Based on Partial Differential Equations of Image Inpainting
开篇：润墨网以专业的文秘视角，为您筛选了一篇Based on Partial Differential Equations of Image Inpainting范文，如需获取更多写作素材，在线客服老师一对一协助。欢迎您的阅读与分享！
Abstract. for TV model repair algorithm only along the gradient perpendicular to the direction of diffusion ，that will cause staircase effect， iterative low efficiency and generate false edge of the shortcomings. The article improved K and P parameters of image restoration algorithm. The algorithm contains both isotropic and anisotropic diffusion， taking regional frequency difference realized in different areas using different iterative equation. The experimental results show that the algorithm is compared with the TV model algorithm has the same restorative effects， avoid the staircase effect and better than the TV model repair speed.
Key words： image repair； isotropic； anisotropy； TV model； ladder effect
Introduction
Image restoration techniques is an important part of image processing， image restoration is based on the known area of the image related information， recovery information that missing in the area information. According to the different characteristics of the theories and methods of image restoration， image restoration techniques can be roughly divided into two categories： 1） based on the structure of the image repair technology； 2） texture synthesis based image restoration techniques. Patches around the area of information dissemination to be repaired area will be based on the structure of the image restoration techniques applied to repair small scratches， stains， and text of the target area， repair algorithm based on the structure of the core idea is to take advantage of the physics of heat diffusion equation in. TV model repair smooth area prone repair ladder effect disadvantage. Previous algorithm based on an improved algorithm， using a combination of isotropic and anisotropic diffusion model， in the pixel gradient smaller areas isotropic diffusion， improving iteration speed， gradient value in pixels the larger area using anisotropic diffusion based on a P-laplace operator， to avoid the effect of the image flat areas ladder repair. Experimental results show that the algorithm has good repair and good convergence.
1.Image restoration model
TV image restoration model proposed by Rudin， Osher， and became one of the most important algorithms in today's image restoration algorithm. TV model is the most important difference compared with the least-squares recovery model is used the gradient L1 norm instead of its L2 norm.
is breakage to the original image signal， is the pollution image signal after the breakage， then the existing image can be expressed as：
Set noise mean value is 0，Random noise variance is ，
That：
Then in the case of no noise， the TV model can be expressed as：
In the case of the noise， the TV model can be expressed as：
Wherein the parameter λ for noise smoothing the role when the image breakage and with noise. TV model energy equation above， it is necessary by the Euler-Lagrange equation to solve the energy equation， and finally the energy equations into a partial differential equation， namely：
Make local coordinate as（ ），namely：
，
Then， between coordinate（η，ξ） and coordinate （ x，y） transformation expressed as：
TV model for partial differential equations of the diffusion term is .
1.1 TV model's shortcomings
The TV model restoration algorithm uses a second-order partial differential equation， complete mathematical theory， numerical implementation simpler to achieve the purpose of de-noising， while maintaining edge. But TV repair Equation iteration process， it is an anisotropic diffusion process. In fact， in the area of image characteristics should use the slower speed of iteration unclear in the image area （such as the smooth area of the image）， the iteration speed repair should be accelerated， and this TV model used alone to the anisotropic diffusion process， the lower its diffusion efficiency. Moreover， the TV model repair process， TV along with orthogonal gradient direction and edge orientation diffusion reflect different ideological diffusion coefficient along different directions. While the actual edge direction does not exist in the smooth region of the image is still spread along the edge direction， which will result in a flat region of noise suppression is not sufficient， or even false edges， the literature has proved false edges because the diffusion coefficient can not be with picture structure characteristic changes in value， generating a staircase effect. Figure 2 shows a set of image restoration experiment obtained by the TV model.
2.Improved TV model
TV model diffusion only in the direction of the tangent line illumination， if it happens to the damaged part of the image is the flat area is small gradient modulus values， repair TV model may cause ladder effect. If damaged parts of the encountered if the edge portion， and this edge is very prominent kind of TV， then use the anisotropic diffusion model can achieve better repair effect， however， the diffusion coefficient is very small， so the repair speed very slow.
TV model， this paper also introduces a parameter - the gradient modulus value semi-adaptive parameters （ ），
there is a gradient protection range control parameters K， so he formed the improved model of TV， then the TV model improved the energy equationis expressed as （below， respectively， in the case of noise and noise-free）：
That’s Lagrange is：
where， is an adaptive operator， need to be calculated in the image restoration process， namely：
When p = 1， the model of evolution as a TV model， apparently only along the gradient perpendicular to the direction of diffusion， can better maintain the edge information.
When p = 2， the model is clearly an isotropic diffusion model， no response to the edge direction and the gradient direction of the difference of the diffusion coefficient， so that edge information fuzzy.
When 1
3.TV model and TV improved model experiments
Shown in Figure 1， according to the TV model and TV Improved Model Image Comparison These experiments were carried out on the Matlab2009.
Fig 1 （a） Original image （b） Scratches image （c）TV Algorithm （d） Improved TV Algorithm
It can be seen that the improved TV model repair effect is obviously better than the TV model. Visual effects， is still very careful observation of Figure 1 （c） of the image can still be seen shallow scratches. But the image in Figure 1 （d） Basic can not see what scratches traces exist， it can be said that the repair effect is very good.
By Table 1 can be observed， the improved TV model repair effect and subjective judgment is consistent， more than the TV model to increase the peak signal-to-noise ratio （PSNR） in decibels. Illustrate the improved model of TV does a great improvement on the restorative effects. Time increase is caused because the Matlab for p = 1 and p
Table 1 The contrast parameters of TV model and improve TV model in repair
4.Conclusion
TV model analysis， found a lack of TV model， that is ncountered repair the flat area may cause the staircase effect， and can not control the protection scope of the gradient. So the introduction of two parameters： K and p. K to control the gradient range in need of protection， to adjust the different images require different repair model with the parameter p. Through the above experiments show that the improved TV model has a big advantage on the effect of image restoration， image repair the TV model can not be fully restored can be better. Therefore， in the airspace， the improved TV model is superior to the TV model.
The Fund supports：NSFC Grant 60972162
References
[1]ZHANG Hong-ying，Peng qi-cong.A Survey on Digital Image Inpaintiong[J].journal of image and graphics，2007，12（1）：1-10.
[2]Liu Shu-chang，Liu peng，Wang yan-hai，et.Research on Large-Capacity High-Speed Video Image Transmission Technology[J].Journal of jilin university：Information Science Edition，2011，29（1）：21-24.
[3]Zhao chun-yan，Zhao yan，Chen he-xin.Registration of depth and video data base on edge detection[J].journal of jilin university：information science edition，2011，29（3）：175-180.
[4]Shao xiang-xin，Guo shu-xu，Wang lang.Image Mosaic algorithm based on extenede phase correlation of edge[J].journal of jilin university：information science edition，2010，28（1）：95-99.