{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,2]],"date-time":"2026-11-02T13:30:20Z","timestamp":1793626220097,"version":"4.5.1"},"reference-count":60,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001665","name":"French National Research Agency","doi-asserted-by":"publisher","award":["ANR-19-P3IA-0002"],"award-info":[{"award-number":["ANR-19-P3IA-0002"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Medical Image Analysis"],"published-print":{"date-parts":[[2027,1]]},"DOI":"10.1016\/j.media.2026.104284","type":"journal-article","created":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T15:16:39Z","timestamp":1788362199000},"page":"104284","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["SoftMorph: Differentiable probabilistic morphological operators for image analysis"],"prefix":"10.1016","volume":"115","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-8793-0624","authenticated-orcid":false,"given":"Lisa","family":"Guzzi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1147-766X","authenticated-orcid":false,"given":"Maria A.","family":"Zuluaga","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6765-8021","authenticated-orcid":false,"given":"Fabien","family":"Lareyre","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gilles","family":"Di Lorenzo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-5017-4748","authenticated-orcid":false,"given":"S\u00e9bastien","family":"Goffart","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1475-4500","authenticated-orcid":false,"given":"Andrea","family":"Chierici","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Juliette","family":"Raffort","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6050-5949","authenticated-orcid":false,"given":"Herv\u00e9","family":"Delingette","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.media.2026.104284_b1","first-page":"548","article-title":"Mammographic image enhancement using modified mathematical morphology and Bi-orthogonal wavelet","volume":"vol. 1","author":"Amutha","year":"2011"},{"key":"10.1016\/j.media.2026.104284_b2","unstructured":"Angulo, J., 2008. A Mathematical Morphology Approach to Cell Shape Analysis. In: Progress in Industrial Mathematics At ECMI 2006, vol. 12, Berlin, Heidelberg, ISBN: 978-3-540-71991-5 978-3-540-71992-2, pp. 543\u2013547, Series Title: Mathematics in Industry."},{"key":"10.1016\/j.media.2026.104284_b3","doi-asserted-by":"crossref","unstructured":"Angulo, J., 2010. Pseudo-morphological Image Diffusion Using the Counter-Harmonic Paradigm. In: Advanced Concepts for Intelligent Vision Systems. Berlin, Heidelberg, ISBN: 978-3-642-17688-3, pp. 426\u2013437.","DOI":"10.1007\/978-3-642-17688-3_40"},{"issue":"5","key":"10.1016\/j.media.2026.104284_b4","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1093\/bioinformatics\/btg057","article-title":"Automatic analysis of DNA microarray images using mathematical morphology","volume":"19","author":"Angulo","year":"2003","journal-title":"Bioinform."},{"issue":"1","key":"10.1016\/j.media.2026.104284_b5","doi-asserted-by":"crossref","first-page":"4128","DOI":"10.1038\/s41467-022-30695-9","article-title":"The medical segmentation decathlon","volume":"13","author":"Antonelli","year":"2022","journal-title":"Nat. Commun."},{"key":"10.1016\/j.media.2026.104284_b6","doi-asserted-by":"crossref","unstructured":"Aouad, T., Talbot, H., 2022. Binary Morphological Neural Network. In: 2022 IEEE International Conference on Image Processing. ICIP, pp. 3276\u20133280.","DOI":"10.1109\/ICIP46576.2022.9897474"},{"key":"10.1016\/j.media.2026.104284_b7","doi-asserted-by":"crossref","unstructured":"Asano, A., Kobayashi, Y., Muraki, C., Muneyasu, M., 2004. Optimization of gray scale morphological opening for noise removal in texture images. In: The 2004 47th Midwest Symposium on Circuits and Systems, 2004. MWSCAS \u201904., vol. 1, Hiroshima, Japan, ISBN: 978-0-7803-8346-3, pp. 1_313\u20131_316.","DOI":"10.1109\/MWSCAS.2004.1353990"},{"key":"10.1016\/j.media.2026.104284_b8","series-title":"Skeletonization","first-page":"71","article-title":"Chapter 