Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T01:44:37.142Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-Phase Image Inpainting: Combine Edge-Fitting with PDE Inpainting

Published online by Cambridge University Press:  03 June 2015

Meiqing Wang ,
Chensi Huang ,
Chao Zeng  and
Choi-Hong Lai
Meiqing Wang*
Affiliation:
College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002, Fujian, China
Chensi Huang
Affiliation:
College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002, Fujian, China
Chao Zeng
Affiliation:
College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002, Fujian, China
Choi-Hong Lai*
Affiliation:
School of Computing and Mathematical Sciences, University of Greenwich, Old Royal Naval College, Park Row, Greenwich, London SE109LS, UK
*
Corresponding author. Email: mqwang@fzu.edu.cn
Email: c.h.lai@gre.ac.uk
Get access

Abstract

The digital image inpainting technology based on partial differential equations (PDEs) has become an intensive research topic over the last few years due to the mature theory and prolific numerical algorithms of PDEs. However, PDE based models are not effective when used to inpaint large missing areas of images, such as that produced by object removal. To overcome this problem, in this paper, a two-phase image inpainting method is proposed. First, some edges which cross the damaged regions are located and the missing parts of these edges are fitted by using the cubic spline interpolation. These fitted edges partition the damaged regions into some smaller damaged regions. Then these smaller regions may be inpainted by using classical PDE models. Experiment results show that the inpainting results by using the proposed method are better than those of BSCB model and TV model.

Keywords

65M1078A48Image inpaintingpartial differential equationsedge fitting
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 6 , December 2012 , pp. 769 - 779
Copyright
Copyright © Global-Science Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Guichard, F., A morphological, affine and galilean invariant scale-space for movies, IEEE Trans. Image Process., 7(3) (1998), pp. 444–456.CrossRefGoogle ScholarPubMed
[2]Kokaram, A. C., Morris, R. D., Fitzgerald, W. J. and Rayner, P. J. W., Interpolation of missing data in image sequences, IEEE Trans. Image Process, 11(4) (1995), pp. 1509–1519.CrossRefGoogle Scholar
[3]Hahn, J., Yuan, J., Tai, Xue-Cheng, Borok, S. and Bruckstein, A. M., Orientation-matching minimization for image denoising and inpainting, Int. J. Comput. Vision, 92(3) (2011), pp. 308–324.CrossRefGoogle Scholar
[4]Chan, T. F. and Shen, J., Variational restoration of non-flat image features:models and algorithms, SIAM J. Appl. Math., 61(4) (2001), pp. 1338–1361.Google Scholar
[5]Chan, T. F. and Shen, J., Mathematical models for local non-texture inpaintings, SIAM J. Appl. Math., 62(3) (2001), pp. 1019–1043.Google Scholar
[6]Tai, X.-C., Osher, S. J. and Holm, R., Image inpainting using a TV-Stokes equation, in: Image Processing Based on Partial Differential Equations, Editors: Tai, , Lie, , Chan, and Osher, , Springer, 2007, pp. 3–22.Google Scholar
[7]Li, S. and Zhao, M., Image inpainting with salient structure completion and texture propagation, Pattern Recognition Lett., 32 (2011), pp. 1256–1266.Google Scholar
[8]Badshah, N. and Chen, K., Image selective segmentation under geometrical constraints using an active contour approach, Commun. Comput. Phys., 7 (2010), pp. 759–778.Google Scholar
[9]Wang, L.-L. and Gu, Y., Efficient dual algorithms for image segmentation using TV-Allen-Cahn type models, Commun. Comput. Phys., 9 (2011), pp. 859–877.Google Scholar
[10]Bertalmio, M., Sapiro, G., Caselles, V. and Ballester, C., Image inpainting, In Proceedings SIGGRAPH 2000, Computer Graphics Proceedings, Annual Conference Series, edited by Akeley, Kurt, (2000), pp. 417–424.Google Scholar
[11]Bertalmio, M., Bertozzi, A. L. and Sapiro, G., Navier-Stokes, fluid dynamics and image and video inpainting, in Proc. ICCV 2001, IEEE CS Press, (2001), pp. 1335–1362.Google Scholar
[12]Rudin, L., Osher, S. and Fatemi, E., Nonlinear total variation based noise removal algorithms, Phys. D, 60 (1992), pp. 259–268.Google Scholar
[13]Chan, T. F. and Shen, J., Non-texture inpainting by curvature driven diffusions (CDD), J. Visual Commun. Image Rep., 12(4) (2001), pp. 436–449.Google Scholar
[14]Zeng, T., Li, X. and Ng, M., Alternating minimization method for total variation based wavelet shrinkage model, Commun. Comput. Phys., 8(5) (2010), pp. 976–994.Google Scholar
[15]Chan, T. F., Kang, S.-H. and Shen, J., Euler’s elastica and curvature based inpaintings, SIAM J. Appl. Math., 63 (2002), pp. 564–592.Google Scholar
[16]Criminisi, A., Perez, P. and Yoyama, K., Region filling and object removal by exemplar-based image inpainting, IEEE Trans. Image Process, 13(9) (2004), pp. 1200–1212.Google Scholar
[17]Shih, K. T. and Chang, R.-C., Digital inpainting-survey and multilayer image inpainting algorithms, Proceedings of the Third International Conference on Information Technology and Applications (ICITA’05), 1 (2005), pp. 15–24.Google Scholar
[18]Xiao, Y., Zeng, T., Yu, J. and Ng, M. K., Restoration of images corrupted by mixed Gaussian-impulse noise via l 1-l 0 minimization, Pattern Recognition, 44 (2011), pp. 1708–1720.CrossRefGoogle Scholar
[19]Sonka, M., Hlavac, V. and Boyle, R., Image Pocessing, Analysis and Machine Vision, 2nd edition, Thomson Learning and PPTPH, 1998, pp. 90–93.Google Scholar
[20]Wang, M. and Lai, C.-H., A Concise Introduction to Image Processing Using C++, Chapman & HallCRC, 2008, pp. 140–143.Google Scholar
[21]Guo, S., Edge Fitting Based BSCB Image Inpainting Model and Its Parallelism, MSc thesis, Fuzhou University, 2009 (in Chinese).Google Scholar
[22]Ward, D. and Cheney, K., Numerical Analysis: Mathematics of Scientific Computing, 3rd edition, China Machine Press, pp. 308–464, 2003.Google Scholar
[23]Zeng, C., Huang, C. and Wang, M., The application of numerical interpolation in PDE image inpainting, The Proceedings of 2008 International Symposium on Distributed Computing and Applications for Business, Engineering and Science (DCABES 2008), pp. 1368–1372, Editors: Xu, W. and Liu, D., Publishing House of Electronics Industry, 2008.Google Scholar