{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:23:43Z","timestamp":1740122623780,"version":"3.37.3"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2019,1,2]],"date-time":"2019-01-02T00:00:00Z","timestamp":1546387200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["LabEx BEZOUT ANR-10-LABX-58","ANR-15-CE40-0006 CoMeDiC"],"award-info":[{"award-number":["LabEx BEZOUT ANR-10-LABX-58","ANR-15-CE40-0006 CoMeDiC"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-14-CE27-0001 GRAPHSIP"],"award-info":[{"award-number":["ANR-14-CE27-0001 GRAPHSIP"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001843","name":"Science and Engineering Research Board","doi-asserted-by":"publisher","award":["EMR\/2015\/000853"],"award-info":[{"award-number":["EMR\/2015\/000853"]}],"id":[{"id":"10.13039\/501100001843","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001413","name":"Indian Space Research Organisation","doi-asserted-by":"publisher","award":["ISRO\/SSPO\/Ch-1\/2016-17"],"award-info":[{"award-number":["ISRO\/SSPO\/Ch-1\/2016-17"]}],"id":[{"id":"10.13039\/501100001413","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2019,7]]},"DOI":"10.1007\/s10851-018-0866-1","type":"journal-article","created":{"date-parts":[[2019,1,2]],"date-time":"2019-01-02T00:12:19Z","timestamp":1546387939000},"page":"745-762","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Some Theoretical Links Between Shortest Path Filters and Minimum Spanning Tree Filters"],"prefix":"10.1007","volume":"61","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2253-4324","authenticated-orcid":false,"given":"Sravan","family":"Danda","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aditya","family":"Challa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B. S. Daya","family":"Sagar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Laurent","family":"Najman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,1,2]]},"reference":[{"issue":"9","key":"866_CR1","doi-asserted-by":"publisher","first-page":"1309","DOI":"10.1080\/00207160701324249","volume":"84","author":"C Alvino","year":"2007","unstructured":"Alvino, C., Unal, G., Slabaugh, G., Peny, B., Fang, T.: Efficient segmentation based on eikonal and diffusion equations. Int. J. Comput. Math. 84(9), 1309\u20131324 (2007)","journal-title":"Int. J. Comput. Math."},{"key":"866_CR2","doi-asserted-by":"crossref","unstructured":"Angulo, J.: Pseudo-morphological image diffusion using the counter-harmonic paradigm. In: International Conference on Advanced Concepts for Intelligent Vision Systems, pp. 426\u2013437. Springer, Berlin, Heidelberg (2010)","DOI":"10.1007\/978-3-642-17688-3_40"},{"issue":"5","key":"866_CR3","doi-asserted-by":"publisher","first-page":"898","DOI":"10.1109\/TPAMI.2010.161","volume":"33","author":"P Arbelaez","year":"2011","unstructured":"Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour detection and hierarchical image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 33(5), 898\u2013916 (2011)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"866_CR4","unstructured":"Bai, X., Sapiro, G.: A geodesic framework for fast interactive image and video segmentation and matting. In: IEEE 11th International Conference on Computer Vision, 2007. ICCV 2007, pp. 1\u20138. IEEE (2007)"},{"issue":"2","key":"866_CR5","first-page":"555","volume":"23","author":"L Bao","year":"2014","unstructured":"Bao, L., Song, Y., Yang, Q., Yuan, H., Wang, G.: Tree filtering: efficient structure-preserving smoothing with a minimum spanning tree. IEEE TIP 23(2), 555\u2013569 (2014)","journal-title":"IEEE TIP"},{"key":"866_CR6","unstructured":"Boykov, Y.Y., Jolly, M.P.: Interactive graph cuts for optimal boundary & region segmentation of objects in ND images. In: Proceedings. Eighth IEEE International Conference on Computer Vision, 2001. ICCV 2001, vol.\u00a01, pp. 105\u2013112. IEEE (2001)"},{"key":"866_CR7","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198507840.001.0001","volume-title":"Gamma-Convergence for Beginners","author":"A Braides","year":"2002","unstructured":"Braides, A.: Gamma-Convergence for Beginners, vol. 22. Clarendon Press, New York (2002)"},{"issue":"4","key":"866_CR8","doi-asserted-by":"publisher","first-page":"1488","DOI":"10.1109\/TIP.2011.2173206","volume":"21","author":"D Brunet","year":"2012","unstructured":"Brunet, D., Vrscay, E.R., Wang, Z.: On the mathematical properties of the structural similarity index. IEEE Trans. Image Process. 