{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T14:04:14Z","timestamp":1782137054661,"version":"3.54.5"},"reference-count":54,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T00:00:00Z","timestamp":1661126400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T00:00:00Z","timestamp":1661126400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key R &D Program of China","doi-asserted-by":"crossref","award":["2021YFE0203700"],"award-info":[{"award-number":["2021YFE0203700"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012166","name":"National Key R &D Program of China","doi-asserted-by":"crossref","award":["14302920"],"award-info":[{"award-number":["14302920"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012166","name":"National Key R &D Program of China","doi-asserted-by":"crossref","award":["14300219"],"award-info":[{"award-number":["14300219"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012166","name":"National Key R &D Program of China","doi-asserted-by":"crossref","award":["14301121"],"award-info":[{"award-number":["14301121"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012166","name":"National Key R &D Program of China","doi-asserted-by":"crossref","award":["NSFC\/RGC N_CUHK 415\/19"],"award-info":[{"award-number":["NSFC\/RGC N_CUHK 415\/19"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012166","name":"National Key R &D Program of China","doi-asserted-by":"crossref","award":["ITF MHP\/038\/20"],"award-info":[{"award-number":["ITF MHP\/038\/20"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["61971234"],"award-info":[{"award-number":["61971234"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"QingLan Project for Colleges and Universities of Jiangsu Province"},{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11501301"],"award-info":[{"award-number":["11501301"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12126304"],"award-info":[{"award-number":["12126304"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12126340"],"award-info":[{"award-number":["12126340"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2022,10]]},"DOI":"10.1007\/s10915-022-01970-0","type":"journal-article","created":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T19:02:49Z","timestamp":1661194969000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Efficient Color Image Segmentation via Quaternion-based $$L_1\/L_2$$ Regularization"],"prefix":"10.1007","volume":"93","author":[{"given":"Tingting","family":"Wu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhihui","family":"Mao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zeyu","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yonghua","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0688-202X","authenticated-orcid":false,"given":"Tieyong","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,8,22]]},"reference":[{"issue":"3","key":"1970_CR1","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1080\/02564602.2014.906861","volume":"31","author":"A Norouzi","year":"2014","unstructured":"Norouzi, A., Rahim, M.S.M., Altameem, A., Saba, T., Rad, A.E., Rehman, A., Uddin, M.: Medical image segmentation methods, algorithms, and applications. IETE Tech. Rev. 31(3), 199\u2013213 (2014)","journal-title":"IETE Tech. Rev."},{"issue":"11","key":"1970_CR2","doi-asserted-by":"crossref","first-page":"3927","DOI":"10.1109\/TIP.2015.2451957","volume":"24","author":"Y Duan","year":"2015","unstructured":"Duan, Y., Chang, H., Huang, W., et al.: The $$L_{0}$$ regularized Mumford-Shah model for bias correction and segmentation of medical images. IEEE Trans. Image Process. 24(11), 3927\u20133938 (2015)","journal-title":"IEEE Trans. Image Process."