{"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/rotation-equivariant-vector-field-networks","title":"Rotation equivariant vector field networks","arxiv_id":"1612.09346","date":"2016-12-29","proceeding":"ICCV 2017 10","authors":["Diego Marcos","Michele Volpi","Nikos Komodakis","Devis Tuia"],"abstract":"In many computer vision tasks, we expect a particular behavior of the output\nwith respect to rotations of the input image. If this relationship is\nexplicitly encoded, instead of treated as any other variation, the complexity\nof the problem is decreased, leading to a reduction in the size of the required\nmodel. In this paper, we propose the Rotation Equivariant Vector Field Networks\n(RotEqNet), a Convolutional Neural Network (CNN) architecture encoding rotation\nequivariance, invariance and covariance. Each convolutional filter is applied\nat multiple orientations and returns a vector field representing magnitude and\nangle of the highest scoring orientation at every spatial location. We develop\na modified convolution operator relying on this representation to obtain deep\narchitectures. We test RotEqNet on several problems requiring different\nresponses with respect to the inputs' rotation: image classification,\nbiomedical image segmentation, orientation estimation and patch matching. In\nall cases, we show that RotEqNet offers extremely compact models in terms of\nnumber of parameters and provides results in line to those of networks orders\nof magnitude larger.","url_abs":"http://arxiv.org/abs/1612.09346v3","url_pdf":"http://arxiv.org/pdf/1612.09346v3.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":"rotation-equivariant-vector-field-networks","repo_url":"https://github.com/di-marcos/RotEqNet","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"rotation-equivariant-vector-field-networks","repo_url":"https://github.com/COGMAR/RotEqNet","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"rotation-equivariant-vector-field-networks","repo_url":"https://github.com/ojas97/roteqnetp3","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"breast-tumour-classification","task_name":"Breast Tumour Classification"},{"task_slug":"colorectal-gland-segmentation","task_name":"Colorectal Gland Segmentation:"},{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"image-segmentation","task_name":"Image Segmentation"},{"task_slug":"multi-tissue-nucleus-segmentation","task_name":"Multi-tissue Nucleus Segmentation"},{"task_slug":"patch-matching","task_name":"Patch Matching"},{"task_slug":"semantic-segmentation","task_name":"Semantic Segmentation"},{"task_slug":"image-classification","task_name":"image-classification"}],"methods":[{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/breast-tumour-classification-on-pcam","task":"Breast Tumour Classification","dataset":"PCam","model":"VF-CNN (C12)","rank_in_archive_order":13,"of":16,"metrics":{"AUC":"0.898"},"uses_additional_data":false},{"leaderboard":"/sota/breast-tumour-classification-on-pcam","task":"Breast Tumour Classification","dataset":"PCam","model":"VF-CNN (C8)","rank_in_archive_order":14,"of":16,"metrics":{"AUC":"0.881"},"uses_additional_data":false},{"leaderboard":"/sota/breast-tumour-classification-on-pcam","task":"Breast Tumour Classification","dataset":"PCam","model":"VF-CNN (C4)","rank_in_archive_order":15,"of":16,"metrics":{"AUC":"0.871"},"uses_additional_data":false},{"leaderboard":"/sota/colorectal-gland-segmentation-on-crag","task":"Colorectal Gland Segmentation:","dataset":"CRAG","model":"VF-CNN (C12)","rank_in_archive_order":12,"of":15,"metrics":{"Dice":"0.782","F1-score":"0.776","Hausdorff Distance (mm)":"251.9"},"uses_additional_data":false},{"leaderboard":"/sota/colorectal-gland-segmentation-on-crag","task":"Colorectal Gland Segmentation:","dataset":"CRAG","model":"VF-CNN (C8)","rank_in_archive_order":13,"of":15,"metrics":{"Dice":"0.758","F1-score":"0.745","Hausdorff Distance (mm)":"287.5"},"uses_additional_data":false},{"leaderboard":"/sota/colorectal-gland-segmentation-on-crag","task":"Colorectal Gland Segmentation:","dataset":"CRAG","model":"VF-CNN (C4)","rank_in_archive_order":14,"of":15,"metrics":{"Dice":"0.721","F1-score":"0.711","Hausdorff Distance (mm)":"318.9"},"uses_additional_data":false},{"leaderboard":"/sota/multi-tissue-nucleus-segmentation-on-kumar","task":"Multi-tissue Nucleus Segmentation","dataset":"Kumar","model":"VF-CNN (C12)","rank_in_archive_order":8,"of":18,"metrics":{"Dice":"0.813","Hausdorff Distance (mm)":"51.4"},"uses_additional_data":false},{"leaderboard":"/sota/multi-tissue-nucleus-segmentation-on-kumar","task":"Multi-tissue Nucleus Segmentation","dataset":"Kumar","model":"VF-CNN (C12)","rank_in_archive_order":11,"of":18,"metrics":{"Dice":"0.808","Hausdorff Distance (mm)":"50.7"},"uses_additional_data":false},{"leaderboard":"/sota/multi-tissue-nucleus-segmentation-on-kumar","task":"Multi-tissue Nucleus Segmentation","dataset":"Kumar","model":"VF-CNN (C4)","rank_in_archive_order":12,"of":18,"metrics":{"Dice":"0.800","Hausdorff Distance (mm)":"49.9"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1612.09346","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}