21(4), 1488\u20131499 (2012)","journal-title":"IEEE Trans. Image Process."},{"key":"866_CR9","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/978-3-319-66272-5_16","volume-title":"Discrete Geometry for Computer Imagery, Lecture Note In Computer Sciences","author":"A Challa","year":"2017","unstructured":"Challa, A., Danda, S., Daya Sagar, B.S., Najman, L.: An Introduction to gamma-convergence for spectral clustering. In: Kropatsch, W.G., Artner, N.M., Janusch, I. (eds.) Discrete Geometry for Computer Imagery, Lecture Note In Computer Sciences, vol. 10502, pp. 185\u2013196. Springer, Vienna (2017)"},{"key":"866_CR10","doi-asserted-by":"crossref","unstructured":"Chang, J.H.R., Wang, Y.C.F.: Propagated image filtering. In: 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 10\u201318. IEEE (2015)","DOI":"10.1109\/CVPR.2015.7298595"},{"key":"866_CR11","doi-asserted-by":"publisher","unstructured":"Ciesielski, K.C., Falc\u00e3o, A.X., Miranda, P.A.V.: Path-value functions for which dijkstra\u2019s algorithm returns optimal mapping. J. Math. Imaging Vis. (2018). \n                    https:\/\/doi.org\/10.1007\/s10851-018-0793-1","DOI":"10.1007\/s10851-018-0793-1"},{"issue":"3","key":"866_CR12","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1007\/s10851-012-0333-3","volume":"44","author":"KC Ciesielski","year":"2012","unstructured":"Ciesielski, K.C., Udupa, J.K., Falc\u00e3o, A.X., Miranda, P.A.: Fuzzy connectedness image segmentation in graph cut formulation: a linear-time algorithm and a comparative analysis. J. Math. Imaging Vis. 44(3), 375\u2013398 (2012)","journal-title":"J. Math. Imaging Vis."},{"issue":"7","key":"866_CR13","doi-asserted-by":"publisher","first-page":"1384","DOI":"10.1109\/TPAMI.2010.200","volume":"33","author":"C Couprie","year":"2011","unstructured":"Couprie, C., Grady, L., Najman, L., Talbot, H.: Power watershed: a unifying graph-based optimization framework. IEEE PAMI 33(7), 1384\u20131399 (2011)","journal-title":"IEEE PAMI"},{"issue":"8","key":"866_CR14","doi-asserted-by":"publisher","first-page":"1362","DOI":"10.1109\/TPAMI.2008.173","volume":"31","author":"J Cousty","year":"2009","unstructured":"Cousty, J., Bertrand, G., Najman, L., Couprie, M.: Watershed cuts: minimum spanning forests and the drop of water principle. IEEE PAMI 31(8), 1362\u20131374 (2009)","journal-title":"IEEE PAMI"},{"issue":"5","key":"866_CR15","doi-asserted-by":"publisher","first-page":"925","DOI":"10.1109\/TPAMI.2009.71","volume":"32","author":"J Cousty","year":"2010","unstructured":"Cousty, J., Bertrand, G., Najman, L., Couprie, M.: Watershed cuts: thinnings, shortest path forests, and topological watersheds. IEEE PAMI 32(5), 925\u2013939 (2010)","journal-title":"IEEE PAMI"},{"key":"866_CR16","first-page":"99","volume":"2008","author":"A Criminisi","year":"2008","unstructured":"Criminisi, A., Sharp, T., Blake, A.: Geos: geodesic image segmentation. Comput. Vis. ECCV 2008, 99\u2013112 (2008)","journal-title":"Comput. Vis. ECCV"},{"key":"866_CR17","doi-asserted-by":"crossref","unstructured":"Danda, S., Challa, A., Sagar, B.D., Najman, L.: Power tree filter: a theoretical framework linking shortest path filters and minimum spanning tree filters. In: International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, pp. 199\u2013210. Springer (2017)","DOI":"10.1007\/978-3-319-57240-6_16"},{"issue":"7","key":"866_CR18","doi-asserted-by":"publisher","first-page":"1571","DOI":"10.1016\/S0031-3203(01)00148-0","volume":"35","author":"AX Falc\u00e3o","year":"2002","unstructured":"Falc\u00e3o, A.X., da Fontoura Costa, L., Da Cunha, B.: Multiscale skeletons by image foresting transform and its application to neuromorphometry. Pattern Recognit. 35(7), 1571\u20131582 (2002)","journal-title":"Pattern Recognit."