{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,10]],"date-time":"2024-09-10T05:51:50Z","timestamp":1725947510787},"reference-count":57,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We propose a novel efficient seed-based method for the multi-object segmentation of images based on graphs, named Hierarchical Layered Oriented Image Foresting Transform (HLOIFT). It uses a tree of the relations between the image objects, with each node in the tree representing an object. Each tree node may contain different individual high-level priors of its corresponding object and defines a weighted digraph, named as layer. The layer graphs are then integrated into a hierarchical graph, considering the hierarchical relations of inclusion and exclusion. A single energy optimization is performed in the hierarchical layered weighted digraph leading to globally optimal results satisfying all the high-level priors. The experimental evaluations of HLOIFT, on medical, natural, and synthetic images, indicate promising results comparable to the related baseline methods that include structural information, but with lower computational complexity. Compared to the hierarchical segmentation by the min-cut\/max-flow algorithm, our approach is less restrictive, leading to globally optimal results in more general scenarios, and has a better running time.<\/jats:p>","DOI":"10.1515\/mathm-2020-0108","type":"journal-article","created":{"date-parts":[[2021,7,17]],"date-time":"2021-07-17T22:01:30Z","timestamp":1626559290000},"page":"21-42","source":"Crossref","is-referenced-by-count":4,"title":["Efficient Hierarchical Multi-Object Segmentation in Layered Graphs"],"prefix":"10.1515","volume":"5","author":[{"given":"Leissi M.C.","family":"Leon","sequence":"first","affiliation":[{"name":"University of S\u00e3o Paulo , Institute of Mathematics and Statistics , CEP 05508-090, S\u00e3o Paulo, SP , Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Krzysztof C.","family":"Ciesielski","sequence":"additional","affiliation":[{"name":"Department of Mathematics , West Virginia University , Morgantown, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paulo A.V.","family":"Miranda","sequence":"additional","affiliation":[{"name":"University of S\u00e3o Paulo , Institute of Mathematics and Statistics , CEP 05508-090, S\u00e3o Paulo, SP , Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2021,7,16]]},"reference":[{"key":"2021122100261972274_j_mathm-2020-0108_ref_001","doi-asserted-by":"crossref","unstructured":"[1] Hans Harley Ccacyahuillca Bejar and Paulo AV Miranda. Oriented relative fuzzy connectedness: theory, algorithms, and its applications in hybrid image segmentation methods. EURASIP Journal on Image and Video Processing, 2015(1):21, 2015.","DOI":"10.1186\/s13640-015-0067-4"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_002","doi-asserted-by":"crossref","unstructured":"[2] Yuri Boykov and Gareth Funka-Lea. Graph cuts and eflcient ND image segmentation. International journal of computer vision, 70(2):109\u2013131, 2006.","DOI":"10.1007\/s11263-006-7934-5"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_003","doi-asserted-by":"crossref","unstructured":"[3] Yuri Boykov and Vladimir Kolmogorov. An experimental comparison of min-cut\/max-flow algorithms for energy minimization in vision. IEEE transactions on pattern analysis and machine intelligence, 26(9):1124\u20131137, 2004.","DOI":"10.1109\/TPAMI.2004.60"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_004","doi-asserted-by":"crossref","unstructured":"[4] H. H. Ccacyahuillca Bejar and P. A. V. Miranda. Oriented relative fuzzy connectedness: Theory, algorithms, and applications in image segmentation. In 2014 27th SIBGRAPI Conference on Graphics, Patterns and Images, pages 304\u2013311, 2014.","DOI":"10.1109\/SIBGRAPI.2014.38"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_005","doi-asserted-by":"crossref","unstructured":"[5] K.C. Ciesielski, J.K. Udupa, A.X. Falc\u00e3o, and P.A.V. Miranda. A unifying graph-cut image segmentation framework: algorithms it encompasses and equivalences