3 - fuzzy skeleton and skeleton by influence zones: a review","author":"Bloch","year":"2017"},{"key":"10.1016\/j.media.2026.104284_b9","series-title":"Discrete Geometry and Mathematical Morphology","first-page":"457","article-title":"On some associations between mathematical morphology and artificial intelligence","author":"Bloch","year":"2021"},{"issue":"9","key":"10.1016\/j.media.2026.104284_b10","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1016\/0031-3203(94)00312-A","article-title":"Fuzzy mathematical morphologies: A comparative study","volume":"28","author":"Bloch","year":"1995","journal-title":"Pattern Recognit."},{"key":"10.1016\/j.media.2026.104284_b11","series-title":"Introduction to Logic","author":"Copi","year":"2016"},{"issue":"2","key":"10.1016\/j.media.2026.104284_b12","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/0165-0114(82)90005-7","article-title":"A general class of fuzzy operators, the demorgan class of fuzzy operators and fuzziness measures induced by fuzzy operators","volume":"8","author":"Dombi","year":"1982","journal-title":"Fuzzy Sets and Systems"},{"key":"10.1016\/j.media.2026.104284_b13","first-page":"285","article-title":"Multidimensional morphological edge detection","volume":"vol. 0845","author":"Feehs","year":"1987"},{"key":"10.1016\/j.media.2026.104284_b14","doi-asserted-by":"crossref","DOI":"10.1016\/j.patcog.2020.107246","article-title":"Deep morphological networks","volume":"102","author":"Franchi","year":"2020","journal-title":"Pattern Recognit."},{"key":"10.1016\/j.media.2026.104284_b15","doi-asserted-by":"crossref","unstructured":"Guzzi, L., Zuluaga, M.A., Lareyre, F., Di Lorenzo, G., Goffart, S., Chierici, A., Raffort, J., Delingette, H., 2024. Differentiable Soft Morphological Filters for Medical Image Segmentation. In: MICCAI 2024 - Medical Image Computing and Computer Assisted Intervention. Marrakesh, Morocco.","DOI":"10.1007\/978-3-031-72111-3_17"},{"issue":"16","key":"10.1016\/j.media.2026.104284_b16","doi-asserted-by":"crossref","first-page":"1854","DOI":"10.3390\/math9161854","article-title":"On machine-learning morphological image operators","volume":"9","author":"Hirata","year":"2021","journal-title":"Mathematics"},{"issue":"2","key":"10.1016\/j.media.2026.104284_b17","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1038\/s41592-020-01008-z","article-title":"nnU-Net: a self-configuring method for deep learning-based biomedical image segmentation","volume":"18","author":"Isensee","year":"2021","journal-title":"Nature Methods"},{"key":"10.1016\/j.media.2026.104284_b18","series-title":"Proceedings of the Fourth Conference on Medical Imaging with Deep Learning","first-page":"158","article-title":"A surprisingly effective perimeter-based loss for medical image segmentation","author":"Jurdi","year":"2021"},{"issue":"1","key":"10.1016\/j.media.2026.104284_b19","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1186\/2043-9113-1-33","article-title":"Mathematical morphology-based approach to the enhancement of morphological features in medical images","volume":"1","author":"Kimori","year":"2011","journal-title":"J. Clin. Bioinform."},{"issue":"4","key":"10.1016\/j.media.2026.104284_b20","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/BF00121878","article-title":"Morphological methods for detection and classification of edges in range images","volume":"2","author":"Krishnapuram","year":"1992","journal-title":"J. Math. Imaging Vision"},{"key":"10.1016\/j.media.2026.104284_b21","series-title":"GD doesn\u2019t make the cut: Three ways that non-differentiability affects neural network training","author":"Kumar","year":"2024"},{"issue":"9","key":"10.1016\/j.media.2026.104284_b22","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1109\/34.161346","article-title":"Thinning methodologies-a comprehensive