# American Institute of Mathematical Sciences

August & September  2019, 12(4&5): 1233-1249. doi: 10.3934/dcdss.2019085

## Analysis of the clustering fusion algorithm for multi-band color image

 1 Beijing Research Center for Information Technology, in Agriculture, Beijing 100097, China 2 National Engineering Research Center for Information, Technology in Agriculture, Beijing 100097, China 3 Beijing Key Lab of Digital Plant, Beijing 100097, China 4 Department of Mathematics and Statistics, The University of North Carolina at Greensboro Greensboro, NC, 27402, United States

* Corresponding author: Xinyu Guo

Received  August 2017 Revised  January 2018 Published  November 2018

Because of the limitations of the technical conditions, the traditional algorithms can not be mapped with many kinds of color, and the treatment effect is poor, which is not conducive to human eye observation. A clustering fusion algorithm based on D-S evidence theory is proposed in this paper to make salt denoising and Gauss denoising operation for the multi-band color image, to improve the image recognition, and better reflect the objective reality, which is not limited by technical conditions; the denoised images are made texture features and edge features extraction; these two kinds of features are fused and carried out the probability distribution to solve the probability of that the each pixel belongs to each class; Based on the DS evidence combination, the probability of four channels is fused, and according to the probability of what kind of each pixel belonging is the largest, it is clustered. Experimental results show that the proposed algorithm can combine different bands of color images to different levels of target features, and retain more effective information, which is conducive to target recognition and detection.

Citation: Jiangchuan Fan, Xinyu Guo, Jianjun Du, Weiliang Wen, Xianju Lu, Brahmani Louiza. Analysis of the clustering fusion algorithm for multi-band color image. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1233-1249. doi: 10.3934/dcdss.2019085
##### References:
 [1] R. Adillon and L. Jorba, Quantified trapezoidal fuzzy numbers, Journal of Intelligent & Fuzzy Systems, 33 (2017), 601-611. Google Scholar [2] E. Baco, O. Ukimura, E. Rud, L. Vlatkovic, A. Svindland, M. Aron, S. Palmer, T. Matsugasumi, A. Marien and J. C. Bernhard, Magnetic resonance imaging-transectal ultrasound image-fusion biopsies accurately characterize the index tumor: correlation with step-sectioned radical prostatectomy specimens in 135 patients, European Urology, 67 (2015), 787-794. Google Scholar [3] I. Barnaure, P. Pollak, S. Momjian, J. Horvath, K. O. Lovblad, C. Bo x, J. Remuinan, P. Burkhard and M. I. Vargas, Evaluation of electrode position in deep brain stimulation by image fusion (mri and ct)., Neuroradiology, 57 (2015), 903-908. Google Scholar [4] A. Bicer, Capraro and m.m. capraro, integrated stem assessment model, vol. 13, 2017, 3959-3968.Google Scholar [5] M. Bonamy, B. LévÊque and A. Pinlou, Planar graphs with delta $\ge 7$ and no triangle adjacent to a c-4 are minimally edge and total choosable, Discrete Mathematics and Theoretical Computer Science, 17 (2016), 131-145. Google Scholar [6] P. S. Brezavscek A. and A. Znidarsic, Factors influencing the behavioural intention to use statistical software: The perspective of the slovenian students of social sciences, Eurasia Journal of Mathematics Science and Technology Education, (), 953-986. Google Scholar [7] C. Chen and J. Shi, Chinese local government's behavior in land supply in the context of housing market macro-control, Journal of Interdisciplinary Mathematics, 20 (2017), 1289-1306. Google Scholar [8] G. H. Chen, Y. Zhao and B. Su, Raw material inventory optimization for mto enterprises under price fluctuations, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 255-270. Google Scholar [9] M. Fei, W. Jiang, W. Mao and Z. Song, New fusional framework combining sparse selection and clustering for key frame extraction, Iet Computer Vision, 10 (2016), 280-287. Google Scholar [10] W. Gao and W. Wang, New isolated toughness condition for fractional (g, f, n)-critical graphs, Colloquium Mathematicum, 147 (2017), 55-65. doi: 10.4064/cm6713-8-2016. Google Scholar [11] M. Ghahremani and H. Ghassemian, Remote sensing image fusion using ripplet transform and compressed sensing, International Journal of Remote Sensing, 12 (2015), 4131-4143. Google Scholar [12] D. Guo, J. Yan and X. Qu, High quality multi-focus image fusion using self-similarity and depth information, Optics Communications, 138-144.Google Scholar [13] F. Jing, M. Li, H. J. Zhang and B. Zhang, Spectral clustering image segmentation based on sparse matrix, 4 (2017), 1308-1313.Google Scholar [14] Y. Li, C. Jia, X. Kong, L. Yang and J. Yu, Locally weighted fusion of structural and attribute information in graph clustering, IEEE Transactions on Cybernetics, PP (2017), 1-14. Google Scholar [15] J. Liang, Y. Han and Q. Hu, Semi-supervised image clustering with multi-modal information, Multimedia Systems, 22 (2016), 149-160. Google Scholar [16] H. J. Liu and X. B. Liu, Relationship between paternalistic leadership and employee's voice behavior based on regression analysis, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 205-215. Google Scholar [17] P. S., B. M. and R. G., Tephra redeposition and mixing in a late-glacial hillside basin determined by fusion of clustering analyses of glass-shard geochemistry, in Journal of Quaternary Science, 82 (2000), 789-802.Google Scholar [18] A. Takahashi, Development status of condensed cluster fusion theory, Current Science, 108 (2015), 514-515. Google Scholar [19] B. K. Teh and S. A. Cheong, Cluster fusion-fission dynamics in the singapore stock exchange, European Physical Journal B, 88 (2015), 1-14. Google Scholar [20] C. Y. Wang, W. Zhao, Q. Liu and H. W. Chen, Optimization of the tool selection based on big data, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 341-360. Google Scholar [21] G. Wei, S. Li and M. R. Farahani, Szeged related indices of tuac6[p, q], Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 553-563. doi: 10.1080/09720529.2016.1228312. Google Scholar [22] Z. Y. Q. and T. J. L., Clustering sorting algorithm based on digital channelized receiver, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 143-148.Google Scholar [23] F. X. Yang, I/o mapping algorithm based on semantic overlay fusion, Bulletin of Science and Technology, 60-62.Google Scholar [24] S. Yin, L. Cao, Y. Ling and G. Jin, One color contrast enhanced infrared and visible image fusion method, Infrared & Laser Engineering, 53 (2010), 146-150. Google Scholar [25] J. Zhang and H. H. Fan, An improved image segmentation algorithm and simulation based on fuzzy clustering, Computer Simulation.Google Scholar

