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Feature-Preserving Image Restoration from Adaptive Triangular Meshes

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Computer Vision - ACCV 2014 Workshops (ACCV 2014)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9009))

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Abstract

The triangulation of images has become an active research area in recent years for its compressive representation and ease of image processing and visualization. However, little work has been done on how to faithfully recover image intensities from a triangulated mesh of an image, a process also known as image restoration or decoding from meshes. The existing methods such as linear interpolation, least-square interpolation, or interpolation based on radial basis functions (RBFs) work to some extent, but often yield blurred features (edges, corners, etc.). The main reason for this problem is due to the isotropically-defined Euclidean distance that is taken into consideration in these methods, without considering the anisotropicity of feature intensities in an image. Moreover, most existing methods use intensities defined at mesh nodes whose intensities are often ambiguously defined on or near image edges (or feature boundaries). In the current paper, a new method of restoring an image from its triangulation representation is proposed, by utilizing anisotropic radial basis functions (ARBFs). This method considers not only the geometrical (Euclidean) distances but also the local feature orientations (anisotropic intensities). Additionally, this method is based on the intensities of mesh faces instead of mesh nodes and thus provides a more robust restoration. The two strategies together guarantee excellent feature-preserving restoration of an image with arbitrary super-resolutions from its triangulation representation, as demonstrated by various experiments provided in the paper.

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References

  1. Adams, M.: An efficient progressive coding method for arbitrarily-sampled image data. IEEE Signal Process. Lett. 15, 629–632 (2008)

    Article  Google Scholar 

  2. Adams, M.: Progressive lossy-to-lossless coding of arbitrarily-sampled image data using the modified scattered data coding method. In: Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, Taipei, Taiwan, pp. 1017–1020 (2009)

    Google Scholar 

  3. Adams, M.: A flexible content-adaptive mesh-generation strategy for image representation. IEEE Trans. Image Process. 20, 2414–2427 (2011)

    Article  MathSciNet  Google Scholar 

  4. Adams, M.: A highly-effective incremental/decremental Delaunay mesh-generation strategy for image representation. Signal Process. 93, 749–764 (2013)

    Article  Google Scholar 

  5. Aizawa, K., Huang, T.: Model-based image coding: advanced video coding techniques for very low bit-rate applications. Proc. IEEE 83, 259–271 (1995)

    Article  Google Scholar 

  6. Altunbasak, Y., Tekalp, A.: Closed-form connectivity-preserving solutions for motion compensation using 2-d meshes. IEEE Trans. Image Process. 6(533), 1255–1269 (1997)

    Article  Google Scholar 

  7. Benoit-Cattin, H., Joachimsmann, P., Planat, A., Valette, S., Baskurt, A., Prost, R.: Active mesh texture coding based on warping and DCT. In: IEEE International Conference on Image Processing, Kobe, Japan (1999)

    Google Scholar 

  8. Brankov, J., Yang, Y., Galatsanos, N.: Image restoration using content-adaptive mesh modeling. In: Proceedings of IEEE International Conference on Image Processing, vol. 2, pp. 997–1000 (2003)

    Google Scholar 

  9. Brankov, J., Yang, Y., Wernick, M.: Tomographic image reconstruction based on a content-adaptive mesh model. IEEE Trans. Med. Imaging 23, 202–212 (2004)

    Article  Google Scholar 

  10. Casciola, G., Lazzaro, D., Montefusco, L., Morigi, S.: Shape preserving surface reconstruction using locally anisotropic RBF interpolants. Comput. Math. Appl. 51, 1185–1198 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  11. Casciola, G., Montefusco, L., Morigi, S.: The regularizing properties of anisotropic radial basis functions. Appl. Math. Comput. 190, 1050–1062 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Casciola, G., Montefusco, L., Morigi, S.: Edge-driven image interpolation using adaptive anisotropic radial basis functions. J. Math. Imaging Vis. 36, 125–139 (2010)

    Article  MathSciNet  Google Scholar 

  13. Chen, J., Paris, S., Wang, J., Matusik, W., Cohen, M., Durand, F.: The video mesh: A data structure for image-based three-dimensional video editing. In: IEEE International Conference on Computational Photography (ICCP), Pittsburgh, PA, USA, pp. 1–8 (2011)

