Abstract
In modern days, image segmentation is one of the most important processing step in the field of computer vision and image processing. It helps to identify object, reconstruct shape, classify and estimate volume of an object. In the last few decades, many algorithms have been developed to eradicate the various segmentation problems such as weak edge detection, inhomogeneous image segmentation, accurate object shape identification and classification. Among them, one of the popular active contour models namely level set model is extensively used to eliminate the problem of topological changes during curve evolution. Earlier, the active contour models were unable to deal with sudden topological changes which led to poor segmentation results. Thus, the paper investigates several level set models in various applications of modern imaging. Therefore, it is necessary to understand the formulation of various level set models with their characteristics before applying them to solve the segmentation problem. In this paper, authors have extensively studied the formulation of various level set models and their application in different types of images. Further, the authors have discussed their contributions to level set framework and open research challenges for researchers.
Similar content being viewed by others
References
Ji Z, Sun Q, Xia Y, Chen Q, Xia D, Feng D (2012) Generalized rough fuzzy cmeans algorithm for brain MR image segmentation. Comput Methods Progr Biomed 108:644–655
Kannan SR, Ramathilagam S, Devi R, Hines E (2012) Strong fuzzy c-means in medical image data analysis. J Syst Softw 85:2425–2438
Fan JL, Zhen WZ, Xie WX (2003) Suppressed fuzzy c-means clustering algorithm. Pattern Recogn Lett 24:1607–1612
Nayak J, B Naik, and H. S. Behera (2015) Fuzzy C-means (FCM)clustering algorithm: a decade review from 2000 to 2014. In: Computational intelligence in data mining, vol 2, pp. 133-149. Springer, New Delhi
Cai H, Yang Z, Cao X, Xia W, Xu X (2014) A new iterative triclass thresholding technique in image segmentation. IEEE Trans Image Process 23(3):1038–1046
Conners RW, Harlow CA (1980) A theoretical comparison of texture algorithms. IEEE Trans Pattern Anal Mach Intell 2(3):204–222
Sørensen L, Nielsen M, Lo P, Ashraf H, Pedersen JH, De Bruijne M (2012) Texture-based analysis of COPD: a data-driven approach. IEEE Trans Med Imaging 31:70–78
Yuan J, Wang D, Li R (2014) Remote sensing image segmentation by combining spectral and texture features. IEEE Trans Geosci Remote Sens 52:16–24
Noor NM, Than JC, Rijal OM, Kassim RM, Yunus A, Zeki AA et al (2015) Automatic lung segmentation using control feedback system: morphology and texture paradigm. J Med Syst 39:1–18
Chaplot S, Patnaik LM (2016) Classification of magnetic resonance brain images using wavelets as input to support vector machines and neural networks. Biomed Signal Process Control 1:86–92
Luts J, Heerschap A, Johan A, Huffel S (2017) A combined MRI and MRSI based multiclass system for brain tumour recognition using LS-SVMs with class probabilities and feature selection. Artif Intell Med 40:87–102
Lin C, Yeh C, Liang S, Chung J, Kumar N (2007) Support-vector based fuzzy neural network for pattern classification. IEEE Trans Fuzzy Syst 14:31–41
Bezdek JC, Hall LO, Clarke LP (1993) Review of MR image segmentation techniques using pattern recognition. Med Phys 20(4):1033–1048
Ganguly S, Bhattacharjee D, Nasipuri M (2016) Hybridization of 2D–3D images for human face recognition, vol 611. Springer, India
Biswas S, Hazra R (2018) Robust edge detection based on modified Moore-neighbor. Optik 168:931–943
Ji Z, Xia Y, Sun Q, Cao G, Chen Q (2015) Active contours driven by local likelihood image fitting energy for image segmentation. Inf Sci 301:285–304
Huang G, H Ji, and W Zhang. (2018) A fast level set method for in homogeneous image segmentation with adaptive scale parameter. Mag Reson Imaging 52: 33–45
Kass M, Witkin A, Terzopoulos D (1987) Snakes: active contour models. Int J Comput Vis 1(4):321–331
Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79(1):12–49
