Abstract
The fuzzy c-means clustering with guided image filter (GF) is a useful method for image segmentation. The single-channel GF can be efficiently applied to the gray-scale guidance image, but for the color guidance image, due to the high run-time overhead on the calculation of the inverse of the covariance matrix, it is a hard work to perform the multi-channel GF. To address this issue, we propose a novel weighting multi-channel guided image filter (WMGF) method. In this method, each channel of the color guidance image is utilized to guide the filtering for the input image independently and a novel weight is defined for each channel according to the variance of the image pixels in a local window, which greatly eliminates the mutual influence between different channels and brings about a low run-time overhead. In addition, based on the WMGF method, we present a new fuzzy c-means clustering algorithm (\(\hbox {FCM}_{\scriptscriptstyle {WMGF }}\)) for the color image segmentation, in which the WMGF is performed on the membership matrix in each iteration of the fuzzy c-means clustering. To further enhance the different noise-immunity and edge preservation, the multivariate morphological reconstruction (MMR) method is introduced into the proposed fuzzy clustering method (MMR\(\_\hbox {FCM}_{\scriptscriptstyle {WMGF }}\)) to obtain higher segmentation precision. Experiments on color images with Salt & Pepper and Gaussian noises demonstrate the superiority of the proposed methods.
Similar content being viewed by others
References
Ahmed MN, Yamany SM, Mohamed N, Farag AA, Moriarty T (2002) A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data. IEEE Trans Med Imaging 21(3):193–199
Aragon Y, Casanova S, Chambers R, Leconte E (2005) Conditional ordering using nonparametric expectiles. J Off Stat 21(4):617–633
Arbelaez P, Maire M, Fowlkes C, Malik J (2010) Contour detection and hierarchical image segmentation. IEEE Trans Pattern Anal Mach Intell 33(5):898–916
Bezdek JC, Ehrlich R, Full W (1984) Fcm: the fuzzy c-means clustering algorithm. Comput Geosci 10(2–3):191–203
Carpineto C, Romano G (2012) Consensus clustering based on a new probabilistic rand index with application to subtopic retrieval. IEEE Trans Pattern Anal Mach Intell 34(12):2315–2326
Carson C, Belongie S, Greenspan H, Malik J (2002) Blobworld: Image segmentation using expectation-maximization and its application to image querying. IEEE Trans Pattern Anal Mach Intell 8:1026–1038
Chen S, Zhang D (2004) Robust image segmentation using fcm with spatial constraints based on new kernel-induced distance measure. IEEE Trans Syst Man Cybern Part B (Cybern) 34(4):1907–1916
De A, Guo C (2014) An image segmentation method based on the fusion of vector quantization and edge detection with applications to medical image processing. Int J Mach Learn Cybern 5(4):543–551
d’Ornellas MC, da Costa JATB (2007) Color mathematical morphology based on partial ordering of spectra. In: XX Brazilian symposium on computer graphics and image processing (SIBGRAPI 2007), pp. 37–44. IEEE
Du M, Ding S, Xue Y (2018) A robust density peaks clustering algorithm using fuzzy neighborhood. Int J Mach Learn Cybern 9(7):1131–1140
Gong M, Liang Y, Shi J, Ma W, Ma J (2012) Fuzzy c-means clustering with local information and kernel metric for image segmentation. IEEE Trans Image Process 22(2):573–584
Guo L, Chen L, Chen CP, Zhou J (2018) Integrating guided filter into fuzzy clustering for noisy image segmentation. Digital Signal Process 83:235–248
Guo L, Chen L, Wu Y, Chen CP (2017) Image guided fuzzy c-means for image segmentation. Int J Fuzzy Syst 19(6):1660–1669
He K, Sun J, Tang X (2012) Guided image filtering. IEEE Trans Pattern Anal Mach Intell 35(6):1397–1409
