{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:52:00Z","timestamp":1760147520105,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T00:00:00Z","timestamp":1675814400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Deep learning methods have achieved outstanding results in many image processing and computer vision tasks, such as image segmentation. However, they usually do not consider spatial dependencies among pixels\/voxels in the image. To obtain better results, some methods have been proposed to apply classic spatial regularization, such as total variation, into deep learning models. However, for some challenging images, especially those with fine structures and low contrast, classical regularizations are not suitable. We derived a new regularization to improve the connectivity of segmentation results and make it applicable to deep learning. Our experimental results show that for both deep learning methods and unsupervised methods, the proposed method can improve performance by increasing connectivity and dealing with low contrast and, therefore, enhance segmentation results.<\/jats:p>","DOI":"10.3390\/s23041887","type":"journal-article","created":{"date-parts":[[2023,2,8]],"date-time":"2023-02-08T02:29:08Z","timestamp":1675823348000},"page":"1887","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A New Regularization for Deep Learning-Based Segmentation of Images with Fine Structures and Low Contrast"],"prefix":"10.3390","volume":"23","author":[{"given":"Jiasen","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, Cleveland, OH 44106, USA"}]},{"given":"Weihong","family":"Guo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, Cleveland, OH 44106, USA"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1002\/cpa.3160420503","article-title":"Optimal approximations by piecewise smooth functions and associated variational problems","volume":"42","author":"Mumford","year":"1989","journal-title":"Commun. Pure Appl. Math."},{"key":"ref_2","unstructured":"Potts, R.B. (1952). Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1109\/83.902291","article-title":"Active contours without edges","volume":"10","author":"Chan","year":"2001","journal-title":"IEEE Trans. Image Process."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Chan, T.F., and Vese, L.A. (1999, January 26\u201327). An active contour model without edges. Proceedings of the International Conference on Scale-Space Theories in Computer Vision, Heidelberg, Germany.","DOI":"10.1007\/3-540-48236-9_13"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Brown, E.S., Chan, T.F., and Bresson, X. (2009). Convex Formulation and Exact Global Solutions for Multi-Phase Piecewise Constant Mumford-Shah Image Segmentation, California Univ LOS Angeles Dept of Mathematics.","DOI":"10.21236\/ADA518796"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"108292","DOI":"10.1016\/j.sigpro.2021.108292","article-title":"A new variational method for selective segmentation of medical images","volume":"190","author":"Zhao","year":"2022","journal-title":"Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3431","DOI":"10.1109\/TIP.2006.881961","article-title":"Unsupervised variational image segmentation\/classification using a Weibull observation model","volume":"15","author":"Ayed","year":"2006","journal-title":"IEEE Trans. Image Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1137\/18M1192366","article-title":"A variational image segmentation model based on normalized cut with adaptive similarity and spatial regularization","volume":"13","author":"Wang","year":"2020","journal-title":"SIAM J. Imaging Sci."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Szegedy, C., Liu, W., Jia, Y., Sermanet, P., Reed, S., Anguelov, D., Erhan, D., Vanhoucke, V., and Rabinovich, A. (2015, January 7\u201312). Going deeper with convolutions. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Boston, MA, USA.","DOI":"10.1109\/CVPR.2015.7298594"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Ronneberger, O., Fischer, P., and Brox, T. (2015, January 5\u20139). U-net: Convolutional networks for biomedical image segmentation. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention, Munich, Germany.","DOI":"10.1007\/978-3-319-24574-4_28"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (2015, January 7\u201312). Deep residual learning for image recognition. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Boston, MA, USA.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Chollet, F. (2017, January 21\u201326). Xception: Deep learning with depthwise separable convolutions. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.195"},{"key":"ref_13","unstructured":"Chen, L.C., Papandreou, G., Kokkinos, I., Murphy, K., and Yuille, A.L. (2016). Semantic image segmentation with deep convolutional nets and fully connected crfs. arXiv."