Biswas, S., Hazra, R. and Prasad, S., (2019) A region-based level set formulation using machine learning approach in medical image segmentation. In: TENCON 2019-2019 IEEE Region 10 Conference (TENCON), pp. 470-475
Biswas, S. and Hazra, R. (2019) A novel level set method for medical image segmentation. In: 2019 IEEE Region 10 Symposium (TENSYMP), pp. 237-242
XAngelini, E., Jin, Y. and Laine, A., (2005) State of the art of level set methods in segmentation and registration of medical imaging modalities. In: Handbook of biomedical image analysis (pp. 47-101). Springer, Boston
Cai Q, Liu H, Qian Y, Zhou S, Duan X, Yang YH (2019) Saliency-guided level set model for automatic object segmentation. Pattern Recognit 93:147–163
Zhang H, Tang L, He C (2019) A variational level set model for multiscale image segmentation. Inf Sci 493:152–175
Wang XF, Min H, Zhang YG (2015) Multi-scale local region-based level set method for image segmentation in the presence of intensity inhomogeneity. Neurocomputing 151:1086–1098
Khadidos A, Sanchez V, Li CT (2017) Weighted level set evolution based on local edge features for medical image segmentation. IEEE Trans Image Process 26(4):1979–1991
Montagnat J, Delingette H, Ayache N (2001) A review of deformable surfaces: topology, geometry and deformation. Image Vis Comput 19(14):1023–1040
Liu C, Liu W, Xing W (2019) A weighted edge-based level set method based on multi-local statistical information for noisy image segmentation. J Vis Commun Image Rep 59:89–107
Huang G, Ji H, Zhang W (2018) A fast level set method for inhomogeneous image segmentation with adaptive scale parameter’’. Magn Reson Imaging 52:33–45
Swierczynski P, Papież BW, Schnabel JA, Macdonald C (2018) A level-set approach to joint image segmentation and registration with application to CT lung imaging. Comput Med Imaging Graph 65:58–68
Roy R, Chakraborti T, Chowdhury AS (2019) A deep learning-shape driven level set synergism for pulmonary nodule segmentation. Pattern Recognit Lett 123:31–38
Siddiqi, M.H., Lee, S., Lee, Y.K. (2012) Object segmentation by comparison of active contour snake and level set in biomedical applications. In: IEEE Internatinal Conference Bioinformatics and Biomedicine (BIBM), Atlanta, USA, pp. 414–417
Osher S, Fedkiw R (2003) Level set methods and dynamic implicit surfaces. Springer, New York, pp 3–16
Caselles V, Catté F, Coll T, Dibos F (1993) A geometric model for active contours in image processing. Numer Math 66(1):1–31
Tao Wenbing, Tai Xue-Cheng (2011) Multiple piecewise constant with geodesic active contours (MPC-GAC) framework for interactive image segmentation using graph cut optimization. Image Vis Comput 29(8):499–508
Ren G, Cao XQ, Pan WM, Yang Y (2011) Image segmentation using binary level set method based on region-based GAC model. Key Eng Mater Trans Tech Publ Ltd 480:1206–1209
Wu B, S Xu, Y Feng, and S Zhang (2018) A new region-based active contours combined with the GAC model. In: 2018 37th Chinese Control Conference (CCC), IEEE. pp. 9590-9594
Li C, Xu C, Gui C, Fox MD (2010) Distance regularized level set evolution and its application to image segmentation. IEEE Trans Image Process 19(12):3243–3254
Prakash KNB, Zhou S, Morgan TC, Hanley DF, Nowinski WL (2012) Segmentation and quantification of intra-ventricular/cerebral hemorrhage in CT scans by modified distance regularized level set evolution technique. Int J Comput Assist Radiol Surg 7(5):785–798
Wang Xuchu, Shan Jinxiao, Niu Yanmin, Tan Liwen, Zhang Shao-Xiang (2014) Enhanced distance regularization for re-initialization free level set evolution with application to image segmentation. Neurocomputing 141:223–235
Altarawneh NM, Luo S, Regan B, Sun C (2015) A modified distance regularized level set model for liver segmentation from CT images. Signal Image Process 6(1):1
Roopini IT, Vasanthi M, Rajinikanth V, Rekha M, and Sangeetha M (2018) Segmentation of tumor from brain MRI using fuzzy entropy and distance regularised level set. In: Computational Signal Processing and Analysis, pp. 297-304, Springer: Singapore