Hu T, Yang M, Yang W, Li A (2019) An end-to-end differential network learning method for semantic segmentation. Int J Mach Learn Cybern 10(7):1909–1924
Jin L, Li D, Song E (2009) Combining vector ordering and spatial information for color image interpolation. Image Vis Comput 27(4):410–416
Kumar S, Pant M, Kumar M, Dutt A (2018) Colour image segmentation with histogram and homogeneity histogram difference using evolutionary algorithms. Int J Mach Learn Cybern 9(1):163–183
Lei T, Jia X, Zhang Y, He L, Meng H, Nandi AK (2018) Significantly fast and robust fuzzy c-means clustering algorithm based on morphological reconstruction and membership filtering. IEEE Trans Fuzzy Syst 26(5):3027–3041
Lei T, Zhang Y, Wang Y, Liu S, Guo Z (2017) A conditionally invariant mathematical morphological framework for color images. Inf Sci 387:34–52
Liang J, Song W (2012) Clustering based on steiner points. Int J Mach Learn Cybern 3(2):141–148
Louverdis G, Vardavoulia MI, Andreadis I, Tsalides P (2002) A new approach to morphological color image processing. Pattern Recogn 35(8):1733–1741
Ma J, Tian D, Gong M, Jiao L (2014) Fuzzy clustering with non-local information for image segmentation. Int J Mach Learn Cybern 5(6):845–859
Martin D, Fowlkes C, Tal D, Malik J (2001) A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Eighth IEEE international conference on computer vision (ICCV). IEEE, pp 416–423
Masulli F, Rovetta S (2006) Soft transition from probabilistic to possibilistic fuzzy clustering. IEEE Trans Fuzzy Syst 14(4):516–527
Meilă M (2003) Comparing clusterings by the variation of information. Learning theory and kernel machines. Springer, Berlin, pp 173–187
Naz S, Majeed H, Irshad H (2010) Image segmentation using fuzzy clustering: a survey. In: 2010 6th international conference on emerging technologies (ICET), IEEE, pp. 181–186
Parape CD, Premachandra C, Tamura M (2015) Optimization of structure elements for morphological hit-or-miss transform for building extraction from vhr airborne imagery in natural hazard areas. Int J Mach Learn Cybern 6(4):641–650
Pitas I, Tsakalides P (1991) Multivariate ordering in color image filtering. IEEE Trans Circ Syst Video Technol 1(3):247–259
Price BL, Morse B, Cohen S (2010) Geodesic graph cut for interactive image segmentation. In: 2010 IEEE computer society conference on computer vision and pattern recognition, IEEE, pp. 3161–3168
Shih FY, Cheng S (2005) Automatic seeded region growing for color image segmentation. Image Vis Comput 23(10):877–886
Vartak AP, Mankar V (2014) Colour image segmentation - a survey. Int J Emerg Technol Adv Eng 3(2):681–688
Tolias YA, Panas SM (1998) Image segmentation by a fuzzy clustering algorithm using adaptive spatially constrained membership functions. IEEE Trans Syst Man Cybern Part A Syst Hum 28(3):359–369
Tsalides P, Vardavoulia MI, Andreadis I (2002) Vector ordering and morphological operations for colour image processing: fundamentals and applications. Pattern Anal Appl 5(3):271–287
Vincent L (1993) Morphological grayscale reconstruction in image analysis: applications and efficient algorithms. IEEE Trans Image Process Publ IEEE Signal Process Soc 2(2):176–201
Acknowledgements
This work was supported in part by the National Natural Science Foundation of China under Grants with No. 61873324, No. 61903156, and No. 61872419, the Natural Science Foundation of Shandong Province under Grant with No. ZR2019MF040 and No. ZR2017MF044.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Xu, G., Zhou, J., Dong, J. et al. Multivariate morphological reconstruction based fuzzy clustering with a weighting multi-channel guided image filter for color image segmentation. Int. J. Mach. Learn. & Cyber. 11, 2793–2806 (2020). https://doi.org/10.1007/s13042-020-01151-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13042-020-01151-1