show all references

##### References:
 [1] R. Adillon and L. Jorba, Quantified trapezoidal fuzzy numbers, Journal of Intelligent & Fuzzy Systems, 33 (2017), 601-611. Google Scholar [2] E. Baco, O. Ukimura, E. Rud, L. Vlatkovic, A. Svindland, M. Aron, S. Palmer, T. Matsugasumi, A. Marien and J. C. Bernhard, Magnetic resonance imaging-transectal ultrasound image-fusion biopsies accurately characterize the index tumor: correlation with step-sectioned radical prostatectomy specimens in 135 patients, European Urology, 67 (2015), 787-794. Google Scholar [3] I. Barnaure, P. Pollak, S. Momjian, J. Horvath, K. O. Lovblad, C. Bo x, J. Remuinan, P. Burkhard and M. I. Vargas, Evaluation of electrode position in deep brain stimulation by image fusion (mri and ct)., Neuroradiology, 57 (2015), 903-908. Google Scholar [4] A. Bicer, Capraro and m.m. capraro, integrated stem assessment model, vol. 13, 2017, 3959-3968.Google Scholar [5] M. Bonamy, B. LévÊque and A. Pinlou, Planar graphs with delta $\ge 7$ and no triangle adjacent to a c-4 are minimally edge and total choosable, Discrete Mathematics and Theoretical Computer Science, 17 (2016), 131-145. Google Scholar [6] P. S. Brezavscek A. and A. Znidarsic, Factors influencing the behavioural intention to use statistical software: The perspective of the slovenian students of social sciences, Eurasia Journal of Mathematics Science and Technology Education, (), 953-986. Google Scholar [7] C. Chen and J. Shi, Chinese local government's behavior in land supply in the context of housing market macro-control, Journal of Interdisciplinary Mathematics, 20 (2017), 1289-1306. Google Scholar [8] G. H. Chen, Y. Zhao and B. Su, Raw material inventory optimization for mto enterprises under price fluctuations, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 255-270. Google Scholar [9] M. Fei, W. Jiang, W. Mao and Z. Song, New fusional framework combining sparse selection and clustering for key frame extraction, Iet Computer Vision, 10 (2016), 280-287. Google Scholar [10] W. Gao and W. Wang, New isolated toughness condition for fractional (g, f, n)-critical graphs, Colloquium Mathematicum, 147 (2017), 55-65. doi: 10.4064/cm6713-8-2016. Google Scholar [11] M. Ghahremani and H. Ghassemian, Remote sensing image fusion using ripplet transform and compressed sensing, International Journal of Remote Sensing, 12 (2015), 4131-4143. Google Scholar [12] D. Guo, J. Yan and X. Qu, High quality multi-focus image fusion using self-similarity and depth information, Optics Communications, 138-144.Google Scholar [13] F. Jing, M. Li, H. J. Zhang and B. Zhang, Spectral clustering image segmentation based on sparse matrix, 4 (2017), 1308-1313.Google Scholar [14] Y. Li, C. Jia, X. Kong, L. Yang and J. Yu, Locally weighted fusion of structural and attribute information in graph clustering, IEEE Transactions on Cybernetics, PP (2017), 1-14. Google Scholar [15] J. Liang, Y. Han and Q. Hu, Semi-supervised image clustering with multi-modal information, Multimedia Systems, 22 (2016), 149-160. Google Scholar [16] H. J. Liu and X. B. Liu, Relationship between paternalistic leadership and employee's voice behavior based on regression analysis, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 205-215. Google Scholar [17] P. S., B. M. and R. G., Tephra redeposition and mixing in a late-glacial hillside basin determined by fusion of clustering analyses of glass-shard geochemistry, in Journal of Quaternary Science, 82 (2000), 789-802.Google