Skip to main content
Log in

Adaptive variable order polynomial based digital zoom of images

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

Digital zoom is widely used in daily life from zooming a captured image to navigating through live maps. The applications are simple but application domains benefit large number of users. This manuscript proposes a novel approach to escalate zoom limits by modifying the zoom tolerance bound of an image. The approach focuses on preserving original information and transfer it to zoomed image. Digital zoom is achieved by first representing the original image as a set mathematical model representing underlying statistical parameters. The sets in model are further analyzed to calculate set variance; which in turn is used for localizing fluctuations and generate polynomial for each set. These polynomial are then used for implementing variable order interpolation scheme. Experimental results confirm that the present technique outperforms existing techniques in terms of image quality measurement parameters. The discussed approach can be implemented on RGB or grayscale images equivalently.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Notes

  1. An extended version of Table 3 can be found at goo.gl/yAYWrT

References

  1. Caltech (2016) Computer vision. online. [Online]. Available: https://goo.gl/3AYpvR

  2. Cha Y, Kim S (2007) The error-amended sharp edge (ease) scheme for image zooming. IEEE Trans Image Process 16(6):1496–1505

    Article  MathSciNet  Google Scholar 

  3. Dai Q, Katsaggelos AK, Yu S, Kang W, Jeon J, Paik J (2014) Directionally adaptive cubic-spline interpolation using optimized interpolation kernel and edge orientation for mobile digital zoom system. In: The 18th IEEE international symposium on consumer electronics (ISCE 2014), pp 1–2

  4. Duchon CE (1979) Lanczos filtering in one and two dimensions. J Appl Meteorol 18(8):1016–1022

    Article  Google Scholar 

  5. Giachetti A, Asuni N (2008) Fast artifacts-free image interpolation. In: BMVC, pp 1–10

  6. Giachetti A, Asuni N (2011) Real-time artifact-free image upscaling. IEEE Trans Image Process 20(10):2760–2768

    Article  MathSciNet  MATH  Google Scholar 

  7. Keys R (1981) Cubic convolution interpolation for digital image processing. IEEE Trans Acoust Speech Signal Process 29(6):1153–1160

    Article  MathSciNet  MATH  Google Scholar 

  8. Kim H, Cha Y, Kim S (2011) Curvature interpolation method for image zooming. IEEE Trans Image Process 20(7):1895–1903

    Article  MathSciNet  MATH  Google Scholar 

  9. Lee S-J, Kang M-C, Uhm K-H, Ko S-J (2016) An edge-guided image interpolation method using taylor series approximation. IEEE Trans Consum Electron 62(2):159–165

    Article  Google Scholar 

  10. Lehmann TM, Gönner C, Spitzer K (1999) Survey: interpolation methods in medical image processing. IEEE Trans Image Process 18(11):1049–1075

    Article  Google Scholar 

  11. Li X, Orchard MT (2001) New edge-directed interpolation. IEEE Trans Image Process 10(10):1521–1527

    Article  Google Scholar 

  12. Liu S, Lu M, Liu G, Pan Z (2017) A novel distance metric: generalized relative entropy. Entropy 19(6):269

    Article  Google Scholar 

  13. Mahajan SH, Harpale VK (2015) Adaptive and non-adaptive image interpolation techniques. In: 2015 international conference on computing communication control and automation (ICCUBEA). IEEE, pp 772–775

  14. Miklos P (2004) Image interpolation techniques. 2nd Siberian-Hungarian joint symposium on intelligent systems

  15. Parker JA, Kenyon RV, Troxel DE (1983) Comparison of interpolating methods for image resampling. IEEE Trans Med Imaging 2(1):31–39

    Article  Google Scholar 

  16. Reichenbach SE, Geng F (2003) Two-dimensional cubic convolution. IEEE Trans Image Process 12(8):857–865

    Article  MathSciNet  MATH  Google Scholar 

  17. Russakoff DB, Tomasi C, Rohlfing T, Maurer CR Jr (2004) Image similarity using mutual information of regions. In: European conference on computer vision. Springer, Berlin, pp 596–607

  18. Stoer J, Bulirsch R (2013) Introduction to numerical analysis, vol 12. Springer Science & Business Media

  19. Unser M, Aldroubi A, Eden M (1991) Fast b-spline transforms for continuous image representation and interpolation. IEEE Trans Pattern Anal Mach Intell 3:277–285

    Article  Google Scholar 

  20. Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13 (4):600–612

    Article  Google Scholar 

  21. Wick DV, Martinez T (2004) Adaptive optical zoom. Opt Eng 43(1):8–9

    Article  Google Scholar 

  22. Zhang L, Wu X (2006) An edge-guided image interpolation algorithm via directional filtering and data fusion. IEEE Trans Image Process 15(8):2226–2238

    Article  Google Scholar 

  23. Zhou D, Shen X, Dong W (2012) Image zooming using directional cubic convolution interpolation. IET Image Process 6(6):627–634

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vinay Kumar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bhushan, V., Kumar, V. Adaptive variable order polynomial based digital zoom of images. Multimed Tools Appl 77, 25131–25148 (2018). https://doi.org/10.1007/s11042-018-5778-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-018-5778-y

Keywords

Navigation