{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T14:00:35Z","timestamp":1760709635023,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,6,8]],"date-time":"2018-06-08T00:00:00Z","timestamp":1528416000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61472278"],"award-info":[{"award-number":["61472278"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>This paper presents a method for synthetic aperture radar (SAR) image segmentation by draing upon a reaction\u2013diffusion (RD) level set evolution (LSE) equation. The well-known RD theory consists of two main parts: reaction and diffusion terms. We first constructed the reaction term using an energy functional, which integrates the gamma statistical distribution with region\u2013edge information from SAR images that can simultaneously suppress speckle noise and drive the active contour toward the object boundaries. Then, we used partial differential equation-based LSE to solve the proposed energy functional. Finally, a diffusion term was introduced into the LSE to ensure stability of the level set function and regularize the segmented region. The experimental results of both simulated and real SAR images showed that the proposed model has good robustness against a speckle noise as well as higher segmentation efficiency and accuracy than some existing models.<\/jats:p>","DOI":"10.3390\/rs10060906","type":"journal-article","created":{"date-parts":[[2018,6,8]],"date-time":"2018-06-08T11:19:31Z","timestamp":1528456771000},"page":"906","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Synthetic Aperture Radar Image Segmentation with Reaction Diffusion Level Set Evolution Equation in an Active Contour Model"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7232-8641","authenticated-orcid":false,"given":"Jiaxing","family":"Liu","sequence":"first","affiliation":[{"name":"School of Computer and Science and Engineering, Tianjin University of Technology, Binshuixidao No. 391, Tianjin 300384, China"}]},{"given":"Xianbin","family":"Wen","sequence":"additional","affiliation":[{"name":"School of Computer and Science and Engineering, Tianjin University of Technology, Binshuixidao No. 391, Tianjin 300384, China"}]},{"given":"Qingxia","family":"Meng","sequence":"additional","affiliation":[{"name":"School of Computer and Science and Engineering, Tianjin University, No. 135 Yaguan Road, Haihe Education Park, Tianjin 300350, China"}]},{"given":"Haixia","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Computer and Science and Engineering, Tianjin University of Technology, Binshuixidao No. 391, Tianjin 300384, China"}]},{"given":"Liming","family":"Yuan","sequence":"additional","affiliation":[{"name":"School of Computer and Science and Engineering, Tianjin University of Technology, Binshuixidao No. 391, Tianjin 300384, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1080\/01431161.2016.1266104","article-title":"Coastline extraction from SAR images using spatial fuzzy clustering and the active contour method","volume":"38","author":"Modava","year":"2017","journal-title":"Int. J. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1049\/iet-ipr.2010.0078","article-title":"Modified two-dimensional Otsu image segmentation algorithm and fast realisation","volume":"6","author":"Chen","year":"2012","journal-title":"IET Image Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2355","DOI":"10.1109\/JSTARS.2013.2251864","article-title":"Satellite oil spill detection using artificial neural networks","volume":"6","author":"Singha","year":"2013","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1456","DOI":"10.1109\/JSTARS.2016.2618891","article-title":"Polarimetric SAR feature extraction with neighborhood preservation-based deep learning","volume":"10","author":"Liu","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1265","DOI":"10.1109\/JSTARS.2015.2502991","article-title":"A multi-kernel joint sparse graph for sar image segmentation","volume":"9","author":"Gu","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2400","DOI":"10.1109\/TGRS.2015.2501162","article-title":"Crim-fcho: Sar image two-stage segmentation with multifeature ensemble","volume":"54","author":"Yu","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"6281","DOI":"10.1080\/01431160802175488","article-title":"Automatic detection and tracking of oil spills in SAR imagery with level set segmentation","volume":"29","author":"Karantzalos","year":"2008","journal-title":"Int. J. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/BF00133570","article-title":"Snakes: Active contour models","volume":"1","author":"Kass","year":"1988","journal-title":"Int. J. Comput. Vis."},{"key":"ref_9","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":"Int. J. Comput. Vis."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1109\/34.387512","article-title":"Finding shortest paths on surfaces using level sets propagation","volume":"17","author":"Kimmel","year":"1995","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1109\/34.841758","article-title":"Geodesic active contours and level sets for the detection and tracking of moving objects","volume":"22","author":"Paragios","year":"2000","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1023\/A:1014080923068","article-title":"Geodesic active regions and level set methods for supervised texture segmentation","volume":"46","author":"Paragios","year":"2002","journal-title":"Int. J. Comput. Vis."