Journal of the Institute of Electronics Engineers of Korea SP (대한전자공학회논문지SP)

The Institute of Electronics and Information Engineers (대한전자공학회)
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Image Interpolation Using Linear Modeling for the Absolute Values of Wavelet Coefficients Across Scale

스케일간 웨이블릿 계수 절대치의 선형 모델링을 이용한 영상 보간

  • Kim Sang-Soo (Dept. of Electronic Engineering. Pusan National University) ;
  • Eom Il-Kyu (Dept. of Information and Communication Miryang National University) ;
  • Kim Yoo-Shin (Research Institute of Computer and Information and Communication)
  • 김상수 (부산대학교 전자공학과) ;
  • 엄일규 (밀양대학교 정보통신공학과) ;
  • 김유신 (부산대학교 컴퓨터 및 정보통신 연구소)
  • Published : 2005.11.01
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Abstract

Image interpolation in the wavelet domain usually takes advantage of the probabilistic models for the intrascale statistics and the interscale dependency. In this paper, we adopt the linear model for the absolute values of wavelet coefficients of interpolated image across scale to estimate the variances of extrapolated bands. The proposed algorithm uses randomly generated wavelet coefficients based on the estimated parameters for probabilistic model. Random number generation according to the estimated probabilistic model may induce the 'salt and pepper' noise in subbands. We reduce the noise power by Wiener filtering. We observe that the proposed method generates the histogram of the subband coefficients similar to the that of original image. Experimental results show that our method outperforms the previous wavelet-domain interpolation method as well as the conventional bicubic method.

웨이블릿 영역에서의 영상 보간은 웨이블릿 계수들의 통계적 특성과 스케일간 의존성을 표현하는 확률모델을 이용한다. 본 논문에서는 보간할 영상에 대해 스케일간 웨이블릿 계수의 절대치를 선형 모델링하여 분산을 추정하고 이를 바탕으로 고주파 부대역의 확률모델을 실현하여 영상을 보간하는 방법을 제안한다. 본 논문의 방법은 확률 모델에 대한 추정된 파라미터에 의해 웨이블릿 계수를 난수 형태로 발생시키는 방법을 사용한다. 확률모델을 따라 난수를 발생할 경우 추정 부대역에 난수에 의한 잡음이 발생하게 된다. 본 논문에서는 후처리 과정으로 Wiener filter를 사용하여 부대역의 잡음을 제거하였다. 제안 방법으로 외삽한 부대역에 대한 확률 밀도함수를 비교적 정확하게 추정한 것을 볼 수 있다. 실험을 통해 제안방법이 bicubic과 같은 전통적인 방법뿐 아니라 웨이블릿 영역에서의 다른 영상보간법보다 나은 주관적, 객관적 성능을 가지고 있음을 보였다.

