{"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/learning-steerable-filters-for-rotation","title":"Learning Steerable Filters for Rotation Equivariant CNNs","arxiv_id":"1711.07289","date":"2017-11-20","proceeding":"CVPR 2018 6","authors":["Maurice Weiler","Fred A. Hamprecht","Martin Storath"],"abstract":"In many machine learning tasks it is desirable that a model's prediction\ntransforms in an equivariant way under transformations of its input.\nConvolutional neural networks (CNNs) implement translational equivariance by\nconstruction; for other transformations, however, they are compelled to learn\nthe proper mapping. In this work, we develop Steerable Filter CNNs (SFCNNs)\nwhich achieve joint equivariance under translations and rotations by design.\nThe proposed architecture employs steerable filters to efficiently compute\norientation dependent responses for many orientations without suffering\ninterpolation artifacts from filter rotation. We utilize group convolutions\nwhich guarantee an equivariant mapping. In addition, we generalize He's weight\ninitialization scheme to filters which are defined as a linear combination of a\nsystem of atomic filters. Numerical experiments show a substantial enhancement\nof the sample complexity with a growing number of sampled filter orientations\nand confirm that the network generalizes learned patterns over orientations.\nThe proposed approach achieves state-of-the-art on the rotated MNIST benchmark\nand on the ISBI 2012 2D EM segmentation challenge.","url_abs":"http://arxiv.org/abs/1711.07289v3","url_pdf":"http://arxiv.org/pdf/1711.07289v3.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":[],"tasks":[{"task_slug":"breast-tumour-classification","task_name":"Breast Tumour Classification"},{"task_slug":"colorectal-gland-segmentation","task_name":"Colorectal Gland Segmentation:"},{"task_slug":"multi-tissue-nucleus-segmentation","task_name":"Multi-tissue Nucleus Segmentation"},{"task_slug":"rotated-mnist","task_name":"Rotated MNIST"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/breast-tumour-classification-on-pcam","task":"Breast Tumour Classification","dataset":"PCam","model":"Steerable G-CNN (C8)","rank_in_archive_order":2,"of":16,"metrics":{"AUC":"0.971"},"uses_additional_data":false},{"leaderboard":"/sota/breast-tumour-classification-on-pcam","task":"Breast Tumour Classification","dataset":"PCam","model":"Steerable G-CNN (C8)","rank_in_archive_order":3,"of":16,"metrics":{"AUC":"0.969"},"uses_additional_data":false},{"leaderboard":"/sota/breast-tumour-classification-on-pcam","task":"Breast Tumour Classification","dataset":"PCam","model":"Steerable G-CNN (C12)","rank_in_archive_order":4,"of":16,"metrics":{"AUC":"0.969"},"uses_additional_data":false},{"leaderboard":"/sota/breast-tumour-classification-on-pcam","task":"Breast Tumour Classification","dataset":"PCam","model":"Steerable G-CNN (e)","rank_in_archive_order":7,"of":16,"metrics":{"AUC":"0.963"},"uses_additional_data":false},{"leaderboard":"/sota/colorectal-gland-segmentation-on-crag","task":"Colorectal Gland Segmentation:","dataset":"CRAG","model":"Steerable G-CNN (C8)","rank_in_archive_order":3,"of":15,"metrics":{"Dice":"0.888","F1-score":"0.861","Hausdorff Distance (mm)":"139.5"},"uses_additional_data":false},{"leaderboard":"/sota/colorectal-gland-segmentation-on-crag","task":"Colorectal Gland Segmentation:","dataset":"CRAG","model":"Steerable G-CNN (C12)","rank_in_archive_order":5,"of":15,"metrics":{"Dice":"0.870","F1-score":"0.855","Hausdorff Distance (mm)":"156.2"},"uses_additional_data":false},{"leaderboard":"/sota/colorectal-gland-segmentation-on-crag","task":"Colorectal Gland Segmentation:","dataset":"CRAG","model":"Steerable G-CNN (C12)","rank_in_archive_order":6,"of":15,"metrics":{"Dice":"0.869","F1-score":"0.837","Hausdorff Distance (mm)":"164.8"},"uses_additional_data":false},{"leaderboard":"/sota/colorectal-gland-segmentation-on-crag","task":"Colorectal Gland Segmentation:","dataset":"CRAG","model":"Steerable G-CNN (e)","rank_in_archive_order":9,"of":15,"metrics":{"Dice":"0.848","F1-score":"0.811","Hausdorff Distance (mm)":"175.9"},"uses_additional_data":false},{"leaderboard":"/sota/multi-tissue-nucleus-segmentation-on-kumar","task":"Multi-tissue Nucleus Segmentation","dataset":"Kumar","model":"Steerable G-CNN (C12)","rank_in_archive_order":4,"of":18,"metrics":{"Dice":"0.820","Hausdorff Distance (mm)":"55.8"},"uses_additional_data":false},{"leaderboard":"/sota/multi-tissue-nucleus-segmentation-on-kumar","task":"Multi-tissue Nucleus Segmentation","dataset":"Kumar","model":"Steerable G-CNN (C12)","rank_in_archive_order":6,"of":18,"metrics":{"Dice":"0.818","Hausdorff Distance (mm)":"54.3"},"uses_additional_data":false},{"leaderboard":"/sota/multi-tissue-nucleus-segmentation-on-kumar","task":"Multi-tissue Nucleus Segmentation","dataset":"Kumar","model":"Steerable G-CNN (C4)","rank_in_archive_order":10,"of":18,"metrics":{"Dice":"0.809","Hausdorff Distance (mm)":"54.2"},"uses_additional_data":false},{"leaderboard":"/sota/multi-tissue-nucleus-segmentation-on-kumar","task":"Multi-tissue Nucleus Segmentation","dataset":"Kumar","model":"Steerable G-CNN (e)","rank_in_archive_order":16,"of":18,"metrics":{"Dice":"0.791","Hausdorff Distance (mm)":"51.0"},"uses_additional_data":false},{"leaderboard":"/sota/rotated-mnist-on-rotated-mnist-1","task":"Rotated MNIST","dataset":"Rotated MNIST","model":"Steerable Filter CNN","rank_in_archive_order":3,"of":3,"metrics":{"Test error":"0.714"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1711.07289","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}