},{"key":"1970_CR3","doi-asserted-by":"crossref","unstructured":"Nirkin, Y., Masi, I., Tran, A.T., Hassner, T., Medioni, G.: Face segmentation, face swapping, and how they impact face recognition. Deep Learning-Based Face Analytics, 21-43 (2021)","DOI":"10.1007\/978-3-030-74697-1_2"},{"issue":"1","key":"1970_CR4","doi-asserted-by":"crossref","first-page":"36","DOI":"10.11648\/j.jeee.20200801.16","volume":"8","author":"J Wang","year":"2020","unstructured":"Wang, J.: The research on face recognition and segmentation based on intelligent background. Journal of Electrical and Electronic Engineering 8(1), 36\u201341 (2020)","journal-title":"Journal of Electrical and Electronic Engineering"},{"issue":"3","key":"1970_CR5","doi-asserted-by":"crossref","first-page":"849","DOI":"10.4208\/aamm.OA-2019-0199","volume":"12","author":"T Wu","year":"2020","unstructured":"Wu, T., Shao, J.: Non-convex and convex coupling image segmentation via TGpV regularization and thresholding. Adv. Appl. Math. Mech. 12(3), 849\u2013878 (2020)","journal-title":"Adv. Appl. Math. Mech."},{"key":"1970_CR6","first-page":"126","volume":"403","author":"T Wu","year":"2021","unstructured":"Wu, T., Shao, J., Gu, X., et al.: Two-stage image segmentation based on nonconvex $$l_2$$-$$l_p$$ approximation and thresholding. Appl. Math. Comput. 403, 126\u2013168 (2021)","journal-title":"Appl. Math. Comput."},{"key":"1970_CR7","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1016\/j.jcp.2017.08.020","volume":"350","author":"D Wang","year":"2017","unstructured":"Wang, D., Li, H., Wei, X., Wang, X.P.: An efficient iterative thresholding method for image segmentation. J. Comput. Phys. 350, 657\u2013667 (2017)","journal-title":"J. Comput. Phys."},{"issue":"18","key":"1970_CR8","doi-asserted-by":"crossref","first-page":"24097","DOI":"10.1007\/s11042-018-5697-y","volume":"77","author":"H Yu","year":"2018","unstructured":"Yu, H., He, F., Pan, Y.: A novel region-based active contour model via local patch similarity measure for image segmentation. Multimedia Tools and Applications 77(18), 24097\u201324119 (2018)","journal-title":"Multimedia Tools and Applications"},{"key":"1970_CR9","doi-asserted-by":"crossref","first-page":"134448","DOI":"10.1109\/ACCESS.2019.2942064","volume":"7","author":"H Jia","year":"2019","unstructured":"Jia, H., Sun, K., Song, W., Peng, X., Lang, C., Li, Y.: Multi-strategy emperor penguin optimizer for RGB histogram-based color satellite image segmentation using masi entropy. IEEE Access 7, 134448\u2013134474 (2019)","journal-title":"IEEE Access"},{"issue":"1","key":"1970_CR10","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1007\/BF00252910","volume":"5","author":"LE Payne","year":"1960","unstructured":"Payne, L.E., Weinberger, H.F.: An optimal poincar\u00e9 inequality for convex domains. Arch. Ration. Mech. Anal. 5(1), 286\u2013292 (1960)","journal-title":"Arch. Ration. Mech. Anal."},{"issue":"2","key":"1970_CR11","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1109\/LSP.2015.2508039","volume":"23","author":"A Pratondo","year":"2015","unstructured":"Pratondo, A., Chui, C.-K., Ong, S.-H.: Robust edge-stop functions for edge-based active contour models in medical image segmentation. IEEE Signal Process. Lett. 23(2), 222\u2013226 (2015)","journal-title":"IEEE Signal Process. Lett."},{"key":"1970_CR12","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.sigpro.2016.06.013","volume":"130","author":"C Liu","year":"2017","unstructured":"Liu, C., Liu, W., Xing, W.: An improved edge-based level set method combining local regional fitting information for noisy image segmentation. Signal Process. 