survey","volume":"14","author":"Lam","year":"1992","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"7553","key":"10.1016\/j.media.2026.104284_b23","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"LeCun","year":"2015","journal-title":"Nature"},{"key":"10.1016\/j.media.2026.104284_b24","doi-asserted-by":"crossref","unstructured":"Masci, J., Angulo, J., Schmidhuber, J., 2013. A Learning Framework for Morphological Operators Using Counter\u2013Harmonic Mean. In: Mathematical Morphology and Its Applications To Signal and Image Processing. Berlin, Heidelberg, ISBN: 978-3-642-38294-9, pp. 329\u2013340.","DOI":"10.1007\/978-3-642-38294-9_28"},{"key":"10.1016\/j.media.2026.104284_b25","series-title":"Neural Information Processing","first-page":"110","article-title":"Morph-CNN: A morphological convolutional neural network for image classification","author":"Mellouli","year":"2017"},{"issue":"9","key":"10.1016\/j.media.2026.104284_b26","doi-asserted-by":"crossref","first-page":"2876","DOI":"10.1109\/TNNLS.2018.2890334","article-title":"Morphological convolutional neural network architecture for digit recognition","volume":"30","author":"Mellouli","year":"2019","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"10.1016\/j.media.2026.104284_b27","doi-asserted-by":"crossref","unstructured":"Menten, M.J., Paetzold, J.C., Zimmer, V.A., Shit, S., Ezhov, I., Holland, R., Probst, M., Schnabel, J.A., Rueckert, D., 2023. A Skeletonization Algorithm for Gradient-Based Optimization. In: Proceedings of the IEEE\/CVF International Conference on Computer Vision. ICCV, pp. 21394\u201321403.","DOI":"10.1109\/ICCV51070.2023.01956"},{"issue":"1","key":"10.1016\/j.media.2026.104284_b28","first-page":"87","article-title":"Image restoration by learning morphological opening-closing network","volume":"4","author":"Mondal","year":"2020","journal-title":"Math. Morphol. - Theory Appl."},{"key":"10.1016\/j.media.2026.104284_b29","series-title":"Discrete Geometry for Computer Imagery","first-page":"262","article-title":"Morphological networks for image De-raining","author":"Mondal","year":"2019"},{"key":"10.1016\/j.media.2026.104284_b30","series-title":"Morphological network: How far can we go with morphological neurons?","author":"Mondal","year":"2022"},{"issue":"4","key":"10.1016\/j.media.2026.104284_b31","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1016\/S0165-1684(99)00161-9","article-title":"A multiscale morphological approach to local contrast enhancement","volume":"80","author":"Mukhopadhyay","year":"2000","journal-title":"Signal Process."},{"key":"10.1016\/j.media.2026.104284_b32","unstructured":"Nakashizuka, M., 2009. A Design Method for Morphological Filters with Approximations of Min\/Max Operators. In: Proceedings : APSIPA ASC 2009 : Asia-Pacific Signal and Information Processing Association, 2009 Annual Summit and Conference. pp. 841\u2013844."},{"key":"10.1016\/j.media.2026.104284_b33","doi-asserted-by":"crossref","unstructured":"Nguyen, N.H., 2021. U-Net based skeletonization and bag of tricks. In: 2021 IEEE\/CVF International Conference on Computer Vision Workshops (ICCVW). Montreal, BC, Canada, ISBN: 978-1-66540-191-3, pp. 2105\u20132109.","DOI":"10.1109\/ICCVW54120.2021.00238"},{"key":"10.1016\/j.media.2026.104284_b34","doi-asserted-by":"crossref","first-page":"114308","DOI":"10.1109\/ACCESS.2021.3104405","article-title":"An introduction to deep morphological networks","volume":"9","author":"Nogueira","year":"2021","journal-title":"IEEE Access"},{"issue":"11","key":"10.1016\/j.media.2026.104284_b35","doi-asserted-by":"crossref","first-page":"1961","DOI":"10.1016\/j.patcog.2005.01.026","article-title":"A novel adaptive morphological approach for degraded character image segmentation","volume":"38","author":"Nomura","year":"2005","journal-title":"Pattern Recognit."