{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T17:52:25Z","timestamp":1772819545825,"version":"3.50.1"},"reference-count":50,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T00:00:00Z","timestamp":1693526400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T00:00:00Z","timestamp":1693526400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T00:00:00Z","timestamp":1693526400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T00:00:00Z","timestamp":1693526400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T00:00:00Z","timestamp":1693526400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T00:00:00Z","timestamp":1693526400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T00:00:00Z","timestamp":1693526400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Mathematics and Computation"],"published-print":{"date-parts":[[2023,9]]},"DOI":"10.1016\/j.amc.2023.128050","type":"journal-article","created":{"date-parts":[[2023,4,27]],"date-time":"2023-04-27T11:52:00Z","timestamp":1682596320000},"page":"128050","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":5,"special_numbering":"C","title":["Image Segmentation Based on the Hybrid Bias Field Correction"],"prefix":"10.1016","volume":"452","author":[{"given":"Zhi-Feng","family":"Pang","sequence":"first","affiliation":[]},{"given":"Zhenyan","family":"Guan","sequence":"additional","affiliation":[]},{"given":"Yue","family":"Li","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6093-6623","authenticated-orcid":false,"given":"Ke","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Hong","family":"Ge","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.amc.2023.128050_bib0001","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.patcog.2015.08.022","article-title":"A variational model with hybrid images data fitting energies for segmentation of images with intensity inhomogeneity","volume":"51","author":"Ali","year":"2016","journal-title":"Pattern Recognition"},{"issue":"8","key":"10.1016\/j.amc.2023.128050_bib0002","doi-asserted-by":"crossref","first-page":"3729","DOI":"10.1109\/TIP.2018.2825101","article-title":"Image segmentation for intensity inhomogeneity in presence of high noise","volume":"27","author":"Ali","year":"2018","journal-title":"IEEE Transactions on Image Processing"},{"key":"10.1016\/j.amc.2023.128050_bib0003","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2200000016","article-title":"Distributed optimization and statistical learning via the alternating direction method of multipliers","volume":"3","author":"Boyd","year":"2011","journal-title":"Foundations and Trends in Machine Learning"},{"issue":"6","key":"10.1016\/j.amc.2023.128050_bib0004","doi-asserted-by":"crossref","first-page":"3004-3016","DOI":"10.1109\/TIP.2012.2188033","article-title":"An alternating direction algorithm for total variation reconstruction of distributed parameters","volume":"21","author":"Br\u00e1s","year":"2012","journal-title":"IEEE Transactions on Image Processing"},{"key":"10.1016\/j.amc.2023.128050_bib0005","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1023\/A:1007979827043","article-title":"Geodesic active contours","volume":"22","author":"Caselles","year":"1997","journal-title":"International Journal of Computer Vision"},{"issue":"2","key":"10.1016\/j.amc.2023.128050_bib0006","doi-asserted-by":"crossref","first-page":"266-277","DOI":"10.1109\/83.902291","article-title":"Active contours without edges","volume":"10","author":"Chan","year":"2001","journal-title":"IEEE Transactions on Image Processing"},{"key":"10.1016\/j.amc.2023.128050_bib0007","doi-asserted-by":"crossref","first-page":"108658","DOI":"10.1016\/j.patcog.2022.108658","article-title":"A spatially constrained skew student\u2019s-t mixture model for brain MR image segmentation and bias field correction","volume":"128","author":"Cheng","year":"2022","journal-title":"Pattern Recognition"},{"issue":"11","key":"10.1016\/j.amc.2023.128050_bib0008","doi-asserted-by":"crossref","first-page":"3927","DOI":"10.1109\/TIP.2015.2451957","article-title":"The l0 regularized mumford-shah model for bias correction and segmentation of medical images","volume":"24","author":"Duan","year":"2015","journal-title":"IEEE Transactions on Image Processing"},{"key":"10.1016\/j.amc.2023.128050_bib0009","article-title":"Partial differential equations","author":"Evans","year":"2010","journal-title":"American Mathematical Society"},{"key":"10.1016\/j.amc.2023.128050_bib0010","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/s12532-015-0078-2","article-title":"Generalized alternating direction