among them. In Proc. of SPIE on Medical Imaging: Image Processing, volume 8314, 2012.","DOI":"10.1117\/12.911810"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_006","doi-asserted-by":"crossref","unstructured":"[6] K.C. Ciesielski, J.K. Udupa, P.K. Saha, and Y. Zhuge. Iterative relative fuzzy connectedness for multiple objects with multiple seeds. Computer Vision and Image Understanding, 107(3):160\u2013182, 2007.","DOI":"10.1016\/j.cviu.2006.10.005"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_007","doi-asserted-by":"crossref","unstructured":"[7] Krzysztof Chris Ciesielski, Alexandre Xavier Falc\u00e3o, and Paulo A. V. Miranda. Path-value functions for which dijkstra\u2019s algorithm returns optimal mapping. Journal of Mathematical Imaging and Vision, Feb 2018.","DOI":"10.1007\/s10851-018-0793-1"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_008","doi-asserted-by":"crossref","unstructured":"[8] Krzysztof Chris Ciesielski, Gabor T. Herman, and T. Yung Kong. General theory of fuzzy connectedness segmentations. Journal of Mathematical Imaging and Vision, 55(3):304\u2013342, Jul 2016.","DOI":"10.1007\/s10851-015-0623-7"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_009","doi-asserted-by":"crossref","unstructured":"[9] Krzysztof Chris Ciesielski, Robin Strand, Filip Malmberg, and Punam K. Saha. Efficient algorithm for finding the exact minimum barrier distance. Computer Vision and Image Understanding, 123:53 \u2013 64, 2014.","DOI":"10.1016\/j.cviu.2014.03.007"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_010","doi-asserted-by":"crossref","unstructured":"[10] Krzysztof Chris Ciesielski and Jayaram K. Udupa. Aflnity functions in fuzzy connectedness based image segmentation i: Equivalence of aflnities. Comput. Vis. Image Underst., 114(1):146\u2013154, January 2010.","DOI":"10.1016\/j.cviu.2009.09.006"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_011","doi-asserted-by":"crossref","unstructured":"[11] Krzysztof Chris Ciesielski and Jayaram K. Udupa. A framework for comparing different image segmentation methods and its use in studying equivalences between level set and fuzzy connectedness frameworks. Computer Vision and Image Understanding, 115(6):721 \u2013 734, 2011.","DOI":"10.1016\/j.cviu.2011.01.003"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_012","doi-asserted-by":"crossref","unstructured":"[12] Jean Cousty, Gilles Bertrand, Laurent Najman, and Michel Couprie. Watershed cuts: Thinnings, shortest path forests, and topological watersheds. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 32(5):925\u2013939, 2010.","DOI":"10.1109\/TPAMI.2009.71"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_013","doi-asserted-by":"crossref","unstructured":"[13] P.A.V. de Miranda, A.X. Falc\u00e3o, and J.K. Udupa. Synergistic arc-weight estimation for interactive image segmentation using graphs. Computer Vision and Image Understanding, 114(1):85 \u2013 99, 2010.","DOI":"10.1016\/j.cviu.2009.08.001"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_014","doi-asserted-by":"crossref","unstructured":"[14] Caio de Moraes Braz, Paulo A. V. Miranda, Krzysztof Chris Ciesielski, and F\u00e1bio A. M. Cappabianco. Optimum cuts in graphs by general fuzzy connectedness with local band constraints. Journal of Mathematical Imaging and Vision, 62:659-672, 2020. https:\/\/doi.org\/10.1007\/s10851-020-00953-w","DOI":"10.1007\/s10851-020-00953-w"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_015","doi-asserted-by":"crossref","unstructured":"[15] Andrew Delong and Yuri Boykov. Globally optimal segmentation of multi-region objects. In Computer Vision, 2009 IEEE 12th International Conference on, pages 285\u2013292. IEEE, 2009.","DOI":"10.1109\/ICCV.2009.5459263"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_016","doi-asserted-by":"crossref","unstructured":"[16] Andrew Delong, Lena Gorelick, Olga Veksler, and Yuri Boykov. Minimizing energies with hierarchical costs. International journal of computer vision, 100(1):38\u201358, 2012.","DOI":"10.1007\/s11263-012-0531-x"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_017","doi-asserted-by":"crossref","unstructured":"[17] C.L. Demario and P.A.V. Miranda. Relaxed oriented image foresting transform for seeded image segmentation. In IEEE International Conference on Image Processing (ICIP), pages 1520\u20131524, Sep 2019.","DOI":"10.1109\/ICIP.2019.8803080"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_018","doi-asserted-by":"crossref","unstructured":"[18] Alexandre X Falc\u00e3o, Jorge Stolfi, and Roberto de Alencar Lotufo. The image foresting transform: Theory, algorithms, and applications. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 26(1):19\u201329, 2004.","DOI":"10.1109\/TPAMI.2004.1261076"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_019","doi-asserted-by":"crossref","unstructured":"[19] Leo Grady. Random walks for image segmentation. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 28(11):1768\u20131783, 2006.","DOI":"10.1109\/TPAMI.2006.233"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_020","doi-asserted-by":"crossref","unstructured":"[20] V. Gulshan, C. Rother, A. Criminisi, A. Blake, and A. Zisserman. Geodesic star convexity for interactive image segmentation. In Proceedings of Computer Vision and Pattern Recognition, pages 3129\u20133136, 2010.","DOI":"10.1109\/CVPR.2010.5540073"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_021","doi-asserted-by":"crossref","unstructured":"[21] K. He, X. Zhang, S. Ren, and J. Sun. Deep residual learning for image recognition. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 770\u2013778, June 2016.","DOI":"10.1109\/CVPR.2016.90"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_022","doi-asserted-by":"crossref","unstructured":"[22] Hossam Isack, Olga Veksler, Milan Sonka, and Yuri Boykov. Hedgehog shape priors for multi-object segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 2434\u20132442, 2016.","DOI":"10.1109\/CVPR.2016.267"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_023","unstructured":"[23] L. M. C. Leon and P. A. V. D. Miranda. Multi-object segmentation by hierarchical layered oriented image foresting transform. In 2017 30th SIBGRAPI Conference on Graphics, Patterns and Images (SIBGRAPI), pages 79\u201386, Oct 2017."},{"key":"2021122100261972274_j_mathm-2020-0108_ref_024","doi-asserted-by":"crossref","unstructured":"[24] L.M. Casta\u00f1eda Leon and P.A. Vechiatto de Miranda. Efficient interactive multi-object segmentation in medical images. In Laura Leal-Taix\u00e9 and Stefan Roth, editors, Computer Vision \u2013 ECCV 2018 Workshops, pages 705\u2013710, Cham, 2019. Springer International Publishing.","DOI":"10.1007\/978-3-030-11018-5_61"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_025","doi-asserted-by":"crossref","unstructured":"[25] Xiaoqiang Li, Jingsong Chen, and Huafu Fan. Interactive image segmentation based on grow cut of two scale graphs. In Wenjun Zhang, Xiaokang Yang, Zhixiang Xu, Ping An, Qizhen Liu, and Yue Lu, editors, Advances on Digital Television and Wireless Multimedia Communications, pages 90\u201395, Berlin, Heidelberg, 2012. Springer Berlin Heidelberg.","DOI":"10.1007\/978-3-642-34595-1_13"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_026","doi-asserted-by":"crossref","unstructured":"[26] F. Malmberg, I. Nystr\u00f6m, A. Mehnert, C. Engstrom, and E. Bengtsson. Relaxed image foresting transforms for interactive volume image segmentation. In Proc.SPIE, volume 7623, pages 7623 \u2013 7623 \u2013 11, 2010.","DOI":"10.1117\/12.840019"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_027","doi-asserted-by":"crossref","unstructured":"[27] Filip Malmberg and Krzysztof Chris Ciesielski. Two polynomial time graph labeling algorithms optimizing max-norm-based objective functions. Journal of Mathematical Imaging and Vision, 62:737\u2013750, Jun 2020.","DOI":"10.1007\/s10851-020-00963-8"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_028","doi-asserted-by":"crossref","unstructured":"[28] K.