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"834","DOI":"10.1109\/TPAMI.2017.2699184","article-title":"Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected crfs","volume":"40","author":"Chen","year":"2017","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_15","unstructured":"Chen, L.C., Papandreou, G., Schroff, F., and Adam, H. (2017). Rethinking atrous convolution for semantic image segmentation. arXiv."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Chen, L.C., Zhu, Y., Papandreou, G., Schroff, F., and Adam, H. (2018, January 8\u201314). Encoder-decoder with atrous separable convolution for semantic image segmentation. Proceedings of the European Conference on Computer Vision (ECCV), Munich, Germany.","DOI":"10.1007\/978-3-030-01234-2_49"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.isprsjprs.2020.01.013","article-title":"ResUNet-a: A deep learning framework for semantic segmentation of remotely sensed data","volume":"162","author":"Diakogiannis","year":"2020","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Yi, F., and Moon, I. (2012, January 19\u201320). Image segmentation: A survey of graph-cut methods. Proceedings of the 2012 International Conference on Systems and Informatics (ICSAI2012), Yantai, China.","DOI":"10.1109\/ICSAI.2012.6223428"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Burrows, L., Chen, K., and Torella, F. (2020, January 15\u201317). On new convolutional neural network based algorithms for selective segmentation of images. Proceedings of the Annual Conference on Medical Image Understanding and Analysis, Oxford, UK.","DOI":"10.1007\/978-3-030-52791-4_8"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/s00371-020-02018-w","article-title":"Attention to fine-grained information: Hierarchical multi-scale network for retinal vessel segmentation","volume":"38","author":"Lyu","year":"2020","journal-title":"Vis. Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1856","DOI":"10.1109\/TIP.2019.2941265","article-title":"Mumford\u2013Shah loss functional for image segmentation with deep learning","volume":"29","author":"Kim","year":"2019","journal-title":"IEEE Trans. Image Process."},{"key":"ref_22","unstructured":"Takikawa, T., Acuna, D., Jampani, V., and Fidler, S. (November, January 27). Gated-scnn: Gated shape cnns for semantic segmentation. Proceedings of the IEEE\/CVF International Conference on Computer Vision, Seoul, Republic of Korea."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1007\/s10851-022-01087-x","article-title":"Deep Convolutional Neural Networks with Spatial Regularization, Volume and Star-Shape Priors for Image Segmentation","volume":"64","author":"Liu","year":"2022","journal-title":"J. Math. Imaging Vis."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Zhong, Q., Li, Y., Yang, Y., and Duan, Y. (2020, January 13\u201319). Minimizing discrete total curvature for image processing. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA.","DOI":"10.1109\/CVPR42600.2020.00949"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"El-Zehiry, N.Y., and Grady, L. (2020, January 14\u201319). Fast global optimization of curvature. Proceedings of the 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA.","DOI":"10.1109\/CVPR.2010.5540057"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1137\/090769521","article-title":"Total generalized variation","volume":"3","author":"Bredies","year":"2010","journal-title":"SIAM J. Imaging Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2408","DOI":"10.1016\/j.sigpro.2013.02.015","article-title":"Fractional order total variation regularization for image super-resolution","volume":"93","author":"Ren","year":"2013","journal-title":"Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1142\/S0219530519410148","article-title":"A regularized convolutional neural network for semantic image segmentation","volume":"19","author":"Jia","year":"2021","journal-title":"Anal. Appl."},{"key":"ref_29","unstructured":"Liu, J., Tai, X.C., and Luo, S. (2020). Convex shape prior for deep neural convolution network based eye fundus images segmentation. arXiv."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"808","DOI":"10.1002\/cpa.21527","article-title":"Threshold dynamics for networks with arbitrary surface tensions","volume":"68","author":"Otto","year":"2015","journal-title":"Commun. Pure Appl. Math."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"836","DOI":"10.1006\/jcph.1999.6223","article-title":"Convolution-generated motion as a link between cellular automata and continuum pattern dynamics","volume":"151","author":"Ruuth","year":"1999","journal-title":"J. Comput. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"868","DOI":"10.1137\/S003613999833397X","article-title":"Convolution-generated motion and generalized Huygens\u2019 principles for interface motion","volume":"60","author":"Merriman","year":"2000","journal-title":"SIAM J. Appl. Math."