method of multipliers: new theoretical insights and applications","volume":"7","author":"Fang","year":"2015","journal-title":"Mathematical Programming Computation"},{"issue":"2","key":"10.1016\/j.amc.2023.128050_bib0011","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1002\/ima.22010","article-title":"A local modified chan-vese model for segmenting inhomogeneous multiphase images","volume":"22","author":"Gao","year":"2012","journal-title":"International Journal of Imaging Systems and Technology"},{"key":"10.1016\/j.amc.2023.128050_bib0012","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1007\/s10851-020-01001-3","article-title":"Effective two-stage image segmentation: a new non-lipschitz decomposition approach with convergent algorithm","volume":"63","author":"Guo","year":"2021","journal-title":"Journal of Mathematical Imaging and Vision"},{"key":"10.1016\/j.amc.2023.128050_bib0013","doi-asserted-by":"crossref","first-page":"1229","DOI":"10.1007\/s10915-016-0280-z","article-title":"Piecewise-smooth image segmentation models with l1 data-fidelity terms","volume":"70","author":"Jung","year":"2017","journal-title":"Journal of Scientific Computing"},{"key":"10.1016\/j.amc.2023.128050_bib0014","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.apm.2019.11.005","article-title":"A retinex-based total variation approach for image segmentation and bias correction","volume":"79","author":"Jin","year":"2020","journal-title":"Applied Mathematical Modelling"},{"key":"10.1016\/j.amc.2023.128050_bib0015","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/BF00133570","article-title":"Snakes:active contour models","volume":"1","author":"Kass","year":"1998","journal-title":"International Journal of Computer Vision"},{"key":"10.1016\/j.amc.2023.128050_bib0016","first-page":"7","article-title":"A level set method for image segmentation in the presence of intensity inhomogeneities with application to MRI","volume":"20","author":"Li","year":"2016","journal-title":"IEEE Transactions on Image Processing"},{"key":"10.1016\/j.amc.2023.128050_sbref0017","doi-asserted-by":"crossref","first-page":"103207","DOI":"10.1016\/j.bspc.2021.103207","article-title":"Bias correction of intensity inhomogeneous images hybridized with superpixel segmentation","volume":"71","author":"Li","year":"2022","journal-title":"Biomedical Signal Processing and Control"},{"key":"10.1016\/j.amc.2023.128050_bib0018","first-page":"1","article-title":"Implicit active contours driven by local binary fitting energy","author":"Li","year":"2007","journal-title":"IEEE Conference on Computer Vision and Pattern Recognition"},{"issue":"7","key":"10.1016\/j.amc.2023.128050_bib0019","doi-asserted-by":"crossref","first-page":"2750-2770","DOI":"10.1137\/090753887","article-title":"Variational fuzzy mumford-shah model for image segmentation","volume":"70","author":"Li","year":"2010","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"7","key":"10.1016\/j.amc.2023.128050_bib0020","doi-asserted-by":"crossref","first-page":"913-923","DOI":"10.1016\/j.mri.2014.03.010","article-title":"Multiplicative intrinsic component optimization (MICO) for MRI bias field estimation and tissue segmentation","volume":"32","author":"Li","year":"2014","journal-title":"Magnetic Resonance Imaging"},{"key":"10.1016\/j.amc.2023.128050_bib0021","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1364\/JOSA.61.000001","article-title":"Lightness and retinex theory","volume":"61","author":"Land","year":"1971","journal-title":"Journal of the Optical Society of America"},{"key":"10.1016\/j.amc.2023.128050_bib0022","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1016\/j.apnum.2018.01.016","article-title":"Proximal ADMM for euler elastica based image decomposition model","volume":"12","author":"Liu","year":"2018","journal-title":"Numerical Mathematics: Theory, Methods and Applications"},{"key":"10.1016\/j.amc.2023.128050_bib0023","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1016\/j.asoc.2018.04.031","article-title":"Local contextual information and gaussian function induced fuzzy clustering algorithm for brain MR image segmentation and intensity inhomogeneity estimation","volume":"68","author":"Mahata","year":"2018","journal-title":"Applied Soft Computing"},{"key":"10.1016\/j.amc.2023.128050_bib0024","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.patcog.2019.02.009","article-title":"A multi-scale level set method based on local features for segmentation of images with intensity inhomogeneity","volume":"91","author":"Min","year":"2019","journal-title":"Pattern