-K. Maninis, S. Caelles, J. Pont-Tuset, and L. Van Gool. Deep extreme cut: From extreme points to object segmentation. In In IEEE Conf. on Computer Vision and Pattern Recognition, pages 616\u2013625, 2018.","DOI":"10.1109\/CVPR.2018.00071"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_029","doi-asserted-by":"crossref","unstructured":"[29] L. A. C. Mansilla, P. A. V. Miranda, and F. A. M. Cappabianco. Oriented image foresting transform segmentation with connectivity constraints. In 2016 IEEE International Conference on Image Processing (ICIP), pages 2554\u20132558, Sept 2016.","DOI":"10.1109\/ICIP.2016.7532820"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_030","doi-asserted-by":"crossref","unstructured":"[30] L.A.C. Mansilla, M.P. Jackowski, and P.A.V. Miranda. Image foresting transform with geodesic star convexity for interactive image segmentation. In IEEE International Conference on Image Processing (ICIP), pages 4054\u20134058, Melbourne, Australia, Sep 2013.","DOI":"10.1109\/ICIP.2013.6738835"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_031","doi-asserted-by":"crossref","unstructured":"[31] L.A.C. Mansilla and P.A.V. Miranda. Image segmentation by oriented image foresting transform: Handling ties and colored images. In 18th International Conference on Digital Signal Processing (DSP), pages 1\u20136, Santorini, Greece, Jul 2013. IEEE.","DOI":"10.1109\/ICDSP.2013.6622806"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_032","doi-asserted-by":"crossref","unstructured":"[32] L.A.C. Mansilla and P.A.V. Miranda. Image segmentation by oriented image foresting transform with geodesic star convexity. In Computer Analysis of Images and Patterns (CAIP), volume 8047, pages 572\u2013579, York, UK, Aug 2013.","DOI":"10.1007\/978-3-642-40261-6_69"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_033","doi-asserted-by":"crossref","unstructured":"[33] P. A. V. Miranda, A. X. Falcao, and J. K. Udupa. Cloud bank: A multiple clouds model and its use in mr brain image segmentation. In 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, pages 506\u2013509, June 2009.","DOI":"10.1109\/ISBI.2009.5193095"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_034","doi-asserted-by":"crossref","unstructured":"[34] Paulo AV Miranda and Alexandre X Falc\u00e3o. Links between image segmentation based on optimum-path forest and minimum cut in graph. Journal of Mathematical Imaging and Vision, 35(2):128\u2013142, 2009.","DOI":"10.1007\/s10851-009-0159-9"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_035","doi-asserted-by":"crossref","unstructured":"[35] Paulo AV Miranda and Lucy AC Mansilla. Oriented image foresting transform segmentation by seed competition. Image Processing, IEEE Transactions on, 23(1):389\u2013398, 2014.","DOI":"10.1109\/TIP.2013.2288867"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_036","doi-asserted-by":"crossref","unstructured":"[36] P.A.V. Miranda, A.X. Falc\u00e3o, and J.K. Udupa. CLOUDS: A model for synergistic image segmentation. In Proceedings of the IEEE International Symposium on Biomedical Imaging (ISBI), pages 209\u2013212, Paris, France, May 2008.","DOI":"10.1109\/ISBI.2008.4540969"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_037","unstructured":"[37] Seyedmehrdad Mohammadianrasanani. The use of a body-wide automatic anatomy recognition system in image analysis of kidneys. Master\u2019s thesis, School of Technology and Health, Royal Institute of Technology, Flemingsberg, Sweden, 2013."},{"key":"2021122100261972274_j_mathm-2020-0108_ref_038","doi-asserted-by":"crossref","unstructured":"[38] Ipek Oguz and Milan Sonka. LOGISMOS\u2013B: layered optimal graph image segmentation of multiple objects and surfaces for the brain. IEEE transactions on medical imaging, 33(6):1220\u20131235, 2014.","DOI":"10.1109\/TMI.2014.2304499"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_039","doi-asserted-by":"crossref","unstructured":"[39] B. Perret, J. Cousty, O. Tankyevych, H. Talbot, and N. Passat. Directed connected operators: Asymmetric hierarchies for image filtering and segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 37(6):1162\u20131176, 