130, 12\u201321 (2017)","journal-title":"Signal Process."},{"issue":"2","key":"1970_CR13","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s11263-006-8711-1","volume":"72","author":"D Cremers","year":"2007","unstructured":"Cremers, D., Rousson, M., Deriche, R.: A review of statistical approaches to level set segmentation: integrating color, texture, motion and shape. Int. J. Comput. Vision 72(2), 195\u2013215 (2007)","journal-title":"Int. J. Comput. Vision"},{"key":"1970_CR14","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/j.patcog.2016.07.022","volume":"61","author":"S Niu","year":"2017","unstructured":"Niu, S., Chen, Q., De Sisternes, L., Ji, Z., Zhou, Z., Rubin, D.L.: Robust noise region-based active contour model via local similarity factor for image segmentation. Pattern Recogn. 61, 104\u2013119 (2017)","journal-title":"Pattern Recogn."},{"key":"1970_CR15","doi-asserted-by":"crossref","unstructured":"Mumford, D.B., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics (1989)","DOI":"10.1002\/cpa.3160420503"},{"key":"1970_CR16","doi-asserted-by":"crossref","unstructured":"Zhang, B., Xu, W., Cai, J. F., Lai, L.: Precise phase transition of total variation minimization. In: 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 4518-4522 (2016)","DOI":"10.1109\/ICASSP.2016.7472532"},{"issue":"2","key":"1970_CR17","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1109\/83.902291","volume":"10","author":"TF Chan","year":"2001","unstructured":"Chan, T.F., Vese, L.A.: Active contours without edges. IEEE Trans. Image Process. 10(2), 266\u2013277 (2001)","journal-title":"IEEE Trans. Image Process."},{"issue":"1","key":"1970_CR18","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1137\/120867068","volume":"6","author":"X Cai","year":"2013","unstructured":"Cai, X., Chan, R., Zeng, T.: A two-stage image segmentation method using a convex variant of the Mumford-Shah model and thresholding. SIAM J. Imag. Sci. 6(1), 368\u2013390 (2013)","journal-title":"SIAM J. Imag. Sci."},{"key":"1970_CR19","doi-asserted-by":"crossref","unstructured":"Cai, X., Chan, R., Zeng, T.: An Overview of SaT Segmentation Methodology and Its Applications in Image Processing. Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging: Mathematical Imaging and Vision, 1-27 (2021)","DOI":"10.1007\/978-3-030-03009-4_75-1"},{"issue":"6","key":"1970_CR20","doi-asserted-by":"crossref","first-page":"B1310","DOI":"10.1137\/18M1202980","volume":"41","author":"X Cai","year":"2019","unstructured":"Cai, X., Chan, R., Schonlieb, C.B., Steidl, G., Zeng, T.: Linkage Between Piecewise Constant Mumford-Shah Model and Rudin-Osher-Fatemi Model and Its Virtue in Image Segmentation. SIAM J. Sci. Comput. 41(6), B1310\u2013B1340 (2019)","journal-title":"SIAM J. Sci. Comput."},{"key":"1970_CR21","doi-asserted-by":"crossref","unstructured":"Cai, X., Steidl, G.: Multiclass segmentation by iterated ROF thresholding. In: International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, 237-250 (2013)","DOI":"10.1007\/978-3-642-40395-8_18"},{"key":"1970_CR22","doi-asserted-by":"crossref","first-page":"2010","DOI":"10.1137\/13090540X","volume":"6","author":"E Esser","year":"2013","unstructured":"Esser, E., Lou, Y., Xin, J.: A method for finding structured sparse solutions to nonnegative least squares problems with applications. SIAM J. Imag. Sci. 6, 2010\u20132046 (2013)","journal-title":"SIAM J. Imag. Sci."},{"key":"1970_CR23","doi-asserted-by":"crossref","first-page":"87","DOI":"10.4310\/CIS.2014.v14.n2.a2","volume":"14","author":"P Yin","year":"2014","unstructured":"Yin, P., Esser, E., Xin, J.: Ratio and difference of $$l_1$$ and $$l_2$$ norms and sparse representation with coherent dictionaries. Commun. Inf. Syst. 14, 87\u2013109 (2014)","journal-title":"Commun. Inf. Syst."