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The FMS algorithm is evaluated on the Berkeley Segmentation Dataset 500. It yields results in terms of boundary adherence that are slightly better than the ones obtained with similar approaches including the Simple Linear Iterative Clustering, the Eikonal-based region growing for efficient clustering and the Iterative Spanning Forest framework for superpixel segmentation algorithms. An interesting feature of the proposed algorithm is that it can take into account texture information to compute the superpixel partition. We illustrate the interest of adding texture information on a specific set of images obtained by recombining textures patches extracted from images representing stripes, originally constructed by Giraud<jats:italic>et al.<\/jats:italic>[20]. On this dataset, our approach works significantly better than color based superpixel algorithms.<\/jats:p>","DOI":"10.1515\/mathm-2020-0105","type":"journal-article","created":{"date-parts":[[2020,12,22]],"date-time":"2020-12-22T11:54:37Z","timestamp":1608638077000},"page":"127-142","source":"Crossref","is-referenced-by-count":1,"title":["Fast marching based superpixels"],"prefix":"10.1515","volume":"4","author":[{"given":"Kaiwen","family":"Chang","sequence":"first","affiliation":[{"name":"Center for Mathematical Morphology, Mines ParisTech , PSL Research University"}]},{"given":"Bruno","family":"Figliuzzi","sequence":"additional","affiliation":[{"name":"Center for Mathematical Morphology, Mines ParisTech , PSL Research University"}]}],"member":"374","published-online":{"date-parts":[[2020,12,17]]},"reference":[{"key":"2022042712261287502_j_mathm-2020-0105_ref_001_w2aab3b7c14b1b6b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"[1] Radhakrishna Achanta, Appu Shaji, Kevin Smith, Aurelien Lucchi, Pascal Fua, and Sabine S\u00fcsstrunk. Slic superpixels compared to state-of-the-art superpixel methods. IEEE transactions on pattern analysis and machine intelligence, 34(11):2274\u20132282, 2012.10.1109\/TPAMI.2012.12022641706","DOI":"10.1109\/TPAMI.2012.120"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_002_w2aab3b7c14b1b6b1ab1ab2Aa","doi-asserted-by":"crossref","unstructured":"[2] Radhakrishna Achanta and Sabine Susstrunk. Superpixels and Polygons Using Simple Non-iterative Clustering. In 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 4895\u20134904, Honolulu, HI, July 2017. IEEE.10.1109\/CVPR.2017.520","DOI":"10.1109\/CVPR.2017.520"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_003_w2aab3b7c14b1b6b1ab1ab3Aa","doi-asserted-by":"crossref","unstructured":"[3] Pablo Arbelaez, Michael Maire, Charless Fowlkes, and Jitendra Malik. Contour detection and hierarchical image segmentation. IEEE Trans. Pattern Anal. Mach. 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Journal of Thermal Spray Technology, pages 1\u201315, 2020.10.1007\/s11666-020-00999-7","DOI":"10.1007\/s11666-020-00999-7"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_008_w2aab3b7c14b1b6b1ab1ab8Aa","doi-asserted-by":"crossref","unstructured":"[8] Pierre Buyssens, Isabelle Gardin, and Su Ruan. Eikonal based region growing for superpixels generation: Application to semi-supervised real time organ segmentation in CT images. IRBM, 35(1):20\u201326, December 2014.10.1016\/j.irbm.2013.12.007","DOI":"10.1016\/j.irbm.2013.12.007"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_009_w2aab3b7c14b1b6b1ab1ab9Aa","doi-asserted-by":"crossref","unstructured":"[9] Pierre Buyssens, Isabelle Gardin, Su Ruan, and Abderrahim Elmoataz. Eikonal-based region growing for efficient clustering. Image and Vision Computing, 32(12):1045\u20131054, December 2014.10.1016\/j.imavis.2014.10.002","DOI":"10.1016\/j.imavis.2014.10.002"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_010_w2aab3b7c14b1b6b1ab1ac10Aa","doi-asserted-by":"crossref","unstructured":"[10] Pierre Buyssens, Matthieu Toutain, Abderrahim Elmoataz, and Olivier L\u00e9zoray. Eikonal-based vertices growing and iterative seeding for efficient graph-based segmentation. In IEEE International Conference on Image Processing (ICIP 2014), page 5 pp., Paris, France, October 2014.10.1109\/ICIP.2014.7025886","DOI":"10.1109\/ICIP.2014.7025886"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_011_w2aab3b7c14b1b6b1ab1ac11Aa","doi-asserted-by":"crossref","unstructured":"[11] Pierre Cettour-Janet, Cl\u00e9ment Cazorla, Va\u00efa Machairas, Quentin Delannoy, Nathalie Bednarek, Fran\u00e7ois Rousseau, Etienne Decenci\u00e8re, and Nicolas Passat. Watervoxels. Image Processing On Line IPOL, 9:317\u2013328, 2019.10.5201\/ipol.2019.250","DOI":"10.5201\/ipol.2019.250"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_012_w2aab3b7c14b1b6b1ab1ac12Aa","unstructured":"[12] Kaiwen Chang and Bruno Figliuzzi. Hierarchical segmentation based upon multi-resolution approximations and the water-shed transform. In Angulo J., Velasco-Forero S., Meyer F.(eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2017. Lecture Notes in Computer Science, vol 10225. Springer, Cham, 2017."