2015.","DOI":"10.1109\/TPAMI.2014.2366145"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_040","doi-asserted-by":"crossref","unstructured":"[40] Leticia Rittner, Jayaram K. Udupa, and Drew A. Torigian. Multiple fuzzy object modeling improves sensitivity in automatic anatomy recognition. In In Proceedings of SPIE on Medical Imaging: Image Processing, volume 9034, San Diego, California, USA, 2014.","DOI":"10.1117\/12.2044297"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_041","doi-asserted-by":"crossref","unstructured":"[41] Carsten Rother, Vladimir Kolmogorov, and Andrew Blake. \u201cgrabcut\u201d: Interactive foreground extraction using iterated graph cuts. ACM Trans. Graph., 23(3):309\u2013314, August 2004.","DOI":"10.1145\/1015706.1015720"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_042","doi-asserted-by":"crossref","unstructured":"[42] Dheeraj Singaraju, Leo Grady, and Ren\u00e9 Vidal. Interactive image segmentation via minimization of quadratic energies on directed graphs. In Computer Vision and Pattern Recognition, 2008. CVPR 2008. IEEE Conference on, pages 1\u20138. IEEE, 2008.","DOI":"10.1109\/CVPR.2008.4587485"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_043","unstructured":"[43] Luc Soler, Alexandre Hostettler, Vincent Agnus, Arnaud Charnoz, Jean-Baptiste Fasquel, Johan Moreau, Anne-Blandine Osswald, Mourad Bouhadjar, and Jacques Marescaux. 3D image reconstruction for comparison of algorithm database : A patient-specific anatomical and medical image database. 2012."},{"key":"2021122100261972274_j_mathm-2020-0108_ref_044","unstructured":"[44] Kaioqiong Sun, Jayaram K. Udupa, Dewey Odhner, Yubing Tong, and Drew A. Torigian. Automatic thoracic anatomy segmentation on ct images using hierarchical fuzzy models and registration. In In Proceedings of SPIE on Medical Imaging: Image-Guided Procedures, Robotic Interventions, and Modeling, volume 9036, San Diego, California, USA, 2014."},{"key":"2021122100261972274_j_mathm-2020-0108_ref_045","doi-asserted-by":"crossref","unstructured":"[45] Anderson C. M. Tavares, Hans H. C. Bejar, and Paulo A. V. Miranda. Seed robustness of oriented relative fuzzy connectedness: core computation and its applications. In Martin A. Styner and Elsa D. Angelini, editors, Medical Imaging 2017: Image Processing, volume 10133, pages 336 \u2013 345. International Society for Optics and Photonics, SPIE, 2017.","DOI":"10.1117\/12.2254646"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_046","doi-asserted-by":"crossref","unstructured":"[46] Anderson Carlos Moreira Tavares, Hans Harley Ccacyahuillca Bejar, and Paulo Andr\u00e9 Vechiatto Miranda. Seed robustness of oriented image foresting transform: Core computation and the robustness coeflcient. In Jes\u00fas Angulo, Santiago Velasco-Forero, and Fernand Meyer, editors, Mathematical Morphology and Its Applications to Signal and Image Processing, pages 119\u2013130, Cham, 2017. Springer International Publishing.","DOI":"10.1007\/978-3-319-57240-6_10"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_047","doi-asserted-by":"crossref","unstructured":"[47] Yubing Tong, J. K. Udupa, D. Odhner, Sanghun Sin, and R. Arens. Abdominal adiposity quantification at MRI via fuzzy model-based anatomy recognition. In In Proceedings of SPIE on Medical Imaging: Biomedical Applications in Molecular, Structural, and Functional Imaging, volume 8672, Orlando, Florida, USA, 2013.","DOI":"10.1117\/12.2007938"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_048","doi-asserted-by":"crossref","unstructured":"[48] Jayaram K. Udupa, Dewey Odhner, Yubing Tong, Monica M. S. Matsumoto, Krzysztof C. Ciesielski, Pavithra Vaideeswaran, Victoria Ciesielski, Babak Saboury, Liming Zhao, Syedmehrdad Mohammadianrasanani, and Drew Torigian. Fuzzy model-based body-wide anatomy recognition in medical images. volume 8671, pages 86712B\u201386712B\u20137, 2013.","DOI":"10.1117\/12.2007983"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_049","doi-asserted-by":"crossref","unstructured":"[49] Jayaram K. Udupa, Dewey Odhner, Liming Zhao, Yubing Tong, Monica M.S. Matsumoto, Krzysztof