Keywords

References

  1. K Kinebuchi, D. D.Muresan, and T. W. Parks, 'Image interpolation using wavelet-based hidden Markov trees,' ICASSP01, Vol. 3, pp. 7-11, May 2001 https://doi.org/10.1109/ICASSP.2001.941330
  2. J. Allebach and P. W. Wong, 'Edge directed interpolation,' ICIP96, Vol. 3, pp. 707 - 710, 1996 https://doi.org/10.1109/ICIP.1996.560768
  3. X. Li and M. T. Orchard, 'New edge-directed interpolation,' IEEE Trans. Image Processing, Vol. 10, No. 10, pp. 1521-1527, Oct. 2001 https://doi.org/10.1109/83.951537
  4. K. Jensen and D. Anastassiou, 'Subpixel edge localization and the interpolation of still images,' IEEE Trans. on Image Processing, Vol. 4, pp. 285-295, Mar. 1995 https://doi.org/10.1109/83.366477
  5. W. K Carey, D. B. Chuang, and S. S. Hemami, 'Regularity-preserving interpolation,' IEEE Trans. Image Processing, Vol. 8, No.9, Sept. 1999 https://doi.org/10.1109/83.784441
  6. M. S. Crouse, R. D. Nowak, and R.G. Baraniuk, 'Wavelet-based statistical signal processing using hidden Markov models,'IEEE Trans. Image Processing, vol.46, pp. 886-902, 1998 https://doi.org/10.1109/78.668544
  7. J. K. Romberg, H. Choi, and R. G. Baraniuk, 'Bayesian tree-structured image modeling using wavelet-domain hidden Markov models,' IEEE. Trans. Image Processing, vol.10, no.7, pp. 1056-1068, 2001 https://doi.org/10.1109/83.931100
  8. Nobuyuki Otsu, 'A threshold selection method form gray-level histogram,' IEEE Trans. Systems, Man, And Cybernetics Vol.. SMC-9, No. 1 Jan. 1979,
  9. S. Mallat and S. Zhong, 'Characterization of signals from multiscale edges,' IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 14, pp. 710-732, July 1992 https://doi.org/10.1109/34.142909
  10. D. D. Muresan and T. W. Parks 'Prediction of image detail,' IEEE International Conference on Image Processing, Sept. 2000 https://doi.org/10.1109/ICIP.2000.899374
  11. S. G. Chang, Z. Cvetkovic, and M. Vetterli, 'Resolution enhancement of images using wavelet transform extrema extrapolation,' IEEE ICASSP'95, pp. 2379-2382 https://doi.org/10.1109/ICASSP.1995.479971
  12. Z. Cvetkovic and M. Vetterli, 'Discrete-time wavelet extrema representation: design and consistent reconstruction,' IEEE Trans. on Signal Processing, Vol. 43, No. 3, pp. 681-693, Mar. 1995 https://doi.org/10.1109/78.370622
  13. Y. Zhu, S. C. Schwartz, M. T. Orchard, 'Wavelet domain image interpolation via statistical estimation,' IEEE ICIP'01, Vol. 3 pp. 7-10 https://doi.org/10.1109/ICIP.2001.958251
  14. H. F. Ates, M. T. Orchard, 'Image interpolation using wavelet-based contour estimation,' IEEE ICASSP'03, Vol. 3, pp. III-109-112 https://doi.org/10.1109/ICASSP.2003.1199119
  15. N. Plaziac, 'Image interpolation using neural networks,' IEEE Trans. Image Processing, Vol. 8, No. 11, pp. 1647-1651, Nov. 1999 https://doi.org/10.1109/83.799893
  16. T. Blu, P. Thevenaz, and M. Unser, 'Linear interpolation Revitalized,' IEEE Trans. Image Processing, Vol. 13, No. 5, pp. 710-719, May 2004 https://doi.org/10.1109/TIP.2004.826093
  17. G. Ramponi, 'Warped Distance For Space Variant Linear Image Interpolation,' IEEE Trans. Image Processing, Vol. 8, pp. 629-639, 1999 https://doi.org/10.1109/83.760311
  18. S. E. Khamy, M. M. Hadhoud, M. I. Dessouky, B. M. Salam, and F. E. Abd El-Samie, 'A New Edge Preserving Pixel-by-Pixel Cubic Image Interpolation Approach,' NRSC Mar. 16-18, 2004
  19. V. R. Algazi, G. E. Ford, and R. Potharlanka, 'Directional interpolation of images based on visual properties and rank order filtering,' IEEE ICASSP, Vol. 4, 1991, pp. 3005-3008 https://doi.org/10.1109/ICASSP.1991.151035
  20. S. Carrato, G. Ramponi, and S. Marsi, 'Simple edge-sensitive image interpolation filter,' IEEE ICIP, Vol. 3, 1996, pp. 711-714 https://doi.org/10.1109/ICIP.1996.560778
  21. S. K. Mitra, H. Li, I. Lin, and T. Yu, 'A new class of nonlinear filters for image enhancement,' IEEE ICASSP'91 pp. 2525-2528 https://doi.org/10.1109/ICASSP.1991.150915
  22. E. P. Simoncelli, 'Bayesian denoising of visual images in the wavelet domain,' Bayesian inference in wavelet based models eds. P Muller and B Vidakovic, Chap.18, pp. 291-300, Lecture notes in statistics, Vol. 141, Springer-Verlag, 1999
  23. M Malfiat and D. Roose, 'Wavelet-based image denoising using a Markov random field a priori model,' IEEE. Transaction on Image Processing, vo.6, no.4, pp.549-565, 1997 https://doi.org/10.1109/83.563320
  24. D. L. Donoho and I. M. Jonhstone, 'Adapting to unknown smoothness via wavelet shrinkage,' J. Amer. Statist. Assoc., vol. 90, no. 432, pp. 1200-1224, 1995 https://doi.org/10.2307/2291512