Recognition"},{"key":"10.1016\/j.amc.2023.128050_bib0025","doi-asserted-by":"crossref","unstructured":"L. Min, Q. Cui, Z. Jin, T. Zeng, Inhomogeneous image segmentation based on local constant and global smoothness priors, 2021, Digital Signal Processing, 111, 102989","DOI":"10.1016\/j.dsp.2021.102989"},{"issue":"1","key":"10.1016\/j.amc.2023.128050_bib0026","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s11060-017-2420-1","article-title":"Radiogenomics of lower-grade glioma: algorithmically-assessed tumor shape is associated with tumor genomic subtypes and patient outcomes in a multi-institutional study with the cancer genome atlas data","volume":"133","author":"Mazurowski","year":"2017","journal-title":"Journal of Neuro-Oncology"},{"key":"10.1016\/j.amc.2023.128050_bib0027","first-page":"6317415","article-title":"Segmentation of intensity corrupted medical images using adaptive weight-based hybrid active contours","author":"Memon","year":"2020","journal-title":"Computational and Mathematical Methods in Medicine"},{"key":"10.1016\/j.amc.2023.128050_bib0028","first-page":"308","article-title":"A novel acm for segmentation of medical image with intensity inhomogeneity","author":"Niu","year":"2017","journal-title":"The 2nd IEEE International Conference on Computational Intelligence and Applications (ICCIA)"},{"key":"10.1016\/j.amc.2023.128050_bib0029","series-title":"Approximation Theory and Methods","author":"Powell","year":"1981"},{"key":"10.1016\/j.amc.2023.128050_bib0030","doi-asserted-by":"crossref","first-page":"108881","DOI":"10.1016\/j.sigpro.2022.108881","article-title":"Adaptive weighted curvature-based active contour for ultrasonic and 3t\/5t MR image segmentation","volume":"205","author":"Pang","year":"2023","journal-title":"Signal Processing"},{"key":"10.1016\/j.amc.2023.128050_sbref0030","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1137\/20M1343956","article-title":"Efficient and convergent preconditioned ADMM for the potts models","volume":"43","author":"Sun","year":"2021","journal-title":"SIAM Journal on Scientific Computing"},{"key":"10.1016\/j.amc.2023.128050_sbref0031","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0191827","article-title":"Hybrid two-stage active contour method with region and edge information for intensity inhomogeneous image segmentation","volume":"13","author":"Soomro","year":"2018","journal-title":"PloS One"},{"key":"10.1016\/j.amc.2023.128050_bib0033","doi-asserted-by":"crossref","first-page":"21925","DOI":"10.1007\/s11042-021-10738-x","article-title":"Active contour model driven by optimized energy functionals for mr brain tumor segmentation with intensity inhomogeneity correction","volume":"80","author":"Saman","year":"2021","journal-title":"Multimedia Tools and Applications"},{"key":"10.1016\/j.amc.2023.128050_bib0034","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/JTEHM.2019.2898870","article-title":"Context dependent fuzzy associated statistical model for intensity inhomogeneity correction from magnetic resonance images","volume":"7","author":"Subudhi","year":"2019","journal-title":"IEEE Journal of Translational Engineering in Health and Medicine"},{"key":"10.1016\/j.amc.2023.128050_bib0035","doi-asserted-by":"crossref","first-page":"101748","DOI":"10.1016\/j.compmedimag.2020.101748","article-title":"Intensity inhomogeneity correction of mri images using inhomonet","volume":"84","author":"Venkatesh","year":"2020","journal-title":"Computerized Medical Imaging and Graphics"},{"key":"10.1016\/j.amc.2023.128050_bib0036","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1023\/A:1020874308076","article-title":"A multiphase level set framework for image segmentation using the mumford and shah model","volume":"50","author":"Vese","year":"2002","journal-title":"International Journal of Computer Vision"},{"key":"10.1016\/j.amc.2023.128050_bib0037","doi-asserted-by":"crossref","first-page":"108017","DOI":"10.1016\/j.sigpro.2021.108017","article-title":"Adaptive total variation based image segmentation with semi-proximal alternating minimization","volume":"183","author":"Wu","year":"2021","journal-title":"Signal Processing"},{"key":"10.1016\/j.amc.2023.128050_bib0038","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1016\/j.patcog.2009.08.002","article-title":"An efficient local chan-vese model for image segmentation","volume":"43","author":"Wang","year":"2010","journal-title":"Pattern Recognition"},{"key":"10.1016\/j.amc.2023.128050_bib0039","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1016\/j.jcp.2017.08.020","article-title":"An efficient iterative thresholding