{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/roto-translation-covariant-convolutional","title":"Roto-Translation Covariant Convolutional Networks for Medical Image Analysis","arxiv_id":"1804.03393","date":"2018-04-10","proceeding":null,"authors":["Erik J. Bekkers","Maxime W. Lafarge","Mitko Veta","Koen AJ Eppenhof","Josien PW Pluim","Remco Duits"],"abstract":"We propose a framework for rotation and translation covariant deep learning\nusing $SE(2)$ group convolutions. The group product of the special Euclidean\nmotion group $SE(2)$ describes how a concatenation of two roto-translations\nresults in a net roto-translation. We encode this geometric structure into\nconvolutional neural networks (CNNs) via $SE(2)$ group convolutional layers,\nwhich fit into the standard 2D CNN framework, and which allow to generically\ndeal with rotated input samples without the need for data augmentation.\n  We introduce three layers: a lifting layer which lifts a 2D (vector valued)\nimage to an $SE(2)$-image, i.e., 3D (vector valued) data whose domain is\n$SE(2)$; a group convolution layer from and to an $SE(2)$-image; and a\nprojection layer from an $SE(2)$-image to a 2D image. The lifting and group\nconvolution layers are $SE(2)$ covariant (the output roto-translates with the\ninput). The final projection layer, a maximum intensity projection over\nrotations, makes the full CNN rotation invariant.\n  We show with three different problems in histopathology, retinal imaging, and\nelectron microscopy that with the proposed group CNNs, state-of-the-art\nperformance can be achieved, without the need for data augmentation by rotation\nand with increased performance compared to standard CNNs that do rely on\naugmentation.","url_abs":"http://arxiv.org/abs/1804.03393v3","url_pdf":"http://arxiv.org/pdf/1804.03393v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"roto-translation-covariant-convolutional","repo_url":"https://github.com/tueimage/se2cnn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"data-augmentation","task_name":"Data Augmentation"},{"task_slug":"medical-image-analysis","task_name":"Medical Image Analysis"},{"task_slug":"translation","task_name":"Translation"}],"methods":[{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1804.03393","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}