Liu C, Liu W, Xing W (2017) An improved edge-based level set method combining local regional fitting information for noisy image segmentation. Signal Process 130:12–21
Yu Haiping, He Fazhi, Pan Yiteng (2019) A novel segmentation model for medical images with intensity inhomogeneity based on adaptive perturbation. Multimed Tools Appl 78(9):11779–11798
Wang L, He L, Mishra A, Li C (2009) Active contours driven by local Gaussian distribution fitting energy. Signal Processing 89(12):2435–2447
Wang L, Shi F, Lin W, Gilmore JH, Shen D (2011) Automatic segmentation of neonatal images using convex optimization and coupled level sets. Neuroimage 58(3):805–817
Wang L, Shi F, Li G, Gao Y, Lin W, Gilmore JH et al (2014) Segmentation of neonatal brain MR images using patch-driven level sets. Neuroimage 84(1):141
Zhang K, Zhang L, Lam KM, Zhang D (2016) A level set approach to image segmentation with intensity inhomogeneity. IEEE Trans Cybern 46(2):546
Ying Zheng, Guangyao Li, Xiehua Sun, Xinmin Zhou (2009) Geometric active contours without re-initia-lization for image segmentation. Pattern Recogn 42(9):1970–1976
Zheng Y, Li G, Sun X, Zhou X (2009) Fast edge integration based active contours for color images. Comput Electr Eng 35(1):141–149
Chen Y, Zhang J, Macione J (2009) An improved level set method for brain MR images segmentation and bias correction. Comput Med Imaging Graph 33(7):510–519
Truc PTH, Kim TS, Lee S, Lee YK (2011) Homogeneity and density distance-driven active contours for medical image segmentation. Comput Biol Med 41(5):292–301
Zhang P, Li R, Li J (2012) Segmentation of holographic images using the level set method. Optik 123(2):132–136
Chan T, Vese L (2001) An active contour model without edges. IEEE Trans Image Process 10(2):266–277
Vese LA, Chan TF (2002) A multiphase level set framework for image segmentation using the Mumford and Shah model. Int J Comput Vis 50(3):271–293
Zhang K, Zhang L, Song H, Zhou W (2010) Active contours with selective local or global segmentation: a new formulation and level set method. Image Vis Comput 28(4):668–76
Liu Shigang, Peng Yali (2012) A local region-based Chan-Vese model for image segmentation. Pattern Recogn 45(7):2769–2779
Zhou Dongguo, Zhou Hong, Shao Yanhua (2016) An improved Chan-Vese model by regional fitting for infrared image segmentation. Infrared Phys Technol 74:81–88
Wang Z, Wang K, Yang F, Pan S, Han Y (2018) Image segmentation of overlapping leaves based on Chan-Vese model and Sobel operator. Inf Process Agric 5(1):1–10
Li C, Kao C, Gore J, Ding Z (2008) Minimization of region-scalable fitting energy for image segmentation. IEEE Trans Image Process 17:1940–1949
He C, Wang Y, Chen Q (2012) Active contours driven by weighted region-scalable fitting energy based on local entropy. Signal Process 9(2):587–600
Jiang X, Xiaoliang W, Xiong Y, Li B (2015) Active contours driven by local and global intensity fitting energies based on local entropy. Optik 126(24):5672–5677
Hou J, Yin Q, P Wu, M Lu (2019) Vessel segmentation based on region-scalable fitting energy. In: The International Conference on Natural Computation. Fuzzy Systems and Knowledge Discovery. Springer, Cham, pp 481–490
C. Li, C. Kao, J. Gore, Z. Ding (2007) Implicit active contours driven by local binary fitting energy. In: Proceedings of the IEEE Conference Computer Vision and Pattern Recognition, Washington, DC, USA, pp. 1–7
Shi Na, Pan Jinxiao (2016) An improved active contours model for image segmentation by level set method. Optik 127(3):1037–1042
Liu L, Cheng D, Tian F, Shi D, Rui W (2017) Active contour driven by multi-scale local binary fitting and Kullback-Leibler divergence for image segmentation. Multimed Tools Appl 76(7):10149–10168
Cheng Dansong, Tian Feng, Liu Lin, Liu Xiaofang, Jin Ye (2018) Image segmentation based on multi-region multi-scale local binary fitting and Kullback-Leibler divergence. Signal Image Video Process 12(5):895–903
Zhang K, Song H, Zhang L (2010) Active contours driven by local image fitting energy. Pattern Recognit 43:1199–1206
Wang Lei, Chang Yan, Wang Hui, Zhenzhou Wu, Jiantao Pu, Yang Xiaodong (2017) An active contour model based on local fitted images for image segmentation. Inf Sci 418:61–73
Gao Y, X Yu, C Wu, Zhou W, Lei X, Zhuang Y (2019) Automatic optic disc segmentation based on modified local image fitting model with shape prior information. J Healthcare Eng
Liu B, Cheng HD, Huang J, Tian J, Tang X, Liu J (2010) Probability density difference-based active contour for ultrasound image segmentation. Pattern Recogn 43(6):2028–2042
Liu W, Shang Y, Yang X, Deklerck R, Cornelis J (2011) A shape prior constraint for implicit active contours. Pattern Recogn Lett 32(15):1937–1947
Yuan Y, He C (2012) Adaptive active contours without edges. Math Comput Model 55(5–6):1705–1721
Yu CY, Zhang WS, Yu YY, Li Y (2013) A novel active contour model for image segmentation using distance regularization term. Comput Math Appl 65(11):1746–1759
Dong F, Chen Z, Wang J (2013) A new level set method for inhomogeneous image segmentation. Image Vis Comput 31(10):809–822
Jiang X, Li B, Wang Q, Chen P (2014) A novel active contour model driven by local and global intensity fitting energies. Optik 125(21):6445–6449
Wang H, Huang TZ, Xu Z, Wang Y (2014) An active contour model and its algorithms with local and global Gaussian distribution fitting energies. Inf Sci 263:43–59
Xie X, Zhang A, Wang C (2015) Local average fitting active contour model with thresholding for noisy image segmentation. Optik 126(9–10):1021–1026
Shi N, Pan J (2016) An improved active contours model for image segmentation by level set method. Optik 127(3):1037–1042
Chen Y, Yue X, Xu RYD, Fujita H (2017) Region scalable active contour model with global constraint. Knowl Based Syst 120:57–73
Ding K, Xiao L, Weng G (2018) Active contours driven by local pre-fitting energy for fast image segmentation. Pattern Recogn Lett 104:29–36
Ge Q, Li C, Shao W, Li H (2015) A hybrid active contour model with structured feature for image segmentation. Signal Process 108:147–158
Liu C, Liu W, Xing W (2017) An improved edge-based level set method combining local regional fitting information for noisy image segmentation. Signal Process 130:12–21
Zhang X, Weng G (2018) Level set evolution driven by optimized area energy term for image segmentation. Optik 168:517–532
Peng Y, Liu S, Qiang Y, Wu X, Hong L (2019) A local mean and variance active contour model for biomedical image segmentation. J Comput Sci 33:11–19
Xu L, Zhu Y, Zhang Y, Yang H (2020) Liver segmentation based on region growing and level set active contour model with new signed pressure force function. Optik 202:163705
Biswas S, Hazra R (2020) A new binary level set model using L0 regularizer for image segmentation. Signal Process 174:107603
Wang B, Gao X, Tao D, Li X (2014) A nonlinear adaptive level set for image segmentation. IEEE Trans Cybern 44(3):418–428
Hamers L (1989) Similarity measures in scientometric research: the Jaccard index versus Salton’s cosine formula. Inf Process Manag 25(3):315–18
Kovacs A, Sziranyi T (2012) Harris function based active contour external force forimage segmentation. Pattern Recognit Lett 33(9):1180–1187
S. Alpert, M. Galun, R. Basri and A. Brandt (2007) Image segmentation by probabilistic bottom-up aggregation and cue integration. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, June, 2007
https://www2.eecs.berkeley.edu/Research/Projects/CS-/vision/bsds/
Biswas S, Hazra R (2021) A level set model by regularizing local fitting energy and penalty energy term for image segmentation. Signal Process 183:108043
T. Lin, M. Maire, S. Belongie, J. Hays, P. Perona, D. Ramanan, P. Dollar, and C. L. Zitnick, (2014) Microsoft COCO: Common objects ’ in context. In: ECCV
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
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
Biswas, S., Hazra, R. State-of-the-Art Level Set Models and Their Performances in Image Segmentation: A Decade Review. Arch Computat Methods Eng 29, 2019–2042 (2022). https://doi.org/10.1007/s11831-021-09646-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11831-021-09646-y