Scholar [18] A. Takahashi, Development status of condensed cluster fusion theory, Current Science, 108 (2015), 514-515. Google Scholar [19] B. K. Teh and S. A. Cheong, Cluster fusion-fission dynamics in the singapore stock exchange, European Physical Journal B, 88 (2015), 1-14. Google Scholar [20] C. Y. Wang, W. Zhao, Q. Liu and H. W. Chen, Optimization of the tool selection based on big data, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 341-360. Google Scholar [21] G. Wei, S. Li and M. R. Farahani, Szeged related indices of tuac6[p, q], Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 553-563. doi: 10.1080/09720529.2016.1228312. Google Scholar [22] Z. Y. Q. and T. J. L., Clustering sorting algorithm based on digital channelized receiver, Journal of Discrete Mathematical Sciences & Cryptography, 20 (2017), 143-148.Google Scholar [23] F. X. Yang, I/o mapping algorithm based on semantic overlay fusion, Bulletin of Science and Technology, 60-62.Google Scholar [24] S. Yin, L. Cao, Y. Ling and G. Jin, One color contrast enhanced infrared and visible image fusion method, Infrared & Laser Engineering, 53 (2010), 146-150. Google Scholar [25] J. Zhang and H. H. Fan, An improved image segmentation algorithm and simulation based on fuzzy clustering, Computer Simulation.Google Scholar
SAR image
TM image
The feature extraction results of the test images by Sobel and Canny operators
Comparison results of clustering fusion results by two different algorithms
Observation parameters of TM image
 Sensor Band wavelength ($\mu$m) TM 1 0.45$\sim$0.52 blue light band 2 0.52$\sim$0.60 green light band 3 0.63$\sim$0.69 Red band, above the visible light band; 4 0.76$\sim$0.90 Near infrared band 5 1.22$\sim$1.75 Middle infrared band 6 10.4$\sim$12.5 Thermal infrared band 7 2.08$\sim$2.35 Far infrared band
 Sensor Band wavelength ($\mu$m) TM 1 0.45$\sim$0.52 blue light band 2 0.52$\sim$0.60 green light band 3 0.63$\sim$0.69 Red band, above the visible light band; 4 0.76$\sim$0.90 Near infrared band 5 1.22$\sim$1.75 Middle infrared band 6 10.4$\sim$12.5 Thermal infrared band 7 2.08$\sim$2.35 Far infrared band
evaluation index value of clustering fusion of SAR image and TM image
 Different algorithms Evaluating indicator Average gradient Information entropy Standard deviation Edge retention Traditional algorithm Band 1 22.5114 7.76 7.0154 52.7669 Band 4 22.4716 7.72 7.0692 48.2687 Band 7 21.0537 6.85 6.9837 45.5618 The proposed algorithm Band 1 32.1645 7.26 6.5945 65.3746 Band 4 33.0692 7.31 5.8861 62.3149 Band 7 32.8974 6.43 5.8233 55.8862
 Different algorithms Evaluating indicator Average gradient Information entropy Standard deviation Edge retention Traditional algorithm Band 1 22.5114 7.76 7.0154 52.7669 Band 4 22.4716 7.72 7.0692 48.2687 Band 7 21.0537 6.85 6.9837 45.5618 The proposed algorithm Band 1 32.1645 7.26 6.5945 65.3746 Band 4 33.0692 7.31 5.8861 62.3149 Band 7 32.8974 6.43 5.8233 55.8862
 [1] Jingwei Liang, Jia Li, Zuowei Shen, Xiaoqun Zhang. Wavelet frame based color image demosaicing. Inverse Problems & Imaging, 2013, 7 (3) : 777-794. doi: 10.3934/ipi.2013.7.777 [2] Ruiliang Zhang, Xavier Bresson, Tony F. Chan, Xue-Cheng Tai. Four color theorem and convex relaxation for image segmentation with any number of regions. Inverse Problems & Imaging, 2013, 7 (3) : 1099-1113. doi: 10.3934/ipi.2013.7.1099 [3] Juan C. Moreno, V. B. Surya Prasath, João C. Neves. Color image processing by vectorial total variation with gradient channels