图像修复技术

regard as the diffusion degree; n expresses the iterative number of times. CDD is a third-order PDE (partial differential equation). We use least bit equation of center distribution solution. Regarding goal image pixel (i, j), assume that
Figure 1:(a) damaged image (b) TV inpainting (c) result satisfied “connectivity and holistic principle” In fg1(c), the four spot curvatures of corner a,b,c,d are ∞ .In the ideal output chart(b) ,the edge of each spot curvature is 0,(c)shows that we can use curvature to adjust diffusion intensity ,even if the diffusion intensity is very
∧ D= 1 | ∇u |
1. Introduction
“Inpainting” is an art world’s tern borrowed from restoration artists. This activity consists of filling in the missing areas or modifying the damaged ones in a nondetectable way by an observer not familiar with the original images [1].Image inpainting is originally an artistic procedure to recover a damaged painting or picture. It has been introduced in and received attention from many researchers in computer vision and image processing. From a technical point of view, digital image inpainting can be described as a procedure to fill a defined inpainting domain such as damaged pixels in a given image. In this case, we can recall some related topics in image processing and computer vision, namely image interpolation, object removal or disocclusion problem, film restoration, and damaged block recovery of compressed digital image or video. In this paper, we presented a new algorithm image inpainting based on PDE [2],[4]which considers the continuity of the isophotes at the boundary and a measure of the change in the information to be propagated. The structure of this paper is as follows. In section 2, image inpainting CDD [5],[6],[7]model is briefly described. We describe our algorithm based on the QCDD model in details in section 3.Resultsand comparisons in section 4. Conclusions and future work are presented in section 5.
2008 ISECS International Colloquium on Computing, Communication, Control, and Management
Image Inpainting Algorithm Based on Partial Differential Equation
Ω Ω
point, these spots for (i+k, j+1), kl-0, | k | + | l |=
Figure 2: damaged the region
⎧ ∂u ⎪ ⎨ ∂t ⎪ ⎩
(u xx + u yy )
(2)
978-0-7695-3290-5/08 $25.00 © 2008 IEEE DOI 10.1109/CCCM.2008.89
120
0, s = 0 ⎧ ⎪ (3) g (s) = ⎨ ∞, s = ∞ ⎪ between 0 and ∞ ， 0 < S < ∞ ⎩ p Taking g ( s ) = s , s > 0, p ≥ 1 , we can see from the
Zhongyu Xu, Xiaoli Lian, Lili Feng School of Computer Science &Engineering, Changchun University of Technology, Changchun,Jilin, 130012, China xuzhongyu01@126.com Abstract
∧
∧
∇ •ϕ =
ϕ ( i + 1 j ) _ ϕ (i − 1 , j )
2 2 h
1
1
+
ϕ (i , j + 1 ) _ ϕ (i , j − 1 )
2 2 h
1 2
2
源自文库
2
(9)
Use the gradient and curvature of the intermediate
∂ Ω ∂ Ω
Ω0
EE
(1)
Therefore the diffusion’s on direction is not along geometry information direction of the isoluxcurve[3] . Regarding the plane curve, the geometry information which it contains is expresses by scalar curvature k.
∧
big ,the diffusion intensity is : D =
2 2
g (k ) |∇ u |
, k is a curvature,
2. CDD model for inpainting
Rudin, Osher, Fatemi presented the TV inpainting
⎛ ∇u ⎞ u y u xx + u x u yy − 2u x u y u xy k = ∇•⎜ ⎟= 3 ⎝ | ∇u | ⎠ 2 2 2
ϕ = (ϕ , ϕ ) = ( D u x , D u y ) (i , j ) , Then
1 2
equation the curvature is big and the diffusion intensity is also big. This model overcomes the shortcomings which we mentioned above. When the image not achieved the steady state to continue to evolve the image, therefore the CDD model is:
Image inpainting technique has been widely used for reconstructing damaged old photographs and removing unwanted objects from images. Now many inpainting algorithm performs well, but they consume much time. In this paper we present a new algorithm based on Partial Differential Equation (PDE) method. This model we called Quick Curvature-Driven Diffusions(QCDD) which can get good effect with much less computation time.QCDD model is developed by the Curvature-Driven Diffusions(CDD) model, both of the two models is supported by “connectivity and holistic principle”, our experiment shows that the model is feasible. model which is famous and the sealing transformation. The algorithm in TV model can realize simply and maintain detail of the edge. However the TV model and other segmenting models have the same shortcomings: cannot satisfy “the connection and holistic principle” while the damage region is wider than the inpainting object. Therefore Chan, Shen considered some mathematical models such as TV [8] mod-el .So they proposed the CDD model which is added the curvature. This model’s conduction coefficient is depended on the curvature of the isophotes and it satisfy the “the connection and holistic principle”. So this model can recover big breakage region, even the tiny edge. Curvature Driven Diffusion model which we called CDD model is a new kind of digital PDE model. In TV model the diffusion carried on along the vertical isoluxcurve direction or reversed direction but the intensity is on the reflection of conductivity coefficient: