Image enhancement algorithm using adaptive fractional differential mask technique

Xuefeng Zhang; Hui Yan

doi:10.3934/mfc.2019022

Article Contents

2019, Volume 2, Issue 4: 347-359. Doi: 10.3934/mfc.2019022

This issue Previous Article A single finite-time synchronization scheme of time-delay chaotic system with external periodic disturbance Next Article

Image enhancement algorithm using adaptive fractional differential mask technique

Xuefeng Zhang^, and
Hui Yan

Northeastern University, 110819, China

^* Corresponding author: Xuefeng Zhang
^* Corresponding author: Xuefeng Zhang

Published: December 2019

The first author is supported by National Natural Science Foundation of P.R.China(61603055)

Abstract / Introduction Full Text(HTML) Figure(11) / Table(2) Related Papers Cited by

Abstract

This paper addresses a novel adaptive fractional order image enhancement method. Firstly, an image segmentation algorithm is proposed, it combines Otsu algorithm and rough entropy to segment image accurately into the objet and the background. On the basis of image segmentation and the knowledge of fractional order differential, an image enhancement model is established. The rough characteristics of each average gray value are obtained by image segmentation method, through these features, we can determine the optimal fractional order of image enhancement. Then image will be enhanced using fractional order differential mask, from which fractional order is obtained adaptively. Several images are used for experiments, the proposed model is compared with other models, and the results of comparison exhibit the superiority of our algorithm in terms of image quality measures.

Keywords:

Mathematics Subject Classification: Primary: 68W40; Secondary: 49M99.

Citation:

Full Text(HTML)

Figure 1. Amplitude - frequency characteristic curves of fractional differential operators (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

Download: Full-size image PowerPoint slide

Figure 2. The superposition of partial differential mask by 8 directions

Download: Full-size image PowerPoint slide

Figure 3. Segmentation results of Lena

Download: Full-size image PowerPoint slide

Figure 4. Segmentation results of Fishing boat

Download: Full-size image PowerPoint slide

Figure 5. The block diagram of the proposed model in this paper

Download: Full-size image PowerPoint slide

Figure 6. The original images

Download: Full-size image PowerPoint slide

Figure 7. Enhancement results of Lena

Download: Full-size image PowerPoint slide

Figure 8. Enhancement results of the moving head

Download: Full-size image PowerPoint slide

Figure 9. Enhancement results of the medical image

Download: Full-size image PowerPoint slide

Figure 10. Enhancement results of the aerial image

Download: Full-size image PowerPoint slide

Figure 11. Enhancement results of the airplane image

Download: Full-size image PowerPoint slide

Table 1. The information entropy of images

			information entropy
	original	$ 0.2 - $	$ 0.8 - $	AFDA	our
Fig.	image	order	order	method	method
7	5.0572	5.0803	5.2640	5.1225	15.2047
8	3.5754	3.5843	3.6526	3.6005	3.6358
9	4.9163	4.9366	5.0044	4.9196	4.9273
10	5.1387	5.2031	4.9300	5.2184	5.3338
11	5.5089	5.5302	6.7563	5.6435	5.9013

| Show Table

DownLoad: CSV

Table 2. The average gradient of images

			average gradient
	original	$ 0.2 - $	$ 0.8 - $	AFDA	our
Fig.	image	order	order	method	method
7	3.0202	3.6840	33.3047	4.6871	10.5149
8	2.2055	2.3810	6.1382	3.9755	4.0240
9	1.5844	1.7256	5.3264	4.3742	2.5745
10	9.3186	12.9233	50.3865	19.8006	23.5776
11	4.3996	5.7272	38.6371	7.5458	14.5694

| Show Table

DownLoad: CSV

Related Papers

Cited by

References

[1]	M. R. S. Ammi and I. Jamial, Finite difference and Legendre spectral method for a time-fractional diffusion-convection equation for image restoration, Discrete Contin. Dyn. Syst. Ser. S, 11 (2018), 103-117. doi: 10.3934/dcdss.2018007.
[2]	J. Bai and X. C. Feng, Fractional-order anisotropic diffusion for image denoising, IEEE Trans. Image Process, 16 (2007), 2492-2502. doi: 10.1109/TIP.2007.904971.
[3]	K. Bashir, X. Tao and S. Gong, Gait Recognition Using Gait Entropy Image, International Conference on Crime Detection and Prevention, London, UK, 2010.
[4]	Y. Q. Chen and B. M. Vinagre, A new IIR-type digital fractional order differentiator, Signal Processing, 83 (2003), 2359-2365. doi: 10.1016/S0165-1684(03)00188-9.
[5]	D. L. Chen, Y. Q. Chen and D. Y. Xue, 1-D and 2-D digital fractional-order Savitzky-Golay differentiator, Springer, 6 (2012), 503-511.
[6]	S. Q. Chen and F. Q. Zhao, The adaptive fractional order differential model for image enhancement based on segmentation, Int. J. Pattern Recognit. Artif. Intell., 32 (2018), 15 pp. doi: 10.1142/S0218001418540058.
[7]	F. F. Dong and Y. M. Chen, A fractional-order derivative based variational framework for image denoising, Inverse Probl. Imaging, 10 (2016), 27-50. doi: 10.3934/ipi.2016.10.27.
[8]	C. B. Gao and J. L. Zhou, Image enhancement based on quaternion fractional directional differentiation, (Chinese) Acta Automat. Sinica, 37 (2011), 150-159. doi: 10.3724/SP.J.1004.2011.00150.
[9]	S. F. Gull and J. Skilling, The entropy of an image, SIAM-AMS Proc., Amer. Math. Soc., Providence, RI, 14 (1984), 167–-189.
[10]	J. Guo, C. E. Siong and D. Rajan, Foreground motion detection by difference-based spatial temporal entropy image, Tencon IEEE Region 10 Conference, Chiang Mai, Thailand, 2004.
[11]	F. Y. Hu, An adaptive approach for texture enhancement based on a fractional differential operator with non-integer step and order, Neurocomputing, 158 (2015), 295-306. doi: 10.1016/j.neucom.2014.10.013.
[12]	G. Huang, L. Xu and Y. F. Pu, Summary of research on image processing using fractional calculus, Application Research of Computers, 27 (2012), 1214-1229.
[13]	Hungenahally and Suresh, Neural Basis for The Design of Fractional-Order Perceptual Filters: Applications in Image Enhancement and Coding, IEEE International Conference on Systems, Vancouver, BC, Canada, 1995.
[14]	K. Kim, S. Kim and K. S. Kim, Effective image enhancement techniques for fog-affected indoor and outdoor images, IET Image Processing, 12 (2018), 465-471. doi: 10.1049/iet-ipr.2016.0819.
[15]	Kim, Yunseop, R. G. Evans and W. M. Iversen, Remote sensing and control of an irrigation system using a distributed wireless sensor network, IEEE Transactions on Instrumentation and Measurement, 57 (2008), 1379-1387.
[16]	T. Konno, Selective targeting of anti-cancer drug and simultaneous image enhancement in solid tumors by arterially administered lipid contrast medium, Cancer, 54 (1934), 2367-2374. doi: 10.1002/1097-0142(19841201)54:11<2367::AID-CNCR2820541111>3.0.CO;2-F.
[17]	H. F. Li, Z. G. Yu and C. L. Mao, Fractional differential and variational method for image fusion and super-resolution, Neurocomputing, 171 (2016), 138-148. doi: 10.1016/j.neucom.2015.06.035.
[18]	B. Li and X. Wei, Image denoising and enhancement based on adaptive fractional calculus of small probability strategy, Neurocomputing, 175 (2016), 704-714. doi: 10.1016/j.neucom.2015.10.115.
[19]	B. Li and X. Wei, Adaptive fractional differential approach and its application to medical image enhancement, Computers and Electrical Engineering, 45 (2015), 324-335. doi: 10.1016/j.compeleceng.2015.02.013.
[20]	Y. W. Liu, Remote sensing image enhancement based on fractional differential, 2010 International Conference on Computational and Information Sciences, 2010, 17–19. doi: 10.1109/ICCIS.2010.218.
[21]	A. Namburu, K. S. Samayamantula and S. R. Edara, Generalised rough intuitionistic fuzzy c-means for magnetic resonance brain image segmentation, IET Image Processing, 11 (2017), 777-785. doi: 10.1049/iet-ipr.2016.0891.
[22]	Nobuyuki. Otsu, A threshold selection method from gray-level histograms, IEEE Transactions on Systems, Man, and Cybernetics, 9 (1979), 62-66. doi: 10.1109/TSMC.1979.4310076.
[23]	S. K. Pal and P. Mitra, Multispectral image segmentation using the rough-set-initialized EM algorithm, IEEE Transactions on Geoscience and Remote Sensing, 40 (2002), 2495-2501. doi: 10.1109/TGRS.2002.803716.
[24]	S. K. Pal, B. U. Shankar and P. Mitra, Granular computing, rough entropy and object extraction, Pattern Recognition Letters, 26 (2005), 2509-2517. doi: 10.1016/j.patrec.2005.05.007.
[25]	W. Pan, K. Qin and Y. Chen, An adaptable-multilayer fractional Fourier transform approach for image registration, IEEE Trans Pattern Anal Mach Intell, 31 (2008), 400-414.
[26]	Z. Pawlak, Rough sets, Internat. J. Comput. Inform. Sci., 11 (1982), 341-356. doi: 10.1007/BF01001956.
[27]	A. Petrosino and G. Salvi, Rough fuzzy set based scale space transforms and their use in image analysis, Internat. J. Approx. Reason, 41 (2006), 212-228. doi: 10.1016/j.ijar.2005.06.015.
[28]	I. Podlubny, Fractional-order systems and PI$^\lambda$D$^\mu$-Controllers, IEEE Trans. Automat. Control, 44 (1999), 208-214. doi: 10.1109/9.739144.
[29]	Y. F. Pu, J. L. Zhou and X. Yuan, Fractional differential mask: A fractional differential-based approach for multiscale texture enhancement, IEEE Trans. Image Process, 19 (2010), 491–-511. doi: 10.1109/TIP.2009.2035980.
[30]	Y. F. Pu, P. Siarry, A. Chatterjee, Z. N. Wang, Z. Yi, Y. G. Liu, J. L. Zhou and Y. Wang, A fractional-order variational framework for Retinex: Fractional-order partial differential equation-based formulation for multi-scale nonlocal contrast enhancement with texture preserving, IEEE Trans. Image Process., 27 (2018), 1214–-1229. doi: 10.1109/TIP.2017.2779601.
[31]	Y. F. Pu and W. X. Wang, Fractional differential masks of digital image and their numerical implementation algorithms, Acta Automatica Sinica, 33 (2007), 1128-1135.
[32]	S. Roy, P. Shivakumara, H. A. Jalab, R. W. Ibrahim, U. Pal and T. Lu, Fractional poisson enhancement model for text detection and recognition in video frames, Pattern Recognitio, 52 (2016), 433-447. doi: 10.1016/j.patcog.2015.10.011.
[33]	Shugo, Hamahashi, O. Shuichi and H. Kitano, Detection of nuclei in 4D Nomarski DIC microscope images of early Caenorhabditis elegans embryos using local image entropy and object tracking, Bmc Bioinformatics, 6 (2005), 125 pp.
[34]	C. Studholme, D. L. G. Hill and D. J. Hawkes, An overlap invariant entropy measure of 3D medical image alignment, Pattern Recognition, 32 (1999), 71-86. doi: 10.1016/S0031-3203(98)00091-0.
[35]	R. Tao, L. Qi and Y. Wang, Theory and Applications of The Fractional Fourier Transform, Tsinghua University Press, 2004.
[36]	R. Tao, B. Deng and Y. Wang, Research progress of the fractional Fourier in signal processing, Sci. China Ser. F, 49 (2006), 1-25. doi: 10.1007/s11432-005-0240-y.
[37]	C. C. Wang, B. C. Jiang, Y. S. Chou and C. C. Chu, Multivariate analysis-based image enhancement model for machine vision inspection, International Journal of Production Research, 49 (2011), 2999-3021. doi: 10.1080/00207541003801242.
[38]	Q. Yang, Y. Z. Zhang, T. B. Zhao and Y. Q. Chen, Single image super-resolution using self-optimizing mask via fractional-order gradient interpolation and reconstruction, ISA Transactions, 82 (2018), 163-171. doi: 10.1016/j.isatra.2017.03.001.
[39]	X. F. Zhang and L. L. Shang, Application of Image Segmentation Algorithm Based on VPRS-PSO Method, Control Engineering of China, 18 2011.
[40]	X. F. Zhang and J. K. Shang, Image segmentation algorithm based on Monte Carlo methods and rough entropy standard, Journal of Petrochemical Universities, 22 (2009), 94-98.
[41]	W. Z. Zhu, H. L. Jiang, E. Wang, Y. Hou, L. D. Xian and J. Debnath, X-ray image global enhancement algorithm in medical image classification, Discrete Contin. Dyn. Syst. Ser. S, 12 (2019), 1297-1309.