},{"issue":"10","key":"1970_CR24","doi-asserted-by":"crossref","first-page":"105008","DOI":"10.1088\/1361-6420\/ac1e7f","volume":"37","author":"B Fan","year":"2021","unstructured":"Fan, B., Xu, C.: Identifying source term in the subdiffusion equation with $$L_2$$-TV regularization. Inverse Prob. 37(10), 105008 (2021)","journal-title":"Inverse Prob."},{"issue":"2","key":"1970_CR25","doi-asserted-by":"crossref","first-page":"258","DOI":"10.3390\/electronics11020258","volume":"11","author":"G Ma","year":"2022","unstructured":"Ma, G., Yan, Z., Li, Z., Zhao, Z.: Efficient Iterative Regularization Method for Total Variation-Based Image Restoration. Electronics 11(2), 258 (2022)","journal-title":"Electronics"},{"issue":"6","key":"1970_CR26","doi-asserted-by":"crossref","first-page":"3649","DOI":"10.1137\/18M123147X","volume":"41","author":"Y Rahimi","year":"2019","unstructured":"Rahimi, Y., Wang, C., Dong, H., Lou, Y.: A scale-invariant approach for sparse signal recovery. SIAM J. Sci. Comput. 41(6), 3649\u20133672 (2019)","journal-title":"SIAM J. Sci. Comput."},{"key":"1970_CR27","unstructured":"Wang, C., Tao, M., Chuah, C.-N., Nagy, J., Lou, Y.: Minimizing $$l_1$$ over $$l_2$$ norms on the gradient. arXiv preprint arXiv:2101.00809 (2021)"},{"key":"1970_CR28","volume-title":"Elements of quaternions","author":"WR Hamilton","year":"1866","unstructured":"Hamilton, W.R.: Elements of quaternions. Longmans, Green, & Company, London (1866)"},{"issue":"3","key":"1970_CR29","doi-asserted-by":"crossref","first-page":"946","DOI":"10.1137\/110853996","volume":"34","author":"M Fazel","year":"2013","unstructured":"Fazel, M., Pong, T.K., Sun, D., Tseng, P.: Hankel matrix rank minimization with applications to system identification and realization. SIAM J. Matrix Anal. Appl. 34(3), 946\u2013977 (2013)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"2","key":"1970_CR30","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1287\/moor.2017.0875","volume":"43","author":"D Han","year":"2018","unstructured":"Han, D., Sun, D., Zhang, L.: Linear rate convergence of the alternating direction method of multipliers for convex composite programming. Math. Oper. Res. 43(2), 622\u2013637 (2018)","journal-title":"Math. Oper. Res."},{"issue":"4","key":"1970_CR31","doi-asserted-by":"crossref","first-page":"045015","DOI":"10.1088\/1361-6420\/ab6df0","volume":"36","author":"J Liu","year":"2020","unstructured":"Liu, J., Lou, Y., Ni, G., Zeng, T.: An image sharpening operator combined with framelet for image deblurring. Inverse Prob. 36(4), 045015 (2020)","journal-title":"Inverse Prob."},{"issue":"3","key":"1970_CR32","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1109\/3477.764879","volume":"29","author":"K Krishna","year":"1999","unstructured":"Krishna, K., Murty, M Narasimha: Genetic K-means algorithm. IEEE Transactions on Systems, Man, and Cybernetics. Part B (Cybernetics) 29(3), 433\u2013439 (1999)","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics. Part B (Cybernetics)"},{"key":"1970_CR33","unstructured":"Deng, Y., Manjunath, B.S., Shin, H.: Color image segmentation. In: Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 446-451 (1999)"},{"issue":"12","key":"1970_CR34","first-page":"23","volume":"107","author":"DJ Bora","year":"2014","unstructured":"Bora, D.J., Gupta, A.K.: A new approach towards clustering based color image segmentation. Int. J. Comput. Appl. 107(12), 23\u201330 (2014)","journal-title":"Int. J. Comput. Appl."