{"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/end-to-end-lane-detection-through","title":"End-to-end Lane Detection through Differentiable Least-Squares Fitting","arxiv_id":"1902.00293","date":"2019-02-01","proceeding":null,"authors":["Wouter Van Gansbeke","Bert de Brabandere","Davy Neven","Marc Proesmans","Luc van Gool"],"abstract":"Lane detection is typically tackled with a two-step pipeline in which a segmentation mask of the lane markings is predicted first, and a lane line model (like a parabola or spline) is fitted to the post-processed mask next. The problem with such a two-step approach is that the parameters of the network are not optimized for the true task of interest (estimating the lane curvature parameters) but for a proxy task (segmenting the lane markings), resulting in sub-optimal performance. In this work, we propose a method to train a lane detector in an end-to-end manner, directly regressing the lane parameters. The architecture consists of two components: a deep network that predicts a segmentation-like weight map for each lane line, and a differentiable least-squares fitting module that returns for each map the parameters of the best-fitting curve in the weighted least-squares sense. These parameters can subsequently be supervised with a loss function of choice. Our method relies on the observation that it is possible to backpropagate through a least-squares fitting procedure. This leads to an end-to-end method where the features are optimized for the true task of interest: the network implicitly learns to generate features that prevent instabilities during the model fitting step, as opposed to two-step pipelines that need to handle outliers with heuristics. Additionally, the system is not just a black box but offers a degree of interpretability because the intermediately generated segmentation-like weight maps can be inspected and visualized. Code and a video is available at github.com/wvangansbeke/LaneDetection_End2End.","url_abs":"https://arxiv.org/abs/1902.00293v3","url_pdf":"https://arxiv.org/pdf/1902.00293v3.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":"end-to-end-lane-detection-through","repo_url":"https://github.com/wvangansbeke/LaneDetection_End2End","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"lane-detection","task_name":"Lane Detection"}],"methods":[{"method_slug":"interpretability","method_name":"Interpretability"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1902.00293","atlas_url":"https://app.syntology.ai/?focus=1902.00293","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1902.00293"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/wvangansbeke/LaneDetection_End2End","reach":null}],"summary":{"ran_draft_wrong":1,"ran_honours":2},"by_repo_kind":{"official":{"samples":3,"ran":3,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":3,"samples":[{"code_sha256_prefix":"6530ce91d9113378","entry":"activation_layer","repo":"wvangansbeke/LaneDetection_End2End","repo_kind":"official","path":"Backprojection_Loss/Networks/LSQ_layer.py","file_url":"https://github.com/wvangansbeke/LaneDetection_End2End/blob/HEAD/Backprojection_Loss/Networks/LSQ_layer.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NOASSERTION","inline_ok":false,"mcp_get_code":{"code_sha256":"6530ce91d9113378"}},{"code_sha256_prefix":"8cffc01f9e38087e","entry":"return_tensor","repo":"wvangansbeke/LaneDetection_End2End","repo_kind":"official","path":"Backprojection_Loss/Networks/LSQ_layer.py","file_url":"https://github.com/wvangansbeke/LaneDetection_End2End/blob/HEAD/Backprojection_Loss/Networks/LSQ_layer.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"NOASSERTION","inline_ok":false,"mcp_get_code":{"code_sha256":"8cffc01f9e38087e"}},{"code_sha256_prefix":"bbd8cf7c86a7bbdb","entry":"square_tensor","repo":"wvangansbeke/LaneDetection_End2End","repo_kind":"official","path":"Backprojection_Loss/Networks/LSQ_layer.py","file_url":"https://github.com/wvangansbeke/LaneDetection_End2End/blob/HEAD/Backprojection_Loss/Networks/LSQ_layer.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"NOASSERTION","inline_ok":false,"mcp_get_code":{"code_sha256":"bbd8cf7c86a7bbdb"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}