C. Ciesielski, Alexandre X. Falcao, Pavithra Vaideeswaran, Victoria Ciesielski, Babak Saboury, Syedmehrdad Mohammadianrasanani, Sanghun Sin, Raanan Arens, and Drew A. Torigian. Body-wide hierarchical fuzzy modeling, recognition, and delineation of anatomy in medical images. Medical Image Analysis, 18(5):752 \u2013 771, 2014.","DOI":"10.1016\/j.media.2014.04.003"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_050","doi-asserted-by":"crossref","unstructured":"[50] J.K. Udupa, D. Odhner, A.X. Falc\u00e3o, K.C. Ciesielski, P.A.V. Miranda, S. Mishra, G.J. Grevera, B. Saboury, and D.A. Torigian. Automatic anatomy recognition via fuzzy object models. In In Proceedings of SPIE on Medical Imaging: Image-Guided Procedures, Robotic Interventions, and Modeling, volume 8316, San Diego, California, USA, 2012.","DOI":"10.1117\/12.911580"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_051","doi-asserted-by":"crossref","unstructured":"[51] J.K. Udupa, D. Odhner, A.X. Falc\u00e3o, K.C. Ciesielski, P.A.V. Miranda, P. Vaideeswaran, S. Mishra, G.J. Grevera, B.Saboury, and D.A. Torigian. Fuzzy object modeling. In Proc.SPIE, volume 7964, pages 7964 \u2013 7964 \u2013 10, 2011.","DOI":"10.1117\/12.878273"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_052","doi-asserted-by":"crossref","unstructured":"[52] Johannes Ul\u00e9n, Petter Strandmark, and Florian Kahl. An eflcient optimization framework for multi-region segmentation based on lagrangian duality. Medical Imaging, IEEE Transactions on, 32(2):178\u2013188, 2013.","DOI":"10.1109\/TMI.2012.2218117"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_053","doi-asserted-by":"crossref","unstructured":"[53] Olga Veksler. Star shape prior for graph-cut image segmentation. Computer Vision\u2013ECCV 2008, pages 454\u2013467, 2008.","DOI":"10.1007\/978-3-540-88690-7_34"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_054","doi-asserted-by":"crossref","unstructured":"[54] Sara Vicente, Vladimir Kolmogorov, and Carsten Rother. Graph cut based image segmentation with connectivity priors. In Computer vision and pattern recognition, 2008. CVPR 2008. IEEE conference on, pages 1\u20138. IEEE, 2008.","DOI":"10.1109\/CVPR.2008.4587440"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_055","doi-asserted-by":"crossref","unstructured":"[55] S. Wolf, L. Schott, U. K\u00f6the, and F. Hamprecht. Learned watershed: End-to-end learning of seeded segmentation. In 2017 IEEE International Conference on Computer Vision (ICCV), pages 2030\u20132038, Oct 2017.","DOI":"10.1109\/ICCV.2017.222"},{"key":"2021122100261972274_j_mathm-2020-0108_ref_056","unstructured":"[56] Steffen Wolf, Alberto Bailoni, Constantin Pape, Nasim Rahaman, Anna Kreshuk, Ullrich K\u00f6the, and Fred A. Hamprecht. The mutex watershed and its objective: Eflcient, parameter-free image partitioning. Available: https:\/\/arxiv.org\/abs\/1904. 12654, 2019."},{"key":"2021122100261972274_j_mathm-2020-0108_ref_057","doi-asserted-by":"crossref","unstructured":"[57] Yin Yin, Xiangmin Zhang, Rachel Williams, Xiaodong Wu, Donald D Anderson, and Milan Sonka. LOGISMOS\u2013layered optimal graph image segmentation of multiple objects and surfaces: cartilage segmentation in the knee joint. IEEE transactions on medical imaging, 29(12):2023\u20132037, 2010.","DOI":"10.1109\/TMI.2010.2058861"}],"container-title":["Mathematical Morphology - Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2020-0108\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2020-0108\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,21]],"date-time":"2021-12-21T04:02:23Z","timestamp":1640059343000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mathm-2020-0108\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,1]]},"references-count":57,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,10,9]]},"published-print":{"date-parts":[[2021,1,1]]}},"alternative-id":["10.1515\/mathm-2020-0108"],"URL":"https:\/\/doi.org\/10.1515\/mathm-2020-0108","relation":{},"ISSN":["2353-3390"],"issn-type":[{"value":"2353-3390","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,1]]}}}