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s10107-011-0484-9","article-title":"Convergence of descent methods for semi-algebraic and tame problems: Proximal algorithms, forward\u2013backward splitting, and regularized Gauss\u2013Seidel methods","volume":"137","author":"Attouch","year":"2013","journal-title":"Math. Program."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1007\/s10107-013-0701-9","article-title":"Proximal alternating linearized minimization for nonconvex and nonsmooth problems","volume":"146","author":"Bolte","year":"2014","journal-title":"Math. Program."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Winitzki, S. (2003, January 18\u201321). Uniform approximations for transcendental functions. Proceedings of the International Conference on Computational Science and Its Applications, Berlin, Germany.","DOI":"10.1007\/3-540-44839-X_82"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"3434","DOI":"10.1109\/TITS.2016.2552248","article-title":"Automatic road crack detection using random structured forests","volume":"17","author":"Shi","year":"2016","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1109\/TMI.2004.825627","article-title":"Ridge-based vessel segmentation in color images of the retina","volume":"23","author":"Staal","year":"2004","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/S0734-189X(87)80186-X","article-title":"Adaptive histogram equalization and its variations","volume":"39","author":"Pizer","year":"1987","journal-title":"Comput. Vis. Gr. Image Process."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1186\/s40537-019-0197-0","article-title":"A survey on image data augmentation for deep learning","volume":"6","author":"Shorten","year":"2019","journal-title":"J. Big Data"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Setiawan, A.W., Mengko, T.R., Santoso, O.S., and Suksmono, A.B. (2013, January 13\u201314). Color retinal image enhancement using CLAHE. Proceedings of the International Conference on ICT for Smart Society, Jakarta, Indonesia.","DOI":"10.1109\/ICTSS.2013.6588092"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"128583","DOI":"10.1016\/j.conbuildmat.2022.128583","article-title":"An image enhancement algorithm to improve road tunnel crack transfer detection","volume":"348","author":"Liu","year":"2022","journal-title":"Constr. Build. Mater."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Alom, M.Z., Hasan, M., Yakopcic, C., Taha, T.M., and Asari, V.K. (2018). Recurrent residual convolutional neural network based on u-net (r2u-net) for medical image segmentation. arXiv.","DOI":"10.1109\/NAECON.2018.8556686"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Wu, Y., Xia, Y., Song, Y., Zhang, D., Liu, D., Zhang, C., and Cai, W. (2019, January 13\u201317). Vessel-Net: Retinal vessel segmentation under multi-path supervision. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention, Shenzhen, China.","DOI":"10.1007\/978-3-030-32239-7_30"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.knosys.2019.04.025","article-title":"DUNet: A deformable network for retinal vessel segmentation","volume":"178","author":"Jin","year":"2019","journal-title":"Knowl. Based Syst."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"2281","DOI":"10.1109\/TMI.2019.2903562","article-title":"Ce-net: Context encoder network for 2d medical image segmentation","volume":"38","author":"Gu","year":"2019","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Zhang, J., Zhang, Y., and Xu, X. (2021, January 6\u201312). Pyramid u-net for retinal vessel segmentation. Proceedings of the ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Toronto, ON, Canada.","DOI":"10.1109\/ICASSP39728.2021.9414164"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"15593","DOI":"10.1007\/s11042-022-12418-w","article-title":"DCU-net: A deformable convolutional neural network based on cascade U-net for retinal vessel segmentation","volume":"81","author":"Yang","year":"2022","journal-title":"Multimed. Tools. Appl."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"103613","DOI":"10.1016\/j.bspc.2022.103613","article-title":"CSAUNet: A cascade self-attention u-shaped network for precise fundus vessel segmentation","volume":"75","author":"Huang","year":"2022","journal-title":"Biomed. Signal Process. Control"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/4\/1887\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:27:42Z","timestamp":1760120862000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/4\/1887"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,8]]},"references-count":48,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["s23041887"],"URL":"https:\/\/doi.org\/10.3390\/s23041887","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2023,2,8]]}}}