Objective

2

As a fundamental issue in the field of image processing

image inpainting has been widely studied in the past two decades. The goal of image inpainting is to reconstruct the original high-quality image from its corrupted observation. Notably

prior knowledge of images is important in image inpainting. Thus

designing an effective regularization to represent image priors is a critical task for image inpainting. The TV(total variation) model usually exploits local structures and high effectiveness to preserve image edges; thus

it has been found to be widely used in image inpainting. However

the regular term of the TV model is a first-order differential

which usually loses image details and tends to suffer from over-smooth effects owing to the piecewise constant assumption. Fortunately

fractional differential is capable of enhancing low-and intermediate-frequency signals and amplifying high-frequency signals moderately; thus

it is introduced into the TV model. However

the existing fractional TV model is limited with regard to its preservation of the information of images with texture and edge details. Furthermore

it does not fully use prior information such as known edges and textures.

Method

2

To address these problems

we propose a new fractional-order TV model that introduces texture structure information into a fractional TV model for image inpainting. A minimum value is used in the TV model to calculate the image gradient when solving the fractional model. Thus

the improved model is robust because it overcomes the problem of the model being non-differentiable at zero point. In this way

the weak texture information is effectively preserved. The improved model determines the texture direction of the region to be restored on the basis of the priors of the known region of the image and fully uses the texture information of the image to improve the accuracy of image inpainting.

Result

2

The Barbara and Lena images are selected as test images. The Barbara image presents a large weak texture area. By contrast

the Lena image includes few texture regions and a highly smooth area. Therefore

these two images are used for the experiment. To improve efficiency

we intercept the texture part of the original image and conduct many experiments by using differently sized templates and different orders of fractional differential. Then

the optimal parameters for different images

such as template size and order

can be obtained. The optimal parameters for the Barbara and Lena images are as follows. For the Barbara image

the optimal order is 0.1

and the optimal template size is 3×3 pixels; for the Lena image

the optimal order is 0.9

and the optimal template size is 5×5 pixels. The algorithm is compared with three algorithms with better restoration effects. Mean square error (MSE) and peak signal-to-noise ratio (PSNR) are introduced to evaluate the performance of the different methods. Experimental results indicate that the proposed algorithm achieves improved inpainting result. Unlike that in the TV model

the PSNR values after the restoration of the Barbara

Lena

and Rock images in the proposed method increase by 5.94%

8.07%

and 3.85%

respectively; and the MSE values decrease by 48.66%

65.89%

and 35%

respectively. Relative to the fractional TV model

the proposed method achieves PSNR values for the Barbara image

Lena image

and Rock image that increase by 4.17%

8.59%

and 1.81%

respectively; its MSE values decrease by 37.90%

68.00%

and 18.68%

respectively.

Conclusion

2

The relationship between inpainting effect

template order

and template size is are demonstrated in experiments

thereby providing the basis for selecting optimal parameters. Although the optimal parameters of different types of images are different

the optimal inpainting order is generally between 0 and 1 because the smooth part of the image corresponds to the low-frequency part of the signal. The texture details of the image correspond to the intermediate-frequency part of the signal. Meanwhile

the TV algorithm is not ideal for the weak texture region. To enhance the gradient information of the region

we must improve the low-and intermediate-frequency parts. Therefore

choosing the order between 0 and 1 is recommended. Furthermore

although the optimal order varies with the type of the image

a weak texture region usually results in a small order. Theoretical analysis and experimental results show that the proposed model can effectively improve the accuracy of image restoration relative to the original TV model and fractional order TV model. The proposed model is suitable for inpainting images with weak texture and edge information. This model is an important extension of the TV model.