},{"key":"2022042712261287502_j_mathm-2020-0105_ref_013_w2aab3b7c14b1b6b1ab1ac13Aa","doi-asserted-by":"crossref","unstructured":"[13] Kaiwen Chang and Bruno Figliuzzi. Fast marching based superpixels generation. In International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, pages 350\u2013361. Springer, 2019.10.1007\/978-3-030-20867-7_27","DOI":"10.1007\/978-3-030-20867-7_27"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_014_w2aab3b7c14b1b6b1ab1ac14Aa","doi-asserted-by":"crossref","unstructured":"[14] Dorin Comaniciu and Peter Meer. Mean shift: A robust approach toward feature space analysis. IEEE Transactions on pattern analysis and machine intelligence, 24(5):603\u2013619, 2002.","DOI":"10.1109\/34.1000236"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_015_w2aab3b7c14b1b6b1ab1ac15Aa","doi-asserted-by":"crossref","unstructured":"[15] Eva Dejnozkov\u00e1 and Petr Dokl\u00e1dal. A parallel algorithm for solving the eikonal equation. In 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings.(ICASSP\u201903)., volume 3, pages III\u2013325. 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Modelling the microstructure and the viscoelastic behaviour of carbon black filled rubber materials from 3d simulations. Technische Mechanik, 32(1-2):22\u201346, 2016."},{"key":"2022042712261287502_j_mathm-2020-0105_ref_019_w2aab3b7c14b1b6b1ab1ac19Aa","doi-asserted-by":"crossref","unstructured":"[19] Brian Fulkerson, Andrea Vedaldi, and Stefano Soatto. Class segmentation and object localization with superpixel neighborhoods. In Computer Vision, 2009 IEEE 12th International Conference on, pages 670\u2013677. IEEE, 2009.10.1109\/ICCV.2009.5459175","DOI":"10.1109\/ICCV.2009.5459175"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_020_w2aab3b7c14b1b6b1ab1ac20Aa","doi-asserted-by":"crossref","unstructured":"[20] Remi Giraud, Vinh-Thong Ta, Nicolas Papadakis, and Yannick Berthoumieu. 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International journal of computer vision, 43(1):7\u201327, 2001.","DOI":"10.1023\/A:1011174803800"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_025_w2aab3b7c14b1b6b1ab1ac25Aa","unstructured":"[25] Peer Neubert and Peter Protzel. Superpixel benchmark and comparison. In Forum Bildverarbeitung 2010, pages 205\u2013218, 2012."},{"key":"2022042712261287502_j_mathm-2020-0105_ref_026_w2aab3b7c14b1b6b1ab1ac26Aa","unstructured":"[26] Alexander Schick, Mika Fischer, and Rainer Stiefelhagen. Measuring and evaluating the compactness of superpixels. In Proceedings of the 21st international conference on pattern recognition (ICPR2012), pages 930\u2013934. IEEE, 2012."},{"key":"2022042712261287502_j_mathm-2020-0105_ref_027_w2aab3b7c14b1b6b1ab1ac27Aa","doi-asserted-by":"crossref","unstructured":"[27] James A Sethian. A fast marching level set method for monotonically advancing fronts. Proceedings of the National Academy of Sciences, 93(4):1591\u20131595, 1996.10.1073\/pnas.93.4.15913998611607632","DOI":"10.1073\/pnas.93.4.1591"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_028_w2aab3b7c14b1b6b1ab1ac28Aa","doi-asserted-by":"crossref","unstructured":"[28] James A Sethian. Fast marching methods. SIAM review, 41(2):199\u2013235, 1999.10.1137\/S0036144598347059","DOI":"10.1137\/S0036144598347059"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_029_w2aab3b7c14b1b6b1ab1ac29Aa","doi-asserted-by":"crossref","unstructured":"[29] Jianbo Shi and Jitendra Malik. Normalized cuts and image segmentation. IEEE Transactions on pattern analysis and machine intelligence, 22(8):888\u2013905, 2000.10.1109\/34.868688","DOI":"10.1109\/34.868688"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_030_w2aab3b7c14b1b6b1ab1ac30Aa","doi-asserted-by":"crossref","unstructured":"[30] David Stutz, Alexander Hermans, and Bastian Leibe. Superpixels: An Evaluation of the State-of-the-Art. Computer Vision and Image Understanding, April 2017.10.1016\/j.cviu.2017.03.007","DOI":"10.1016\/j.cviu.2017.03.007"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_031_w2aab3b7c14b1b6b1ab1ac31Aa","doi-asserted-by":"crossref","unstructured":"[31] John E Vargas-Mu\u00f1oz, Ananda S Chowdhury, Eduardo B Alexandre, Felipe L Galv\u00e3o, Paulo A Vechiatto Miranda, and Alexandre X Falc\u00e3o. An iterative spanning forest framework for superpixel segmentation. IEEE Transactions on Image Processing, 28(7):3477\u20133489, 2019.10.1109\/TIP.2019.289794130735996","DOI":"10.1109\/TIP.2019.2897941"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_032_w2aab3b7c14b1b6b1ab1ac32Aa","doi-asserted-by":"crossref","unstructured":"[32] Luc Vincent and Pierre Soille. Watersheds in digital spaces: an efficient algorithm based on immersion simulations. IEEE Transactions on Pattern Analysis & Machine Intelligence, (6):583\u2013598, 1991.","DOI":"10.1109\/34.87344"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_033_w2aab3b7c14b1b6b1ab1ac33Aa","doi-asserted-by":"crossref","unstructured":"[33] Xiaolin Xiao, Yue-Jiao Gong, and Yicong Zhou. Adaptive superpixel segmentation aggregating local contour and texture features. In 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1902\u20131906. IEEE, 2017.10.1109\/ICASSP.2017.7952487","DOI":"10.1109\/ICASSP.2017.7952487"},{"key":"2022042712261287502_j_mathm-2020-0105_ref_034_w2aab3b7c14b1b6b1ab1ac34Aa","doi-asserted-by":"crossref","unstructured":"[34] C Lawrence Zitnick and Sing Bing Kang. Stereo for image-based rendering using image over-segmentation. 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