The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Image noise reduction algorithms using nonparametric method

비모수 방법을 사용한 영상 잡음 제거 알고리즘

  • Woo, Ho-young (Department of Applied Statistics, Chung-Ang University) ;
  • Kim, Yeong-hwa (Department of Applied Statistics, Chung-Ang University)
  • 우호영 (중앙대학교 응용통계학과) ;
  • 김영화 (중앙대학교 응용통계학과)
  • Received : 2019.07.16
  • Accepted : 2019.08.23
  • Published : 2019.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

Noise reduction is an important field in image processing and requires a statistical approach. However, it is difficult to assume a specific distribution of noise, and a spatial filter that reflects regional characteristics is a small sample and cannot be accessed in a parametric manner. The first order image differential and the second order image differential show a clear difference according to the noise level included in the image and can be more clearly understood using the canyon edge detector. The Fligner-Killeen test was performed and the bootstrap method was used to statistically check the noise level. The estimated noise level was set between 0 and 1 using the cumulative distribution function of the beta distribution. In this paper, we propose a nonparametric noise reduction algorithm that accounts for the noise level included in the image.

영상처리 분야에서 중요한 분야인 잡음 제거는 통계적인 접근이 필요하지만 잡음에 대한 특정한 분포를 가정하기 어려우며 지역적 특징을 반영하는 공간 필터는 소표본에 해당하므로 모수적인 방법으로 접근할 수 없다. 1차 영상 미분과 2차 영상 미분은 영상에 포함된 잡음 수준에 따라 확연한 차이를 보이며 캐니 에지 검출기를 사용하면 보다 명확히 알 수 있다. 잡음 수준을 통계적으로 확인하고자 Fligner-Killeen 검정을 진행하고 붓스트랩 방법을 사용하였으며 추정된 잡음의 수준을 베타분포의 누적분포함수를 이용하여 0과 1사이의 값을 갖도록 하였다. 본 연구에서는 영상에 포함된 잡음 수준을 고려하는 잡음 제거 알고리즘을 제시하고자 한다.

Keywords

References

  1. Canny, J. (1986). Collision detection for moving polyhedra, IEEE Transactions on Pattern Analysis and Machine Intelligence, 5, 200-209. https://doi.org/10.1109/TPAMI.1986.4767773
  2. Conover, W. J., Johnson, M. E., and Johnson, M. M. (1981). A comparative study of tests for homogeneity of variances, with applications to the outer continental shelf bidding data, Technometrics, 23, 351-361. https://doi.org/10.1080/00401706.1981.10487680
  3. Efron, B. (1979). Computers and the theory of statistics: thinking the unthinkable, SIAM Review, 21, 460-480. https://doi.org/10.1137/1021092
  4. Efron, B. and Tibshirani, R. (1986). Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy, Statistical Science, 1, 54-75. https://doi.org/10.1214/ss/1177013815
  5. Fligner, M. A. and Killeen, T. J. (1976). Distribution-free two-sample tests for scale, Journal of the American Statistical Association, 71, 210-213. https://doi.org/10.1080/01621459.1976.10481517
  6. Gonzalez, R. C. and Wood, R. E. (2016). Digital Image Processing (3rd ed), Pearson Prentice-Hall, Delhi.
  7. Hall, P. (1992). The Bootstrap and Edgeworth Expansion, Springer, New York.
  8. Jain, S., Jagtapb, V., and Pisea, N. (2015). Computer aided melanoma skin cancer detection using image processing, Procedia Computer Science, 48, 735-740. https://doi.org/10.1016/j.procs.2015.04.209
  9. Khirade, S. D. and Patil, A. B. (2015). Plant disease detection using image processing. In 2015 Interna- tional Conference on Computing Communication Control and Automation (ICCUBEA), (pp. 768-771), IEEE, Pune, India.
  10. Kim, Y. H. (2012). Adaptive noise reduction algorithm for image based on block approach, Communications for Statistical Applications and Methods, 19, 225-235. https://doi.org/10.5351/CKSS.2012.19.2.225
  11. Kim, Y. H. and Nam, J. (2009). Statistical algorithm and application for the noise variance estimation, Journal of the Korean Data & Information Science Society, 20, 869-878.
  12. Marr, D. and Hildreth, E. (1980). Theory of edge detection, Proceedings of the Royal Society B, 207, 187-217.
  13. Peters, R. A. (1995). A new algorithm for image noise reduction using mathematical morphology, IEEE Transactions on Image Processing, 4, 554-568. https://doi.org/10.1109/83.382491
  14. Roberts, L. G. (1965). Machine perception of Three-dimensional solids. In J. T. Tippett, et al. (Eds), Optical and Electro-optical Information Processing, MIT Press.
  15. Rosenfeld, A. and Kak, A. C. (1982). Digital Picture Processing (2nd ed), Academic Press, New York.
  16. Sobel, I. E. (1970). Camera Models and Machine Perception (No. AIM-121), Computer Science Department, Stanford University.
  17. Song, Y., Han, Y., and Lee, S. (2013). Effective impulse noise reduction method based on local correlation, The Imaging Science Journal, 61, 47-56. https://doi.org/10.1179/1743131X11Y.0000000051
  18. Toulouse, T., Rossi, L., Celik, T., and Akhloufi, M. (2016). Automatic fire pixel detection using image processing: a comparative analysis of rule-based and machine learning-based methods, Signal, Image and Video Processing, 10(4), 647-654. https://doi.org/10.1007/s11760-015-0789-x
  19. Van De Ville, D., Nachtegael, M., Van der Weken, D., Kerre, E. E., Philips, W., and Lemahieu, I. (2003). Noise reduction by fuzzy image filtering, IEEE Transactions on Fuzzy Systems, 11, 429-436. https://doi.org/10.1109/TFUZZ.2003.814830