    Google Scholar 

  14. Coleman, S., Scotney, B., Herron, M.: Image feature detection on content-based meshes. In: Proceedings of IEEE International Conference on Image Processing, vol. 1, pp. 844–847 (2002)

    Google Scholar 

  15. Davoine, F., Antonini, M., Chassery, J., Barlaud, M.: Fractal image compression based on Delaunay triangulation and vector quantization. IEEE Trans. Image Process. 5, 338–346 (1996)

    Article  Google Scholar 

  16. Delaunay, B.: Sur la sphere vide. Classe des Science Mathematics et Naturelle 7, 793–800 (1934)

    Google Scholar 

  17. Demaret, L., Robert, G., Laurent, N., Buisson, A.: Scalable image coder mixing DCT and triangular meshes. In: IEEE International Conference on Image Processing, Vancouver, BC, Canada, vol. 3, pp. 849–852 (2000)

    Google Scholar 

  18. Divo, E., Kassab, A.: An efficient localized RBF meshless method for fluid flow and conjugate hear transfer. ASME J. Heat Transfer 129, 124–136 (2007)

    Article  Google Scholar 

  19. Garcia, M., Vintimilla, B.: Acceleration of filtering and enhancement operations through geometric processing of gray-level images. In: IEEE International Conference on Image Processing, Vancouver, BC, Canada, vol. 1, pp. 97–100 (2000)

    Google Scholar 

  20. Garland, M., Heckbert, P.: Fast polygonal approximation of terrains and height fields. Technical Report CMU-CS-95-181, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, USA (1995)

    Google Scholar 

  21. Guo, Y., Liu, F., Shi, J., Zhou, Z., Gleicher, M.: Image retargeting using mesh parametrization. IEEE Trans. Multimedia 11, 856–867 (2009)

    Article  Google Scholar 

  22. Hsu, P., Liu, K., Chen, T.: A low bit-rate video codec based on two-dimensional mesh motion compensation with adaptive interpolation. IEEE Trans. Circuits Syst. Video Technol. 11, 111–117 (2001)

    Article  Google Scholar 

  23. Hung, K., Chang, C.: New irregular sampling coding method for transmitting images progressively. In: IEEE Proceedings of Vision, Image and Signal Processing, vol. 150, pp. 44–50 (2003)

    Google Scholar 

  24. Kosec, G., Sarler, B.: Local RBF collocation method for Darcy flow. Comput. Model. Eng. Sci. 25, 197–208 (2008)

    Google Scholar 

  25. Lechat, P., Sanson, H., Labelle, L.: Image approximation by minimization of a geometric distance applied to a 3-D finite elements based model. In: Proceedings of IEEE International Conference on Image Processing, vol. 2, pp. 724–727 (1997)

    Google Scholar 

  26. Li, P., Adams, M.: A tuned mesh-generation strategy for image representation based on data-dependent triangulation. IEEE Trans. Image Process. 22, 2004–2018 (2013)

    Article  MathSciNet  Google Scholar 

  27. Marquant, G., Pateux, S., Labit, C.: Mesh and “crack lines”: application to object-based motion estimation and higher scalability. In: IEEE International Conference on Image Processing, Vancouver, BC, Canada, vol. 2, pp. 554–557 (2000)

    Google Scholar 

  28. Nosratinia, A.: New kernels for fast mesh-based motion estimation. IEEE Trans. Circuits Syst. Video Technol. 11, 40–51 (2001)

    Article  Google Scholar 

  29. Petrou, M., Piroddi, R., Talebpour, A.: Texture recognition from sparsely and irregularly sampled data. Comput. Vis. Image Underst. 102, 95–104 (2006)

    Article  Google Scholar 

  30. Ramponi, G., Carrato, S.: An adaptive irregular sampling algorithm and its application to image coding. Image Vis. Comput. 19, 451–460 (2001)