},{"key":"1970_CR35","doi-asserted-by":"crossref","first-page":"11258","DOI":"10.1109\/ACCESS.2019.2891673","volume":"7","author":"H Liang","year":"2019","unstructured":"Liang, H., Jia, H., Xing, Z., Ma, J., Peng, X.: Modified grasshopper algorithm-based multilevel thresholding for color image segmentation. IEEE Access 7, 11258\u201311295 (2019)","journal-title":"IEEE Access"},{"issue":"3","key":"1970_CR36","first-page":"1","volume":"87","author":"X-C Tai","year":"2021","unstructured":"Tai, X.-C., Deng, L.-J., Yin, K.: A multigrid algorithm for maxflow and min-cut problems with applications to multiphase image segmentation. J. Sci. Comput. 87(3), 1\u201322 (2021)","journal-title":"J. Sci. Comput."},{"key":"1970_CR37","doi-asserted-by":"crossref","unstructured":"Jain, S., Laxmi, V.: Color image segmentation techniques: a survey. In: Proceedings of the International Conference on Microelectronics, Computing & Communication Systems, pp. 189-197 (2018)","DOI":"10.1007\/978-981-10-5565-2_17"},{"issue":"5","key":"1970_CR38","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1109\/26.592558","volume":"45","author":"S-C Pei","year":"1997","unstructured":"Pei, S.-C., Cheng, C.-M.: A novel block truncation coding of color images using a quaternion-moment-preserving principle. IEEE Trans. Commun. 45(5), 583\u2013595 (1997)","journal-title":"IEEE Trans. Commun."},{"key":"1970_CR39","doi-asserted-by":"crossref","unstructured":"Subakan, \u00d6zlem N., Vemuri, B.C.: Color image segmentation in a quaternion framework. In: International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, pp. 401-414 (2009)","DOI":"10.1007\/978-3-642-03641-5_30"},{"issue":"1\u20132","key":"1970_CR40","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.cviu.2006.11.014","volume":"107","author":"L Shi","year":"2007","unstructured":"Shi, L., Funt, B.: Quaternion color texture segmentation. Comput. Vis. Image Underst. 107(1\u20132), 88\u201396 (2007)","journal-title":"Comput. Vis. Image Underst."},{"key":"1970_CR41","unstructured":"Ray, S., Turi, R.H.: Determination of number of clusters in k-means clustering and application in colour image segmentation. In: Proceedings of the 4th International Conference on Advances in Pattern Recognition and Digital Techniques, pp. 137-143 (1999)"},{"key":"1970_CR42","unstructured":"Hoyer, P.O.: Non-negative sparse coding. In: Proceedings of the 12th IEEE Workshop on Neural Networks for Signal Processing, pp. 557-565 (2002)"},{"issue":"11","key":"1970_CR43","doi-asserted-by":"crossref","first-page":"3927","DOI":"10.1109\/TIP.2015.2451957","volume":"24","author":"Y Duan","year":"2015","unstructured":"Duan, Y., Chang, H., Huang, W., Zhou, J., Lu, Z., Wu, C.: The $$l_0$$ regularized Mumford-Shah model for bias correction and segmentation of medical images. IEEE Trans. Image Process. 24(11), 3927\u20133938 (2015)","journal-title":"IEEE Trans. Image Process."},{"issue":"4","key":"1970_CR44","first-page":"7","volume":"19","author":"LC Evans","year":"1998","unstructured":"Evans, L.C.: Partial differential equations. Grad. Stud. Math. 19(4), 7 (1998)","journal-title":"Grad. Stud. Math."},{"key":"1970_CR45","doi-asserted-by":"crossref","unstructured":"Feichtinger, H.G., Zimmermann, G.: A banach space of test functions for gabor analysis, pp. 123-170 (1998)","DOI":"10.1007\/978-1-4612-2016-9_4"},{"key":"1970_CR46","doi-asserted-by":"crossref","unstructured":"Ortega, J.M.: Numerical analysis: a second course (1990)","DOI":"10.1137\/1.9781611971323"},{"key":"1970_CR47","doi-asserted-by":"crossref","first-page":"146182","DOI":"10.1109\/ACCESS.2020.3015270","volume":"8","author":"X Jia","year":"2020","unstructured":"Jia, X., Lei, T., Du, X., Liu, S., Meng, H., Nandi, A.K.: Robust self-sparse fuzzy clustering for image segmentation. IEEE Access 8, 