Journal of the Korea Institute of Information and Communication Engineering (한국정보통신학회논문지)

The Korea Institute of Information and Commucation Engineering (한국정보통신학회)
권호 표지
DOI QR코드

DOI QR Code

Kernel Analysis of Weighted Linear Interpolation Based on Even-Odd Decomposition

짝수 홀수 분해 기반의 가중 선형 보간법을 위한 커널 분석

  • Oh, Eun-ju (Department of Media Software, SangMyung University) ;
  • Yoo, Hoon (Department of Electronics, SangMyung University)
  • Received : 2018.08.01
  • Accepted : 2018.08.10
  • Published : 2018.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper presents a kernel analysis of weighted linear interpolation based on even-odd decomposition (EOD). The EOD method has advantages in that it provides low-complexity and improved image quality than the CCI method. However, since the kernel of EOD has not studied before and its analysis has not been addressed yet, this paper proposes the kernel function and its analysis. The kernel function is divided into odd and even terms. And then, the kernel is accomplished by summing the two terms. The proposed kernel is adjustable by a parameter. The parameter influences efficiency in the EOD based WLI process. Also, the kernel shapes are proposed by adjusting the parameter. In addition, the discussion with respect to the parameter is given to understand the parameter. A preliminary experiment on the kernel shape is presented to understand the adjustable parameter and corresponding kernel.

본 논문은 짝수 홀수 분해법에 기초한 가중된 선형 보간법(weighted Linear Interpolation; WLI) 커널 분석을 제안한다. 짝수 홀수 분해법은 기존에 알려진 CCI 보간법보다 복잡도가 낮고 개선된 화질을 제공해준다는 점에서 장점을 가지고 있다. 하지만 기존에는 EOD에 대한 커널이 부재했을 뿐 더러, 그에 대한 분석이 이루어지 않았기에 본 논문은 EOD에 대한 커널 식을 제공한다. EOD에 의해 짝 홀수로 나누어진 벡터에 대한 커널 식을 제공하고 최종적으로 두 벡터의 합인 EOD 커널식을 제공한다. 최종적으로 유도된 EOD의 커널 식은 매개변수 ${\omega}$에 의해 정의된다. ${\omega}$에 의해 정의된 커널 식이 WLI이며, 여기서 ${\omega}$는 보간 과정에 있어 성능을 좌우하는 역할로 사용된다. 또한 매개변수의 변화에 다른 커널의 형태의 변화에 관한 것도 제시한다. 또한, 매개변수에 대한 이해와 해당되는 커널의 형태 변화를 이해하기 위해서 실험과 토론을 제시한다.

Keywords

HOJBC0_2018_v22n11_1455_f0001.png 이미지

Fig. 1 Kernel of CCI

HOJBC0_2018_v22n11_1455_f0002.png 이미지

Fig. 2 Basic concept of EOD

HOJBC0_2018_v22n11_1455_f0003.png 이미지

Fig.3 kernel of odd vector

HOJBC0_2018_v22n11_1455_f0004.png 이미지

Fig. 4 kernel of even vector

HOJBC0_2018_v22n11_1455_f0005.png 이미지

Fig. 5 kernel of WLI (ω = 1)