},{"key":"10.1016\/j.media.2026.104284_b36","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-5217-8","article-title":"Mathematical principles of fuzzy logic","author":"Nov\u00e1k","year":"1999"},{"key":"10.1016\/j.media.2026.104284_b37","first-page":"2901","article-title":"Adaptive fuzzy morphological filtering of images","volume":"vol. 5","author":"Oh","year":"1998"},{"key":"10.1016\/j.media.2026.104284_b38","unstructured":"Paetzold, J., Schoppe, O., Al-Maskari, R., Tetteh, G., Efremov, V., Todorov, M.I., Cai, R., Mai, H., Rong, Z., Ertuerk, A., Menze, B.H., 2019. Transfer learning from synthetic data reduces need for labels to segment brain vasculature and neural pathways in 3D. In: International Conference on Medical Imaging with Deep Learning\u2013Extended Abstract Track."},{"issue":"7","key":"10.1016\/j.media.2026.104284_b39","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1016\/S0167-8655(98)00031-2","article-title":"A 3D 6-subiteration thinning algorithm for extracting medial lines","volume":"19","author":"Pal\u00e0gyi","year":"1998","journal-title":"Pattern Recognit. Lett."},{"key":"10.1016\/j.media.2026.104284_b40","series-title":"2019 IEEE\/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)","first-page":"1186","article-title":"U-net based convolutional neural network for skeleton extraction","author":"Panichev","year":"2019"},{"issue":"5","key":"10.1016\/j.media.2026.104284_b41","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1109\/83.382491","article-title":"A new algorithm for image noise reduction using mathematical morphology","volume":"4","author":"Peters","year":"1995","journal-title":"IEEE Trans. Image Process."},{"key":"10.1016\/j.media.2026.104284_b42","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1016\/j.procs.2021.08.060","article-title":"Morphological cross entropy loss for improved semantic segmentation of small and thin objects","volume":"192","author":"Pihlak","year":"2021","journal-title":"Procedia Comput. Sci."},{"issue":"9","key":"10.1016\/j.media.2026.104284_b43","doi-asserted-by":"crossref","first-page":"3110","DOI":"10.3390\/s21093110","article-title":"Panoramic dental radiography image enhancement using multiscale mathematical morphology","volume":"21","author":"Rom\u00e1n","year":"2021","journal-title":"Sensors"},{"key":"10.1016\/j.media.2026.104284_b44","series-title":"Medical Image Computing and Computer-Assisted Intervention\u2013MICCAI 2015: 18th International Conference, Munich, Germany, October 5-9, 2015, Proceedings, Part III 18","first-page":"234","article-title":"U-net: Convolutional networks for biomedical image segmentation","author":"Ronneberger","year":"2015"},{"issue":"2","key":"10.1016\/j.media.2026.104284_b45","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1109\/TIFS.2006.873606","article-title":"Teeth segmentation in digitized dental X-ray films using mathematical morphology","volume":"1","author":"Said","year":"2006","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"issue":"1","key":"10.1016\/j.media.2026.104284_b46","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1109\/34.67627","article-title":"Optimal morphological pattern restoration from noisy binary images","volume":"13","author":"Schonfeld","year":"1991","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"10.1016\/j.media.2026.104284_b47","article-title":"Mathematical morphology and its applications to image processing","volume":"vol. 2","author":"Serra","year":"1994"},{"issue":"12","key":"10.1016\/j.media.2026.104284_b48","doi-asserted-by":"crossref","DOI":"10.1142\/S0218001422520231","article-title":"Deep morphological neural networks","volume":"36","author":"Shen","year":"2022","journal-title":"Int. J. Pattern Recognit. Artif. Intell."},{"key":"10.1016\/j.media.2026.104284_b49","series-title":"Image Processing and Mathematical Morphology: Fundamentals and Applications","author":"Shih","year":"2017"},{"issue":"06","key":"10.1016\/j.media.2026.104284_b50","doi-asserted-by":"crossref","DOI":"10.1142\/S0218001419540247","article-title":"Development of deep learning framework for mathematical morphology","volume":"33","author":"Shih","year":"2019","journal-title":"Int. J. Pattern Recognit. Artif. Intell."