146182\u2013146195 (2020)","journal-title":"IEEE Access"},{"issue":"9","key":"1970_CR48","doi-asserted-by":"crossref","first-page":"2078","DOI":"10.1109\/TFUZZ.2019.2930030","volume":"28","author":"T Lei","year":"2019","unstructured":"Lei, T., Liu, P., Jia, X., Zhang, X., Meng, H., Nandi, A.K.: Automatic fuzzy clustering framework for image segmentation. IEEE Trans. Fuzzy Syst. 28(9), 2078\u20132092 (2019)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"9","key":"1970_CR49","doi-asserted-by":"crossref","first-page":"1753","DOI":"10.1109\/TFUZZ.2018.2889018","volume":"27","author":"T Lei","year":"2018","unstructured":"Lei, T., Jia, X., Zhang, Y., Liu, S., Meng, H., Nandi, A.K.: Superpixel-based fast fuzzy c-means clustering for color image segmentation. IEEE Trans. Fuzzy Syst. 27(9), 1753\u20131766 (2018)","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"3","key":"1970_CR50","doi-asserted-by":"crossref","first-page":"1313","DOI":"10.1007\/s10915-017-0402-2","volume":"72","author":"X Cai","year":"2017","unstructured":"Cai, X., Chan, R., Nikolova, M., Zeng, T.: A three-stage approach for segmenting degraded color images: Smoothing, lifting and thresholding (SLaT). J. Sci. Comput. 72(3), 1313\u20131332 (2017)","journal-title":"J. Sci. Comput."},{"key":"1970_CR51","doi-asserted-by":"crossref","first-page":"762","DOI":"10.1016\/j.measurement.2018.11.006","volume":"134","author":"S Jha","year":"2019","unstructured":"Jha, S., Kumar, R., Priyadarshini, I., Smarandache, F., Long, H.V., et al.: Neutrosophic image segmentation with dice coefficients. Measurement 134, 762\u2013772 (2019)","journal-title":"Measurement"},{"key":"1970_CR52","doi-asserted-by":"crossref","first-page":"108017","DOI":"10.1016\/j.sigpro.2021.108017","volume":"183","author":"T Wu","year":"2021","unstructured":"Wu, T., Gu, X., Wang, Y., Zeng, T.: Adaptive total variation based image segmentation with semi-proximal alternating minimization. Signal Process. 183, 108017 (2021)","journal-title":"Signal Process."},{"issue":"2","key":"1970_CR53","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1137\/20M1341490","volume":"14","author":"C Wang","year":"2021","unstructured":"Wang, C., Tao, M., Nagy, J.G., et al.: Limited-Angle CT Reconstruction via the $$L_1\/L_2$$ Minimization. SIAM J. Imag. Sci. 14(2), 749\u2013777 (2021)","journal-title":"SIAM J. Imag. Sci."},{"key":"1970_CR54","volume-title":"Convex analysis and minimization algorithms I: Fundamentals","author":"JB Hiriart-Urruty","year":"2013","unstructured":"Hiriart-Urruty, J.B., Lemar\u00e9chal, C.: Convex analysis and minimization algorithms I: Fundamentals. Springer Science & Business Media, Paris (2013)"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-022-01970-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-022-01970-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-022-01970-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,16]],"date-time":"2022-12-16T17:09:30Z","timestamp":1671210570000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-022-01970-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,22]]},"references-count":54,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["1970"],"URL":"https:\/\/doi.org\/10.1007\/s10915-022-01970-0","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,22]]},"assertion":[{"value":"6 March 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 August 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 August 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 August 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have not disclosed any competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}}],"article-number":"9"}}