doi:10.1016/j.imavis.2005.12.008 
Copyright © 2006 Elsevier B.V. All rights reserved.
Image restoration using digital inpainting and noise removal
aFaculty of Mathematics, Federal University of Uberlândia, Caixa Postal 593, CEP 38.400-902, Uberlândia, MG, Brazil.
bDepartment of Computing, Federal University of Goiás, Campus Catalão, Caixa Postal 56, CEP 75704-020, Catalão, GO, Brazil.
Received 26 May 2004;
revised 4 August 2005;
accepted 18 December 2005.
Available online 30 May 2006.
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Abstract
Inpainting and denoising are two important tasks in the field of image processing with broad applications in image and vision analysis. In this paper, we present a new approach for image restoration. Our method simultaneously fills in missing, corrupted, or undesirable information while it removes noise. The denoising is performed by the smoothing equation working inside and outside of the inpainting domain but in completely different ways. Inside the inpainting domain, the smoothing is carried out by the Mean Curvature Flow, while the smoothing of the outside of the inpainting domain is carried out in a way as to encourage smoothing within a region and discourage smoothing across boundaries. Besides smoothing, the approach here presented permits the transportation of available information from the outside towards the inside of the inpainting domain. This combination permits the simultaneous use of filling-in and differentiated smoothing of different regions of an image. The experimental results show the effective performance of the combination of these two procedures in restoring scratched photos, disocclusion (or removal of entire objects from the image) in vision analysis and text removal from images.
Keywords: Inpaint; Image processing; Noise removal; Edge detection; Diffusion equation; Transport equation
Fig. 2. Top to bottom, left to right: Lenna image degraded by black and white spots and by blank region (flower format), inpainting domain, three intermediate steps and final results of the proposed model.
Fig. 3. (a) Degraded image with Poisson noise and a blank domain. (b and c) Partial results and (d) final result of proposed model.
Fig. 4. (a) Degraded image with Gaussian noise (10 dB) and a blank domain. (b and c) Partial results and (d) final result of proposed model obtained after 100 iterations and using as parameter k=0.05, Δti=0.1, Δts=0.2 and A=B=10.
Fig. 5. (a) Degraded image corrupted Gaussian noise (0 dB) and a blank domain. (b and c) Partial results and (d) final result of proposed model.
Fig. 6. (a) Degraded image by Gaussian noise (0 dB) and by a blank domain. (b and c) Partial results and (d) final result of proposed model.
Fig. 7. Plots of the 80th line of Fig. 6. Left to right: degraded image, partial and final results.
Fig. 8. Top to bottom, left to right: degraded image by characters, inpainting domain, three intermediate steps and final results of the proposed model. Parameters: 50 iterations, A=10, B=1, k=3, Δti=0.1 and Δts=0.2.
Fig. 9. Reconstruction of the shadow area after the removal of the bag. From top to bottom and left to right: the initial image, the inpainting domain, partial and final results.
Fig. 10. Landscape reconstruction: (a) the initial image; (b) the inpainting domain; (c) partial result; and (d) the result obtained by the proposed model running 300 iterations and parameters k=0.5, A=B=10, Δti=0.02 and Δts=0.2.
Fig. 11. (a) Initial image, (b) inpainting domain, (c–e) partial results and (f) final result obtained by the proposed model running 200 iterations using A=3, B=10, k=1, Δti=0.02 and Δts=0.2; (g) final result obtained by the proposed model running using different parameters; (h and i) results obtained by the BSCB model using two different choice to parameter values.
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