzy front image of colored text image defocus.In the present embodiment, coloured image decomposition step 1 and the embodiment 1 of defocusing blurring, by the colored text picture breakdown that affected by Gauss's defocusing blurring, it is the two dimension list primary colors character image that three single primary components of red, green, blue form, the single primary colors character image size of every width two dimension is 512 * 512 pixels, see Fig. 8 a,, Fig. 8 b, Fig. 8 c, note by abridging as g.

In setting up image removal defocusing blurring model 2, scale parameter σ is 2; In reaction item, parameter k is that 1, q is 2, u ₁be 37, v ₁be 49, u ₂be 167, v ₂be 195, u ₃be 215.Other step in this step is identical with embodiment 1, has set up the iconic model of the single primary colors removal of red, green, blue three width two dimension defocusing blurring.

Image removal defocusing blurring model is being carried out in discretize treatment step 3, time discrete step-length τ is 10, time discrete step-length τ can choose arbitrarily in 5～10 scopes, if τ is 8 etc., spatial spreading step-length h is 400, iterations n is 20, and iterations n chooses according to processed image blurring degree.Other step in this step is identical with embodiment 1, image is removed to defocusing blurring model and carry out discretize processing.

Other step is identical with embodiment 1.The coloured image after defocusing blurring is removed in output, the results are shown in Figure 9.

Inventor adopts the method for the present embodiment and Wiener filtering side, Richadson-Lucy deconvolution method to carry out the experiment of contrast removal defocusing blurring to character image defocusing blurring, the results are shown in Figure 10, Figure 11.Figure 10 is that Wiener Filtering is removed the image after defocusing blurring, and Figure 11 is that Richardson-Lucy deconvolution method is removed the image after defocusing blurring.As shown in comparing result, adopt the inventive method to remove defocusing blurring and retain original image information effect character image and be obviously better than other two kinds of methods.

Claims (1)

1. remove a method for coloured image defocusing blurring, it is characterized in that being formed by following step:

(1) coloured image of defocusing blurring decomposes

The coloured image of one width defocusing blurring is decomposed into the two dimension list primary colour image of three width defocusing blurrings of three single primary components formations of red, green, blue, removes respectively defocusing blurring and process;

(2) set up image and remove defocusing blurring model

By the single primary colors defocus blurred image of red, green, blue three width two dimension, employing anisotropy method of diffusion is set up the single primary colour image removal of red, green, blue three width two dimension defocusing blurring model and is:

$g_t=\mathrm{div}(s\left(\right|(\frac{{\∂G}_{\mathrm{\σ}}}{\∂x}+\frac{{\∂G}_{\mathrm{\σ}}}{\∂y})\×g\left|\right)\×(\frac{\∂g}{\∂x}+\frac{\∂g}{\∂y}))+f\left(g\right)$

g(x,y,0)＝g ₀(x,y)，(x,y)∈R ²

In formula, g _tfor setting up image, remove defocusing blurring model, g ₀(x, y) is initial input image, and g is processed image, and div is divergence operator; X, y is respectively the position coordinates of each pixel in image; G _σfor Gaussian smoothing kernel function, the σ filter scale factor is 1 or 2; R ²presentation video region; F (g) is reaction; for diffusion term, represent a non-negative monotonic decreasing function, the s that satisfies condition (0)=1, according to the following formula

$s\left(\right|(\frac{{\∂G}_{\mathrm{\σ}}}{\∂x}+\frac{{\∂G}_{\mathrm{\σ}}}{\∂y})\×g\left|\right)=(1+\left(\right|\frac{{\∂G}_{\mathrm{\σ}}}{\∂x}+\frac{{\∂G}_{\mathrm{\σ}}}{\∂y}\left|\right)\×(\frac{{\∂G}_{\mathrm{\σ}}}{\∂x}+\frac{{\∂G}_{\mathrm{\σ}}}{\∂y})\×g{)}^2$

Gaussian smoothing kernel function in above formula is:

$G_{\mathrm{\σ}}(x,y)=\frac{1}{{2\mathrm{\π\σ}}^2}\exp (-\frac{(x^2+y^2)}{{2\mathrm{\σ}}^2})$

Reaction item function in above formula is:

$f\left(g\right)=\left\{\begin{array}{cc}-(u-g),& g\≤u_1\\ -\frac{\log \left((g-u_k)(g-v_k)\right)}{v_k-u_k},& g\∈[u_k,v_k)\\ \frac{\log \left((g-u_{k+1})(g-v_k)\right)}{u_{k+1}-v_k},& g\∈[v_k,u_{k+1})\\ -(g-u_{k+1}),& g\≥u_{q+1}\end{array}\right.$

In above formula, k is that 1, q is 2; u ₁be 15 or 37, v ₁be 43 or 49, u ₂be 67 or 167, v ₂be 123 or 195, u ₃be 203 or 215;

(3) image is removed to defocusing blurring model and carry out discretize processing

The single primary colour image of the red, green, blue of foundation three width two dimension is removed to defocusing blurring model and adopt method of finite difference to carry out discretize processing, the image that forms discretize is removed defocusing blurring model;

Adopting method of finite difference to carry out discretize is treated to:

$\begin{array}{c}\frac{(g_{i,j}^{n+1}-g_{i,j}^n)}{\mathrm{\τ}}=\frac{{\left(\right|{\▿G}_{\mathrm{\σ}}\×g^n\left|\right)}_{i,j}^n}{h}\{2\×[(g_{i+1,j}^n+g_{i-1,j}^n)+(g_{i,j+1}^n+g_{i,j-1}^n)]+(g_{i+1,j+1}^n+g_{i-1,j-1}^n)+(g_{i+1,j-1}^n+\\ g_{i-1,j+1}^n)-12g_{i,j}^n\}+{\left(\frac{\∂\left(\right|{\▿G}_{\mathrm{\σ}}\×g^n\left|\right)}{\∂x}\right)}_{i,j}^n{\left(g_x\right)}_{i,j}^n+{\left(\frac{\∂\left(\right|{\▿G}_{\mathrm{\σ}}\×g^n\left|\right)}{\∂y}\right)}_{i,j}^n{\left(g_y\right)}_{i,j}^n+f\left(g_{i,j}^n\right)\end{array}$

This difference scheme is two layers of explicit form, i, and j is respectively the position coordinates of image slices vegetarian refreshments, and truncation error is O (τ+h ²); In above formula, time discrete step-length τ is 5～10, and spatial spreading step-length h is 400; Wherein:

(g _x) _i,j＝(2(g _i+1,j-g _i-1,j)+g _i+1,j+1-g _i-1,j+1+g _i+1,j-1-g _i-1,j-1)/4(g _y) _i,j＝(2(g _i,j+1-g _i,j-1)+g _i+1,j+1-g _i+1,j-1+g _i-1,j+1-g _i-1,j-1)/4

(4) coloured image after defocusing blurring is removed in output

Adopt the method for iteration to process the single primary colors defocus blurred image of red, green, blue three width two dimension, obtain red, green, blue three width and remove after defocusing blurrings two-dimentional single primary colour image clearly, by the synthetic width coloured image of the red, green, blue single primary colour image of three width two dimensions, output.