# 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 and 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. [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. [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. [4] A. Bicer, Capraro and m.m. capraro, integrated stem assessment model, vol. 13, 2017, 3959-3968. [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. [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. [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. [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. [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. [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. [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. [12] D. Guo, J. Yan and X. Qu, High quality multi-focus image fusion using self-similarity and depth information, Optics Communications, 138-144. [13] F. Jing, M. Li, H. J. Zhang and B. Zhang, Spectral clustering image segmentation based on sparse matrix, 4 (2017), 1308-1313. [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. [15] J. Liang, Y. Han and Q. Hu, Semi-supervised image clustering with multi-modal information, Multimedia Systems, 22 (2016), 149-160. [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. [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. [18] A. Takahashi, Development status of condensed cluster fusion theory, Current Science, 108 (2015), 514-515. [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. [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. [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. [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. [23] F. X. Yang, I/o mapping algorithm based on semantic overlay fusion, Bulletin of Science and Technology, 60-62. [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. [25] J. Zhang and H. H. Fan, An improved image segmentation algorithm and simulation based on fuzzy clustering, Computer Simulation.

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##### References:
 [1] R. Adillon and L. Jorba, Quantified trapezoidal fuzzy numbers, Journal of Intelligent & Fuzzy Systems, 33 (2017), 601-611. [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. [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. [4] A. Bicer, Capraro and m.m. capraro, integrated stem assessment model, vol. 13, 2017, 3959-3968. [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. [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. [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. [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. [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. [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. [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. [12] D. Guo, J. Yan and X. Qu, High quality multi-focus image fusion using self-similarity and depth information, Optics Communications, 138-144. [13] F. Jing, M. Li, H. J. Zhang and B. Zhang, Spectral clustering image segmentation based on sparse matrix, 4 (2017), 1308-1313. [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. [15] J. Liang, Y. Han and Q. Hu, Semi-supervised image clustering with multi-modal information, Multimedia Systems, 22 (2016), 149-160. [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. [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. [18] A. Takahashi, Development status of condensed cluster fusion theory, Current Science, 108 (2015), 514-515. [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. [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. [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. [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. [23] F. X. Yang, I/o mapping algorithm based on semantic overlay fusion, Bulletin of Science and Technology, 60-62. [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. [25] J. Zhang and H. H. Fan, An improved image segmentation algorithm and simulation based on fuzzy clustering, Computer Simulation.
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
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