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WENO based adaptive image zooming algorithm (2312.00229v1)

Published 30 Nov 2023 in math.NA and cs.NA

Abstract: Image zooming or upsampling is a widely used tool in image processing and an essential step in many algorithms. Upsampling increases the number of pixels and introduces new information into the image, which can lead to numerical effects such as ringing artifacts, aliasing effects, and blurring of the image. In this paper, we propose an efficient polynomial interpolation algorithm based on the WENO algorithm for image upsampling that provides high accuracy in smooth regions, preserves edges and reduces aliasing effects. Although this is not the first application of WENO interpolation for image resampling, it is designed to have comparable complexity and memory load with better image quality than the separable WENO algorithm. We show that the algorithm performs equally well on smooth 2D functions, artificial pixel art, and real digital images. Comparison with similar methods on test images shows good results on standard metrics and also provides visually satisfactory results. Moreover, the low complexity of the algorithm is ensured by a small local approximation stencil and the appropriate choice of smoothness indicators.

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References (25)
  1. Applied Mathematics and Computation 403, 126,131 (2021). DOI https://doi.org/10.1016/j.amc.2021.126131. URL https://www.sciencedirect.com/science/article/pii/S009630032100179X
  2. Journal of Scientific Computing 43(2), 158–182 (2010). DOI 10.1007/s10915-010-9351-8. URL http://dx.doi.org/10.1007/s10915-010-9351-8
  3. Applied Numerical Mathematics 62(8), 975–987 (2012). DOI https://doi.org/10.1016/j.apnum.2012.03.005. URL https://www.sciencedirect.com/science/article/pii/S0168927412000530
  4. Image and Vision Computing 20, 805–812 (2002)
  5. Mathematical Communications 19(3), 517–529 (2014)
  6. SIAM Journal on Imaging Sciences 7(2), 1284–1308 (2014). DOI 10.1137/130907057. URL https://doi.org/10.1137/130907057
  7. Developers, I.: Imagemagick tool (2018). URL http://www.imagemagick.org/
  8. Int. J. Numer. Anal. Model. 6(2), 284–292 (2009)
  9. Getreuer, P.: Image Interpolation with Geometric Contour Stencils. Image Processing On Line 1, 98–116 (2011). DOI 10.5201/ipol.2011.g_igcs
  10. Getreuer, P.: Linear methods for image interpolation. Image Processing On Line 1(1), 238–259 (2011)
  11. Addison-Wesley, New York (1992)
  12. IEEE Trans. Acoust., Speech, Signal Processing 26(6), 508–517 (1978)
  13. Keys, R.G.: Cubic convolution interpolation for digital image processing. IEEE Trans. Acoust., Speech, Signal Processing 29(6), 1153–1160 (1981)
  14. IEEE Transactions on Image Processing 20(7), 1895–1903 (2011). DOI 10.1109/tip.2011.2107523. URL https://doi.org/10.1109/tip.2011.2107523
  15. Kodak, E.: Kodak lossless true color image suite (photocd pcd0992). URL http://r0k.us/graphics/kodak/
  16. Applied Mathematics and Computation 269, 569–583 (2015). DOI https://doi.org/10.1016/j.amc.2015.07.086. URL https://www.sciencedirect.com/science/article/pii/S0096300315010085
  17. Acta Mathematicae Applicatae Sinica, English Series 25(3), 503–538 (2009). DOI 10.1007/s10255-008-8826-y. URL https://doi.org/10.1007/s10255-008-8826-y
  18. In: C. V, G. Fotia, L. Puccio (eds.) Applied and Industrial Mathematics in Italy II, Ser. Adv. Math. Appl. Sci., vol. 75, pp. 480–491. World Scientific Publishing (2007)
  19. Springer Berlin Heidelberg, Berlin, Heidelberg (2008). DOI 10.1007/978-3-540-69812-8_9. URL http://dx.doi.org/10.1007/978-3-540-69812-8_9
  20. In: C. Blanc, A. Ghizzetti, A. Ostrowski, J. Todd, A. van Wijngaarden (eds.) Spline Function and Approximation Theory, ISNM, vol. 21, pp. 277–358. Birkhäuser Verlag Basel und Stuttgart (1973)
  21. Shu, C.W.: Essentially non-oscillatory and weighted essentially non-oscillatory schemes. Acta Numerica 29, 701–762 (2020). DOI 10.1017/S0962492920000057
  22. In: Inverse Problems, pp. 165–187 (2000)
  23. In: T. Huang, Z. Zeng, C. Li, C.S. Leung (eds.) Neural Information Processing, pp. 398–405. Springer Berlin Heidelberg, Berlin, Heidelberg (2012)
  24. IEEE Transactions on Image Processing 13(4), 600–612 (2004)
  25. IEEE Transactions on Image Processing 15(8), 2226–2238 (2006). DOI 10.1109/TIP.2006.877407

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