},{"issue":"1","key":"866_CR19","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1109\/TPAMI.2004.1261076","volume":"26","author":"AX Falcao","year":"2004","unstructured":"Falcao, A.X., Stolfi, J., de Alencar Lotufo, R.: The image foresting transform: theory, algorithms, and applications. IEEE PAMI 26(1), 19 (2004)","journal-title":"IEEE PAMI"},{"key":"866_CR20","doi-asserted-by":"crossref","unstructured":"Farbman, Z., Fattal, R., Lischinski, D., Szeliski, R.: Edge-preserving decompositions for multi-scale tone and detail manipulation. In: ACM Transactions on Graphics (TOG), vol.\u00a027, p.\u00a067. ACM (2008)","DOI":"10.1145\/1360612.1360666"},{"issue":"6","key":"866_CR21","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1145\/367766.368168","volume":"5","author":"RW Floyd","year":"1962","unstructured":"Floyd, R.W.: Algorithm 97: shortest path. Commun. ACM 5(6), 345 (1962)","journal-title":"Commun. ACM"},{"issue":"11","key":"866_CR22","doi-asserted-by":"publisher","first-page":"1768","DOI":"10.1109\/TPAMI.2006.233","volume":"28","author":"L Grady","year":"2006","unstructured":"Grady, L.: Random walks for image segmentation. IEEE PAMI 28(11), 1768\u20131783 (2006)","journal-title":"IEEE PAMI"},{"issue":"10","key":"866_CR23","doi-asserted-by":"publisher","first-page":"2306","DOI":"10.1016\/j.patcog.2008.11.004","volume":"42","author":"J Grazzini","year":"2009","unstructured":"Grazzini, J., Soille, P.: Edge-preserving smoothing using a similarity measure in adaptive geodesic neighbourhoods. Pattern Recognit. 42(10), 2306\u20132316 (2009)","journal-title":"Pattern Recognit."},{"key":"866_CR24","doi-asserted-by":"crossref","unstructured":"He, K., Sun, J., Tang, X.: Guided image filtering. In: European Conference on Computer Vision 2010, pp. 1\u201314. Springer (2010)","DOI":"10.1007\/978-3-642-15549-9_1"},{"issue":"4","key":"866_CR25","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1016\/j.imavis.2006.04.018","volume":"25","author":"R Lerallut","year":"2007","unstructured":"Lerallut, R., Decenci\u00e8re, \u00c9., Meyer, F.: Image filtering using morphological amoebas. Image Vis. Comput. 25(4), 395\u2013404 (2007)","journal-title":"Image Vis. Comput."},{"key":"866_CR26","unstructured":"Lotufo, R.d.A., Falc\u00e3o, A.A., Zampirolli, F.A.: Fast Euclidean distance transform using a graph-search algorithm. In: Proceedings XIII Brazilian Symposium on Computer Graphics and Image Processing, 2000, pp. 269\u2013275. IEEE (2000)"},{"issue":"4","key":"866_CR27","doi-asserted-by":"publisher","first-page":"2275","DOI":"10.1137\/17M1118580","volume":"10","author":"L Najman","year":"2017","unstructured":"Najman, L.: Extending the PowerWatershed framework thanks to \n                    \n                      \n                    \n                    $$\\Gamma $$\n                    \n                      \n                        \u0393\n                      \n                    \n                  -convergence. SIAM J. Imaging Sci. 10(4), 2275\u20132292 (2017). \n                    https:\/\/doi.org\/10.1137\/17M1118580","journal-title":"SIAM J. Imaging Sci."},{"key":"866_CR28","doi-asserted-by":"crossref","unstructured":"Najman, L., Pesquet, J.C., Talbot, H.: When convex analysis meets mathematical morphology on graphs. In: International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, pp. 473\u2013484. Springer (2015)","DOI":"10.1007\/978-3-319-18720-4_40"},{"issue":"1","key":"866_CR29","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1006\/cviu.2000.0902","volume":"82","author":"PK Saha","year":"2001","unstructured":"Saha, P.K., Udupa, J.K.: Relative fuzzy connectedness among multiple objects: theory, algorithms, and applications in image segmentation. Comput. Vis. Image Underst. 82(1), 42\u201356 (2001)","journal-title":"Comput. Vis. Image Underst."