},{"key":"10.1016\/j.media.2026.104284_b51","doi-asserted-by":"crossref","unstructured":"Shit, S., Paetzold, J.C., Sekuboyina, A., Ezhov, I., Unger, A., Zhylka, A., Pluim, J.P.W., Bauer, U., Menze, B.H., 2021. clDice - a Novel Topology-Preserving Loss Function for Tubular Structure Segmentation. In: 2021 IEEE\/CVF Conference on Computer Vision and Pattern Recognition. CVPR, ISBN: 978-1-66544-509-2, pp. 16555\u201316564.","DOI":"10.1109\/CVPR46437.2021.01629"},{"issue":"3","key":"10.1016\/j.media.2026.104284_b52","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1016\/1047-3203(92)90024-N","article-title":"Fuzzy mathematical morphology","volume":"3","author":"Sinha","year":"1992","journal-title":"J. Vis. Commun. Image Represent."},{"issue":"4","key":"10.1016\/j.media.2026.104284_b53","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1109\/TMI.2004.825627","article-title":"Ridge-based vessel segmentation in color images of the Retina","volume":"23","author":"Staal","year":"2004","journal-title":"IEEE Trans. Med. Imaging"},{"key":"10.1016\/j.media.2026.104284_b54","first-page":"253","article-title":"A mathematical morphology-based filter for noise reduction and detail preservation in low-dose dental CT images","volume":"264","author":"Stringhini","year":"2019","journal-title":"Stud. Health Technol. Inform."},{"issue":"5","key":"10.1016\/j.media.2026.104284_b55","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1007\/s11554-019-00886-7","article-title":"Real-time thinning algorithms for 2D and 3D images using GPU processors","volume":"17","author":"Wagner","year":"2020","journal-title":"J. Real-Time Image Process."},{"key":"10.1016\/j.media.2026.104284_b56","doi-asserted-by":"crossref","DOI":"10.7717\/peerj.453","article-title":"Scikit-image: image processing in python","volume":"2","author":"Van der Walt","year":"2014","journal-title":"PeerJ"},{"issue":"3","key":"10.1016\/j.media.2026.104284_b57","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1109\/TIP.2005.863029","article-title":"Morphology-based multifractal estimation for texture segmentation","volume":"15","author":"Xia","year":"2006","journal-title":"IEEE Trans. Image Process."},{"key":"10.1016\/j.media.2026.104284_b58","series-title":"The 2nd International Conference on Information Science and Engineering","first-page":"3840","article-title":"Noise image restoration based on mathematical morphology","author":"yong","year":"2010"},{"key":"10.1016\/j.media.2026.104284_b59","first-page":"517","article-title":"An algorithm of image segmentation based on fuzzy mathematical morphology","volume":"vol. 2","author":"Yucheng","year":"2009"},{"key":"10.1016\/j.media.2026.104284_b60","doi-asserted-by":"crossref","unstructured":"Zhao Yu-qian, Gui Wei-hua, Chen Zhen-cheng, Tang Jing-tian, Li Ling-yun, 2005. Medical Images Edge Detection Based on Mathematical Morphology. In: 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference. Shanghai, China, ISBN: 978-0-7803-8741-6, pp. 6492\u20136495.","DOI":"10.1109\/IEMBS.2005.1615986"}],"container-title":["Medical Image Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1361841526003531?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1361841526003531?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,11,2]],"date-time":"2026-11-02T12:58:23Z","timestamp":1793624303000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1361841526003531"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2027,1]]},"references-count":60,"alternative-id":["S1361841526003531"],"URL":"https:\/\/doi.org\/10.1016\/j.media.2026.104284","relation":{"has-preprint":[{"id-type":"doi","id":"10.36227\/techrxiv.172840358.89754519\/v1","asserted-by":"object"}]},"ISSN":["1361-8415"],"issn-type":[{"value":"1361-8415","type":"print"}],"subject":[],"published":{"date-parts":[[2027,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"SoftMorph: Differentiable probabilistic morphological operators for image analysis","name":"articletitle","label":"Article Title"},{"value":"Medical Image Analysis","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.media.2026.104284","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"104284"}}