HOJBC0_2018_v22n11_1455_f0006.png 이미지

Fig. 6 kernel of WLI according to parameter ω

References

  1. R. G. Keys, "Cubic convolution interpolation for digital image processing," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 29, no. 6, pp. 1153-1160, Dec. 1981. https://doi.org/10.1109/TASSP.1981.1163711
  2. H. Yoo, "Closed-form least-squares technique for adaptive linear image interpolation," IET Electronics Letters, vol. 43, no. 4, pp. 210-212, Feb. 2007. https://doi.org/10.1049/el:20073606
  3. W. Dong, L. Zhang, R. Lukac, and G. Shi. "Sparse representation based image interpolation with nonlocal autoregressive modeling," IEEE Transactions on Image Processing, vol. 22, no. 4, pp. 1382-1394, Apr. 2013. https://doi.org/10.1109/TIP.2012.2231086
  4. J. J. Huang, W. C. Siu, and T. R. Liu, "Fast image interpolation via random forests," IEEE Transactions on Image Processing, vol. 24, no. 10, pp. 3232-3245. Oct. 2015. https://doi.org/10.1109/TIP.2015.2440751
  5. Y. Zou, G. Zhang, M. Linderman, and W. Xu, "A comparison among spatial interpolation techniques for daily rainfall data in Sichuan Province, China," International Journal of Climatology, vol. 35, no. 10, pp. 2898-2907, Aug. 2015. https://doi.org/10.1002/joc.4180
  6. E. H. W. Meijering, "A chronology of interpolation: From ancient astronomy to modern signal and image processing," Proceedings on the IEEE, vol. 90, no. 3, pp. 319-342, Mar. 2002. https://doi.org/10.1109/5.993400
  7. S. H. Hong, L. Wang, T. K. Truong, T. C. Lin, and L. J. Wang, "Novel approaches to the parametric cubic-spline interpolation," IEEE Transactions on Image Processing, vol. 22, no. 3, pp. 1233-1241, Mar. 2013. https://doi.org/10.1109/TIP.2012.2230009
  8. H. Yoo, "Closed-form least-squares technique for adaptive linear image interpolation," IET Electronics Letters, vol. 43, no. 4, pp. 210-212, Feb. 2007. https://doi.org/10.1049/el:20073606
  9. T. Athawale and A. Entezari, "Uncertainty quantification in linear interpolation for isosurface extraction," IEEE Transactions on visualization and computer graphics, vol. 19, no. 12, pp. 2723-2732, Dec. 2013. https://doi.org/10.1109/TVCG.2013.208
  10. H. Yoo and J. Jeong, "Direction-oriented interpolation and its application to de-interlacing," IEEE Transactions on Consumer Electronics, vol. 48, no. 4, pp. 954-962, 2002. https://doi.org/10.1109/TCE.2003.1196426
  11. D. H. Shin and H. Yoo, "Computational integral imaging reconstruction method of 3D images using pixel-to-pixel mapping and image interpolation," Elsevier Optics Communications, vol. 282, no. 14, pp. 2760-2767, 15 July 2009.
  12. J. E. Bae and H. Yoo, "Efficient image-stitching using preprocessing for a super resolution image," Journal of Korea Institute of Information and Communication Engineering, vol. 21, no. 9, pp. 1738-1743, Sep. 2017 https://doi.org/10.6109/JKIICE.2017.21.9.1738
  13. H. A. Jung and H. Yoo, "A fast and accurate method of extracting lens array lattice in integral imaging," Journal of Korea Institute of Information and Communication Engineering, vol. 21, no. 9, pp. 1711-1717, Sep. 2017. https://doi.org/10.6109/JKIICE.2017.21.9.1711
  14. H.-G. Kim and H. Yoo, "Image enhancement for computed tomography using directional interpolation for sparselysampled sinogram," Elsevier Optik, vol. 166, pp.227-235, Aug. 2018. https://doi.org/10.1016/j.ijleo.2018.03.139
  15. H. Yoo "Transformations and Their Analysis from a RGBD Image to Elemental Image Array for 3D Integral Imaging and Coding," KSII Transactions on Internet and Information Systems, vol. 12, no. 5, May 2018.
  16. Y. Lee and H. Yoo, "Three-dimensional visualization of objects in scattering medium using integral imaging and spectral analysis," Elsevier Optics and Lasers in Engineering, vol. 77, no. 2, pp. 31-38, Feb. 2016. https://doi.org/10.1016/j.optlaseng.2015.07.007
  17. H. Yoo, D-K Shin, and M. Cho, "Improved depth extraction method of 3D objects using computational integral imaging reconstruction based on multiple windowing techniques," Elsevier Optics and Lasers in Engineering, vol. 66, no. 3, pp. 105-111, Mar. 2015 (online 19 Sep. 2014). https://doi.org/10.1016/j.optlaseng.2014.08.015
  18. J. H. Lee and D. H. Choi, "Palm Lines Extraction on a High Resolution Image using Mosaic-like Method," Asia-pacific Journal of Multimedia Services Convergent with Art, Humanities, and Sociology, Vol. 6, No. 3, pp. 9-17, March 2016.
  19. J. E. Bae, H. J. Cho, H. Yoo, "Geometric symmetry using rotational scanning method for circular form detection," Information Technology, Electronics and Mobile Communication Conference (IEMCON), Vol.9, pp.1000-1002, 2018.
  20. H. Yoo, S. P. Lee, and B. C. Jang, "Design of Two-Point Interpolation Filters by Modifying Linear Interpolation Kernel," Far East Journal of Electronics and Communications, vol. 10, no. 2, pp. 131-139, 2013.
  21. H. Yoo, and B. D. Choi, "Design of Piecewise Weighted Linear Interpolation Based on Even-Odd Decomposition and Its Application to Image Resizing," IEEE Transactions on Consumer Electronics, vol. 55, no. 4, pp. 2280-2286, Nov. 2009. https://doi.org/10.1109/TCE.2009.5373799
  22. H. J. Cho and H. Yoo, "Efficient Modifications of Cubic Convolution Interpolation Based on Even-Odd Decomposition," The Transactions of The Korean Institute of Electrical Engineers, Vol. 63, No. 5, pp. 690-695, May. 2014. https://doi.org/10.5370/KIEE.2014.63.5.690