coupling. Inverse Problems & Imaging, 2016, 10 (2) : 461-497. doi: 10.3934/ipi.2016008 [4] Xavier Bresson, Tony F. Chan. Fast dual minimization of the vectorial total variation norm and applications to color image processing. Inverse Problems & Imaging, 2008, 2 (4) : 455-484. doi: 10.3934/ipi.2008.2.455 [5] J. Delon, A. Desolneux, Jose-Luis Lisani, A. B. Petro. Automatic color palette. Inverse Problems & Imaging, 2007, 1 (2) : 265-287. doi: 10.3934/ipi.2007.1.265 [6] Inês Cruz, M. Esmeralda Sousa-Dias. Reduction of cluster iteration maps. Journal of Geometric Mechanics, 2014, 6 (3) : 297-318. doi: 10.3934/jgm.2014.6.297 [7] Valentin Ovsienko, MichaeL Shapiro. Cluster algebras with Grassmann variables. Electronic Research Announcements, 2019, 26: 1-15. doi: 10.3934/era.2019.26.001 [8] Yunmei Chen, Jiangli Shi, Murali Rao, Jin-Seop Lee. Deformable multi-modal image registration by maximizing Rényi's statistical dependence measure. Inverse Problems & Imaging, 2015, 9 (1) : 79-103. doi: 10.3934/ipi.2015.9.79 [9] Octav Cornea and Francois Lalonde. Cluster homology: An overview of the construction and results. Electronic Research Announcements, 2006, 12: 1-12. [10] Z. G. Feng, Kok Lay Teo, N. U. Ahmed, Yulin Zhao, W. Y. Yan. Optimal fusion of sensor data for Kalman filtering. Discrete & Continuous Dynamical Systems - A, 2006, 14 (3) : 483-503. doi: 10.3934/dcds.2006.14.483 [11] Gerhard Keller, Carlangelo Liverani. Coupled map lattices without cluster expansion. Discrete & Continuous Dynamical Systems - A, 2004, 11 (2&3) : 325-335. doi: 10.3934/dcds.2004.11.325 [12] Xiao Lan Zhu, Zhi Guo Feng, Jian Wen Peng. Robust design of sensor fusion problem in discrete time. Journal of Industrial & Management Optimization, 2017, 13 (2) : 825-834. doi: 10.3934/jimo.2016048 [13] Takashi Hara and Gordon Slade. The incipient infinite cluster in high-dimensional percolation. Electronic Research Announcements, 1998, 4: 48-55. [14] Shuping Li, Zhen Jin. Impacts of cluster on network topology structure and epidemic spreading. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3749-3770. doi: 10.3934/dcdsb.2017187 [15] Xiwei Liu, Tianping Chen, Wenlian Lu. Cluster synchronization for linearly coupled complex networks. Journal of Industrial & Management Optimization, 2011, 7 (1) : 87-101. doi: 10.3934/jimo.2011.7.87 [16] S.M. Booker, P.D. Smith, P. Brennan, R. Bullock. In-band disruption of a nonlinear circuit using optimal forcing functions. Discrete & Continuous Dynamical Systems - B, 2002, 2 (2) : 221-242. doi: 10.3934/dcdsb.2002.2.221 [17] Stéphane Heuraux, Filipe da Silva. Simulations on wave propagation in fluctuating fusion plasmas for Reflectometry applications and new developments. Discrete & Continuous Dynamical Systems - S, 2012, 5 (2) : 307-328. doi: 10.3934/dcdss.2012.5.307 [18] Michael Gekhtman, Michael Shapiro, Serge Tabachnikov, Alek Vainshtein. Higher pentagram maps, weighted directed networks, and cluster dynamics. Electronic Research Announcements, 2012, 19: 1-17. doi: 10.3934/era.2012.19.1 [19] A. Procacci, Benedetto Scoppola. Convergent expansions for random cluster model with $q>0$ on infinite graphs. Communications on Pure & Applied Analysis, 2008, 7 (5) : 1145-1178. doi: 10.3934/cpaa.2008.7.1145 [20] Yinying Duan, Yong Ye, Zhichao Liu. Risk assessment for enterprise merger and acquisition via multiple classifier fusion. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 747-759. doi: 10.3934/dcdss.2019049

2018 Impact Factor: 0.545