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Li, C., Xu, C., Gui, C., and Fox, M.D. (2010). Distance regularized level set evolution and its application to image segmentation. IEEE Trans. Image Process. A Publ. IEEE Signal Process. Soc., 19.","DOI":"10.1109\/TIP.2010.2069690"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1109\/34.857003","article-title":"A variational model for image classification and restoration","volume":"22","author":"Samson","year":"2000","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_15","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_16","first-page":"2717","article-title":"SAR image segmentation with active contours and level sets","volume":"4","author":"Ayed","year":"2004","journal-title":"Int. Conf. Image Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1109\/TPAMI.2005.106","article-title":"Multiregion level-set partitioning of synthetic aperture radar images","volume":"27","author":"Ayed","year":"2005","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1940","DOI":"10.1109\/TIP.2008.2002304","article-title":"Minimization of region-scalable fitting energy for image segmentation","volume":"17","author":"Li","year":"2008","journal-title":"IEEE Trans. Image Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1109\/LGRS.2008.2001768","article-title":"Sar image segmentation based on level set with stationary global minimum","volume":"5","author":"Shuai","year":"2008","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1199","DOI":"10.1016\/j.patcog.2009.10.010","article-title":"Active contours driven by local image fitting energy","volume":"43","author":"Zhang","year":"2010","journal-title":"Pattern Recognit."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2046","DOI":"10.1109\/TPAMI.2011.274","article-title":"Sar image segmentation based on level set approach and {cal g}_a^0 model","volume":"34","author":"Marques","year":"2012","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_22","unstructured":"Liu, G., Xia, G.S., Yang, W., and Xue, N. (2014). SAR image segmentation via non-local active contours. Geosci. Remote Sens. Symp., 3730\u20133733."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/j.sigpro.2016.12.021","article-title":"Active contours driven by region-scalable fitting and optimized Laplacian of Gaussian energy for image segmentation","volume":"134","author":"Ding","year":"2017","journal-title":"Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4190","DOI":"10.1109\/TGRS.2012.2227754","article-title":"Multiphase SAR Image Segmentation with G0-Statistical-Model-Based Active Contours","volume":"51","author":"Feng","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Yu, L. (2015). Convex active contour model for target detection in synthetic aperture radar images. J. Appl. Remote Sens., 9.","DOI":"10.1117\/1.JRS.9.095084"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhang, X., Wen, X., Xu, H., and Meng, Q. (2016). Synthetic aperture radar image segmentation based on edge-region active contour model. J. Appl. Remote Sens., 10.","DOI":"10.1117\/1.JRS.10.036014"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2724","DOI":"10.1109\/TGRS.2011.2107915","article-title":"Sar image despeckling based on local homogeneous-region segmentation by using pixel-relativity measurement","volume":"49","author":"Feng","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1860","DOI":"10.1109\/TGRS.2015.2490078","article-title":"Meaningful object segmentation from sar images via a multiscale nonlocal active contour model","volume":"54","author":"Xia","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2021","DOI":"10.1109\/TGRS.2014.2352555","article-title":"Nl-sar: A unified nonlocal framework for resolution-preserving (pol) (in) sar denoising","volume":"53","author":"Deledalle","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1109\/TIP.2012.2214046","article-title":"Reinitialization-free level set evolution via reaction diffusion","volume":"22","author":"Zhang","year":"2012","journal-title":"IEEE Trans. Image Process."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Gemez, L., Alvarez, L., Mazorra, L., and Frery, A.C. (2015). Classification of complex Wishart matrices with a diffusion-reaction system guided by stochastic distances. Philos. Trans., 373.","DOI":"10.1098\/rsta.2015.0118"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/S0092-8240(05)80008-4","article-title":"The chemical basis of morphogenesis","volume":"52","author":"Turing","year":"1990","journal-title":"Bull. Math. Biol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1109\/TIP.2003.816005","article-title":"Minimum description length synthetic aperture radar image segmentation","volume":"12","author":"Galland","year":"2003","journal-title":"IEEE Trans. Image Process."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Sethian, J.A. (1999). Level Set Methods and Fast Marching Method, Cambridge University Press.","DOI":"10.1137\/S0036144598347059"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2007","DOI":"10.1109\/TIP.2011.2146190","article-title":"A level set method for image segmentation in the presence of intensity inhomogeneities with application to mri","volume":"20","author":"Li","year":"2011","journal-title":"IEEE Trans. Image Process."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1023\/A:1023030907417","article-title":"Regularized laplacian zero crossings as optimal edge integrators","volume":"53","author":"Kimmel","year":"2003","journal-title":"Int. J. Comput. Vis."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Salazar, A., Igual, J., Safont, G., and Vergara, L. (2015, January 7\u20139). Image applications of agglomerative clustering using mixtures of non-Gaussian distributions. Proceedings of the International Conference on Computational Science and Computational Intelligence (CSCI), Las Vegas, NV, USA.","DOI":"10.1109\/CSCI.2015.118"},{"key":"ref_38","first-page":"884","article-title":"Region Competition: Unifying Snakes, Region Growing, and Bayes\/MDL for Multiband Image Segmentation","volume":"18","author":"Zhu","year":"1996","journal-title":"Int. Conf. Comput. Vis."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/6\/906\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:07:53Z","timestamp":1760195273000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/6\/906"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,8]]},"references-count":38,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["rs10060906"],"URL":"https:\/\/doi.org\/10.3390\/rs10060906","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2018,6,8]]}}}