},{"key":"866_CR30","unstructured":"Sinop, A.K., Grady, L.: A seeded image segmentation framework unifying graph cuts and random walker which yields a new algorithm. In: IEEE 11th International Conference on Computer Vision, 2007. ICCV 2007, pp. 1\u20138. IEEE (2007)"},{"key":"866_CR31","doi-asserted-by":"crossref","unstructured":"Stawiaski, J., Meyer, F.: Minimum spanning tree adaptive image filtering. In: 2009 16th IEEE ICIP, pp. 2245\u20132248. IEEE (2009)","DOI":"10.1109\/ICIP.2009.5413942"},{"key":"866_CR32","volume-title":"Computer Vision: Algorithms and Applications","author":"R Szeliski","year":"2010","unstructured":"Szeliski, R.: Computer Vision: Algorithms and Applications. Springer, New York (2010)"},{"key":"866_CR33","unstructured":"Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: Sixth International Conference on Computer Vision, 1998. ICCV 1998, pp. 839\u2013846. IEEE (1998)"},{"key":"866_CR34","doi-asserted-by":"crossref","unstructured":"Van\u00a0Vliet, L.J.: Robust local max-min filters by normalized power-weighted filtering. In: Pattern Recognition, 2004. ICPR 2004. Proceedings of the 17th International Conference on, vol.\u00a01, pp. 696\u2013699. IEEE (2004)","DOI":"10.1109\/ICPR.2004.1334273"},{"key":"866_CR35","doi-asserted-by":"crossref","unstructured":"Vineet, V., Harish, P., Patidar, S., Narayanan, P.: Fast minimum spanning tree for large graphs on the GPU. In: Proceedings of the Conference on High Performance Graphics 2009, pp. 167\u2013171. ACM (2009)","DOI":"10.1145\/1572769.1572796"},{"issue":"4","key":"866_CR36","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1007\/s11222-007-9033-z","volume":"17","author":"U Luxburg Von","year":"2007","unstructured":"Von Luxburg, U.: A tutorial on spectral clustering. Stat. Comput. 17(4), 395\u2013416 (2007)","journal-title":"Stat. Comput."},{"issue":"6","key":"866_CR37","first-page":"174","volume":"30","author":"L Xu","year":"2011","unstructured":"Xu, L., Lu, C., Xu, Y., Jia, J.: Image smoothing via \n                    \n                      \n                    \n                    $${L}_0$$\n                    \n                      \n                        \n                          L\n                          0\n                        \n                      \n                    \n                   gradient minimization. ACM Trans. Graph. (TOG) 30(6), 174 (2011)","journal-title":"ACM Trans. Graph. (TOG)"},{"issue":"6","key":"866_CR38","first-page":"139","volume":"31","author":"L Xu","year":"2012","unstructured":"Xu, L., Yan, Q., Xia, Y., Jia, J.: Structure extraction from texture via relative total variation. ACM Trans. Graph. (TOG) 31(6), 139 (2012)","journal-title":"ACM Trans. Graph. (TOG)"},{"issue":"6","key":"866_CR39","doi-asserted-by":"publisher","first-page":"1126","DOI":"10.1109\/TPAMI.2015.2441070","volume":"38","author":"Y Xu","year":"2016","unstructured":"Xu, Y., G\u00e9raud, T., Najman, L.: Connected filtering on tree-based shape-spaces. IEEE Trans. Pattern Anal. Mach. Intell. 38(6), 1126\u20131140 (2016)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"4","key":"866_CR40","doi-asserted-by":"publisher","first-page":"834","DOI":"10.1109\/TPAMI.2014.2353642","volume":"37","author":"Q Yang","year":"2015","unstructured":"Yang, Q.: Stereo matching using tree filtering. IEEE PAMI 37(4), 834\u2013846 (2015)","journal-title":"IEEE PAMI"},{"issue":"1","key":"866_CR41","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1109\/T-C.1971.223083","volume":"100","author":"CT Zahn","year":"1971","unstructured":"Zahn, C.T.: Graph-theoretical methods for detecting and describing gestalt clusters. IEEE Trans. Comput. 100(1), 68\u201386 (1971)","journal-title":"IEEE Trans. Comput."}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-018-0866-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10851-018-0866-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-018-0866-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T19:05:22Z","timestamp":1577905522000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10851-018-0866-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,2]]},"references-count":41,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2019,7]]}},"alternative-id":["866"],"URL":"https:\/\/doi.org\/10.1007\/s10851-018-0866-1","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"type":"print","value":"0924-9907"},{"type":"electronic","value":"1573-7683"}],"subject":[],"published":{"date-parts":[[2019,1,2]]},"assertion":[{"value":"4 May 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 December 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 January 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}