method for image segmentation","volume":"350","author":"Wang","year":"2017","journal-title":"Journal of Computational Physics"},{"issue":"5","key":"10.1016\/j.amc.2023.128050_bib0040","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1049\/ipr2.12419","article-title":"Medical image segmentation using deep learning:a survey","volume":"16","author":"Wang","year":"2022","journal-title":"IET Image Processing"},{"key":"10.1016\/j.amc.2023.128050_bib0041","doi-asserted-by":"crossref","first-page":"115633","DOI":"10.1016\/j.eswa.2021.115633","article-title":"A level set method based on additive bias correction for image segmentation","volume":"185","author":"Weng","year":"2021","journal-title":"Expert Systems with Applications"},{"key":"10.1016\/j.amc.2023.128050_bib0042","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1016\/j.apm.2017.10.018","article-title":"A retinex modulated piecewise constant variational model for image segmentation and bias correction","volume":"54","author":"Wu","year":"2018","journal-title":"Applied Mathematical Modelling"},{"issue":"16","key":"10.1016\/j.amc.2023.128050_bib0043","doi-asserted-by":"crossref","first-page":"83-88","DOI":"10.3182\/20120711-3-BE-2027.00310","article-title":"An ADMM algorithm for a class of total variation regularized estimation problems","volume":"45","author":"Wahlberg","year":"2012","journal-title":"IFAC Proceedings Volumes"},{"issue":"1","key":"10.1016\/j.amc.2023.128050_bib0044","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s10915-018-0757-z","article-title":"Global convergence of ADMM in nonconvex nonsmooth optimization","volume":"78","author":"Wang","year":"2019","journal-title":"Journal of Scientific Computing"},{"key":"10.1016\/j.amc.2023.128050_bib0045","doi-asserted-by":"crossref","first-page":"107564","DOI":"10.1016\/j.sigpro.2020.107564","article-title":"A weighted bounded hessian variational model for image labeling and segmentation","volume":"173","author":"Yang","year":"2020","journal-title":"Signal Processing"},{"key":"10.1016\/j.amc.2023.128050_bib0046","doi-asserted-by":"crossref","first-page":"11779","DOI":"10.1007\/s11042-018-6735-5","article-title":"A novel segmentation model for medical images with intensity inhomogeneity based on adaptive perturbation","volume":"78","author":"Yu","year":"2019","journal-title":"Multimedia Tools and Applications"},{"issue":"3","key":"10.1016\/j.amc.2023.128050_bib0047","doi-asserted-by":"crossref","first-page":"653","DOI":"10.3934\/ipi.2019030","article-title":"A dual EM algorithm for TV regularized gaussian mixture model in image segmentation","volume":"13","author":"Yan","year":"2019","journal-title":"Inverse Problems & Imaging"},{"issue":"2","key":"10.1016\/j.amc.2023.128050_bib0048","first-page":"546-557","article-title":"A level set approach to image segmentation with intensity inhomogeneity","volume":"46","author":"Zhang","year":"2015","journal-title":"IEEE Transactions on Cybernetics"},{"key":"10.1016\/j.amc.2023.128050_bib0049","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1007\/s10915-013-9710-3","article-title":"Image segmentation using eulers elastica as the regularization","volume":"57","author":"Zhu","year":"2013","journal-title":"Journal of Scientific Computing"},{"issue":"3","key":"10.1016\/j.amc.2023.128050_bib0050","first-page":"577-600","article-title":"Image segmentation with dynamic artifacts detection and bias correction","volume":"11","author":"Zosso","year":"2017","journal-title":"Inverse Problems and Imaging"}],"container-title":["Applied Mathematics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300323002199?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300323002199?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T16:54:26Z","timestamp":1758819266000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0096300323002199"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9]]},"references-count":50,"alternative-id":["S0096300323002199"],"URL":"https:\/\/doi.org\/10.1016\/j.amc.2023.128050","relation":{},"ISSN":["0096-3003"],"issn-type":[{"value":"0096-3003","type":"print"}],"subject":[],"published":{"date-parts":[[2023,9]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Image Segmentation Based on the Hybrid Bias Field Correction","name":"articletitle","label":"Article Title"},{"value":"Applied Mathematics and Computation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.amc.2023.128050","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2023 Elsevier Inc. All rights reserved.","name":"copyright","label":"Copyright"}],"article-number":"128050"}}