    Article  Google Scholar 

  31. Rippa, S.: Adaptive approximation by piecewise linear polynomials on triangulations of subsets of scattered data. SIAM J. Sci. Stat. Comput. 13, 1123–1141 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  32. Sarkis, M., Diepold, K.: A fast solution to the approximation of 3-D scattered point data from stereo images using triangular meshes. In: Proceedings of IEEE-RAS International Conference on Humanoid Robots, Pittsburgh, PA, USA, pp. 235–241 (2007)

    Google Scholar 

  33. Sarler, B., Vertnik, R.: Meshfree explicit local radial basis function collocation method for diffusion problems. Comput. Math. Appl. 51, 1269–1282 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  34. Singh, A., Terzopoulos, D., Goldgof, D.: Deformable models in medical image analysis. IEEE Computer Society Press (1998)

    Google Scholar 

  35. Shewchuk, J.: Triangle: A two-dimensional quality mesh generator and Delaunay triangulator (2005). http://www.cs.cmu.edu/quake/triangle.html

  36. Su, D., Willis, P.: Demosaicing of color images using pixel level data-dependent triangulation. In: Proceedings of Theory and Practice of Computer Graphics, pp. 16–23 (2003)

    Google Scholar 

  37. Su, D., Willis, P.: Image interpolation by pixel-level data-dependent triangulation. Comput. Graph. Forum 23, 189–201 (2004)

    Article  Google Scholar 

  38. Toklu, C., Tekalp, A., Erdem, A.: Semi-automatic video object segmentation in the presence of occlusion. IEEE Trans. Circuits Syst. Video Technol. 10, 624–629 (2000)

    Article  Google Scholar 

  39. Tu, X., Adams, M.: Improved mesh models of images through the explicit representation of discontinuities. Can. J. Electr. Comput. Eng. 36, 78–86 (2013)

    Article  Google Scholar 

  40. Vertnik, R., Sarler, B.: Meshless local radial basis function collocation method for convective-diffusive solid-liquid phase change problems. Int. J. Numer. Meth. Heat Fluid Flow 16, 617–640 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  41. Vertnik, R., Sarler, B.: Solution of incompressible turbulent flow by a mesh-free method. Comput. Model. Eng. Sci. 44, 65–95 (2009)

    MathSciNet  Google Scholar 

  42. Wang, J., Liu, G.: On the optimal shape parameters of radial basis functions used for 2-d meshless methods. Comput. Methods Appl. Mech. Eng. 191, 2611–2630 (2002)

    Article  MATH  Google Scholar 

  43. Wang, Y., Lee, O.: Active mesh - a feature seeking and tracking image sequence representation scheme. IEEE Trans. Image Process. 3, 610–624 (1994)

    Article  Google Scholar 

  44. Wang, Y., Lee, O., Vetro, A.: Use of 2-D deformable mesh structures for video coding, part II-the analysis problem and a region-based coder employing an active mesh representation. IEEE Trans. Circuits Syst. Video Technol. 6, 647–659 (1996)

    Article  Google Scholar 

  45. Yang, Y., Miles, N., Jovan, G.: A fast approach for accurate content-adaptive mesh generation. IEEE Trans. Image Process. 12, 866–881 (2003)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. University of Wisconsin Milwaukee, Milwaukee, WI, 53211, USA

    Ke Liu, Ming Xu & Zeyun Yu

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  1. Ke Liu
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  2. Ming Xu
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  3. Zeyun Yu
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Correspondence to Zeyun Yu .

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Editors and Affiliations

  1. Center for Visual Information Technology, International Institute of Information Technology, Hyderabad, India

    C.V. Jawahar

  2. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Shiguang Shan

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Liu, K., Xu, M., Yu, Z. (2015). Feature-Preserving Image Restoration from Adaptive Triangular Meshes. In: Jawahar, C., Shan, S. (eds) Computer Vision - ACCV 2014 Workshops. ACCV 2014. Lecture Notes in Computer Science(), vol 9009. Springer, Cham. https://doi.org/10.1007/978-3-319-16631-5_3

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  • DOI: https://doi.org/10.1007/978-3-319-16631-5_3

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  • Online ISBN: 978-3-319-16631-5

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