{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:42:54Z","timestamp":1775054574766,"version":"3.50.1"},"publisher-location":"Cham","reference-count":21,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030766566","type":"print"},{"value":"9783030766573","type":"electronic"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-76657-3_34","type":"book-chapter","created":{"date-parts":[[2021,5,15]],"date-time":"2021-05-15T20:02:23Z","timestamp":1621108943000},"page":"470-482","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Going Beyond p-convolutions to Learn Grayscale Morphological Operators"],"prefix":"10.1007","author":[{"given":"Alexandre","family":"Kirszenberg","sequence":"first","affiliation":[]},{"given":"Guillaume","family":"Tochon","sequence":"additional","affiliation":[]},{"given":"\u00c9lodie","family":"Puybareau","sequence":"additional","affiliation":[]},{"given":"Jesus","family":"Angulo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,5,16]]},"reference":[{"key":"34_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"426","DOI":"10.1007\/978-3-642-17688-3_40","volume-title":"Advanced Concepts for Intelligent Vision Systems","author":"J Angulo","year":"2010","unstructured":"Angulo, J.: Pseudo-morphological image diffusion using the counter-harmonic paradigm. In: Blanc-Talon, J., Bone, D., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2010. LNCS, vol. 6474, pp. 426\u2013437. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-17688-3_40"},{"key":"34_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-0399-4","volume-title":"Handbook of Means and Their Inequalities","author":"PS Bullen","year":"2013","unstructured":"Bullen, P.S.: Handbook of Means and Their Inequalities, vol. 560. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-94-017-0399-4"},{"key":"34_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-319-57240-6_1","volume-title":"Mathematical Morphology and Its Applications to Signal and Image Processing","author":"V Charisopoulos","year":"2017","unstructured":"Charisopoulos, V., Maragos, P.: Morphological perceptrons: geometry and training algorithms. In: Angulo, J., Velasco-Forero, S., Meyer, F. (eds.) ISMM 2017. LNCS, vol. 10225, pp. 3\u201315. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-57240-6_1"},{"key":"34_CR4","doi-asserted-by":"crossref","unstructured":"Davidson, J.L., Ritter, G.X.: Theory of morphological neural networks. In: Digital Optical Computing II, vol. 1215, pp. 378\u2013388. International Society for Optics and Photonics (1990)","DOI":"10.1117\/12.18085"},{"key":"34_CR5","doi-asserted-by":"publisher","first-page":"107246","DOI":"10.1016\/j.patcog.2020.107246","volume":"102","author":"G Franchi","year":"2020","unstructured":"Franchi, G., Fehri, A., Yao, A.: Deep morphological networks. Pattern Recogn. 102, 107246 (2020)","journal-title":"Pattern Recogn."},{"key":"34_CR6","volume-title":"Fundamentals of Artificial Neural Networks","author":"MH Hassoun","year":"1995","unstructured":"Hassoun, M.H., et al.: Fundamentals of Artificial Neural Networks. MIT Press, Cambridge (1995)"},{"key":"34_CR7","unstructured":"Lange, M., Z\u00fchlke, D., Holz, O., Villmann, T., Mittweida, S.G.: Applications of lp-norms and their smooth approximations for gradient based learning vector quantization. In: ESANN, pp. 271\u2013276 (2014)"},{"issue":"7553","key":"34_CR8","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1038\/nature14539","volume":"521","author":"Y LeCun","year":"2015","unstructured":"LeCun, Y., Bengio, Y., Hinton, G.: Deep learning. Nature 521(7553), 436\u2013444 (2015)","journal-title":"Nature"},{"key":"34_CR9","unstructured":"LeCun, Y., Cortes, C., Burges, C.J.: The MNIST database of handwritten digits 10(34), 14 (1998). http:\/\/yann.lecun.com\/exdb\/mnist\/"},{"key":"34_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1007\/978-3-642-38294-9_28","volume-title":"Mathematical Morphology and Its Applications to Signal and Image Processing","author":"J Masci","year":"2013","unstructured":"Masci, J., Angulo, J., Schmidhuber, J.: A learning framework for morphological operators using counter\u2013harmonic mean. In: Hendriks, C.L.L., Borgefors, G., Strand, R. (eds.) ISMM 2013. LNCS, vol. 7883, pp. 329\u2013340. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-38294-9_28"},{"key":"34_CR11","doi-asserted-by":"publisher","unstructured":"Mellouli, D., Hamdani, T.M., Ayed, M.B., Alimi, A.M.: Morph-CNN: a morphological convolutional neural network for image classification. In: Liu, D., Xie, S., Li, Y., Zhao, D., El-Alfy, E.S. (eds.) International Conference on Neural Information Processing, vol. 10635, pp. 110\u2013117. Springer, Heidelberg (2017). https:\/\/doi.org\/10.1007\/978-3-319-70096-0_12","DOI":"10.1007\/978-3-319-70096-0_12"},{"issue":"1","key":"34_CR12","first-page":"87","volume":"4","author":"R Mondal","year":"2020","unstructured":"Mondal, R., Dey, M.S., Chanda, B.: Image restoration by learning morphological opening-closing network. Math. Morphol. Theor. Appl. 4(1), 87\u2013107 (2020)","journal-title":"Math. Morphol. Theor. Appl."},{"key":"34_CR13","unstructured":"Nogueira, K., Chanussot, J., Dalla Mura, M., Schwartz, W.R., Santos, J.A.D.: An introduction to deep morphological networks. arXiv preprint arXiv:1906.01751 (2019)"},{"key":"34_CR14","doi-asserted-by":"crossref","unstructured":"Ritter, G.X., Sussner, P.: An introduction to morphological neural networks. In: Proceedings of 13th International Conference on Pattern Recognition, vol. 4, pp. 709\u2013717. IEEE (1996)","DOI":"10.1109\/ICPR.1996.547657"},{"key":"34_CR15","volume-title":"Image Analysis and Mathematical Morphology","author":"J Serra","year":"1983","unstructured":"Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, Cambridge (1983)"},{"key":"34_CR16","unstructured":"Shen, Y., Zhong, X., Shih, F.Y.: Deep morphological neural networks. arXiv preprint arXiv:1909.01532 (2019)"},{"issue":"06","key":"34_CR17","doi-asserted-by":"publisher","first-page":"1954024","DOI":"10.1142\/S0218001419540247","volume":"33","author":"FY Shih","year":"2019","unstructured":"Shih, F.Y., Shen, Y., Zhong, X.: Development of deep learning framework for mathematical morphology. Int. J. Pattern Recogn. Artif. Intell. 33(06), 1954024 (2019)","journal-title":"Int. J. Pattern Recogn. Artif. Intell."},{"key":"34_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-05088-0","volume-title":"Morphological Image Analysis: Principles And Applications","author":"P Soille","year":"2013","unstructured":"Soille, P.: Morphological Image Analysis: Principles And Applications. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-662-05088-0"},{"key":"34_CR19","doi-asserted-by":"crossref","unstructured":"Sussner, P.: Morphological perceptron learning. In: Proceedings of the 1998 IEEE International Symposium on Intelligent Control (ISIC), pp. 477\u2013482. IEEE (1998)","DOI":"10.1109\/ISIC.1998.713708"},{"key":"34_CR20","doi-asserted-by":"crossref","unstructured":"Wilson, S.S.: Morphological networks. In: Visual Communications and Image Processing IV, vol. 1199, pp. 483\u2013495. International Society for Optics and Photonics (1989)","DOI":"10.1117\/12.970058"},{"key":"34_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"310","DOI":"10.1007\/978-3-030-20867-7_24","volume-title":"Mathematical Morphology and Its Applications to Signal and Image Processing","author":"Y Zhang","year":"2019","unstructured":"Zhang, Y., Blusseau, S., Velasco-Forero, S., Bloch, I., Angulo, J.: Max-plus operators applied to filter selection and model pruning in neural networks. In: Burgeth, B., Kleefeld, A., Naegel, B., Passat, N., Perret, B. (eds.) ISMM 2019. LNCS, vol. 11564, pp. 310\u2013322. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-20867-7_24"}],"container-title":["Lecture Notes in Computer Science","Discrete Geometry and Mathematical Morphology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-76657-3_34","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T22:03:14Z","timestamp":1747260194000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-76657-3_34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030766566","9783030766573"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-76657-3_34","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"16 May 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"DGMM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Discrete Geometry and Mathematical Morphology","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Uppsala","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Sweden","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24 May 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27 May 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"dgmm2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.dgmm2021.se\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"59","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"36","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"61% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"1,3","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}