[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84194-en":3,"doc-seo-84194-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84194,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Widest-Path Reachability Fields for Connectivity-Preserving Slender Structure Segmentation","Segmenting slender curvilinear structures such as retinal vessels, cracks, and roads requires strict topological correctness because even a one-pixel discontinuity can fracture an otherwise continuous network and break downstream measurements. Standard binary-mask training with pixel-wise overlap losses often yields connectivity-broken predictions due to a mismatch between uniformly distributed gradients and sparse connectivity bottlenecks. This paper introduces Topological Gradient Starvation and proposes WidestPath Reachability Fields (WPRF), a plug-and-play differentiable Max-Min reachability objective with bottleneck-aware gradient routing. WPRF improves 87% of experiments under fixed hyperparameters and yields +7.2 clDice on fragile datasets.","Widest-Path Reachability Fields for Connectivity-Preserving Slender Structure  \nSegmentation  \nYoucheng Zong , Student Member, IEEE, Runda Jia , Minxuan Hu , Weilan Su ,  \nand Dakuo He  \narXiv :2607 .07 123v 1 [ cs .CV] 8 Jul 2026  \nAbstract—Segmenting slender curvilinear structures such as retinal vessels, cracks, and roads demands topological correctness, as even a single-pixel discontinuity can fragment a continuous network and invalidate downstream analysis. Under standard binary-mask supervision, models optimized for pixel-level overlap frequently produce topologically broken predictions. We trace this to a fundamental mismatch: pixel-wise losses distribute gradients uniformly, yet connectivity hinges on a sparse set of bottleneck pixels. These pixels are vastly outnumbered by thick structures and background, rendering their aggregate gradient contribution negligible. We term this phenomenon topological gradient starvation (TGS). To address it, we propose WidestPath Reachability Fields (WPRF), a differentiable Max-Min reachability objective that redirects gradient flow to connectivity bottlenecks. The module is plug-and-play, backbone-agnostic, and incurs no inference overhead. WPRF implements a differentiable Max-Min objective via dynamic programming on a domainrestricted graph, coupled with a bottleneck-aware observation term that balances gradient contributions across varying structures. Compared to prior topology-aware losses that rely on posthoc skeletonization or homology computation, WPRF directly optimizes end-to-end reachability via differentiable Max-Min algebra, enabling gradient flow to concentrate on connectivity bottlenecks without auxiliary structures. We introduce OMVIS, a new oral microvessel segmentation dataset. Experiments across nine architectures and six datasets validate the bottleneckfocused gradient routing mechanism. WPRF improves 87% of experiments with fixed hyperparameters and achieves clDice gains of 7.2 percentage points on structurally fragile datasets.  \nIndex Terms—Slender structure segmentation, connectivity preservation, topological gradient starvation, widest-path reachability, gradient routing.  \nI. INTRODUCTION  \nSegmenting slender curvilinear structures in medical imaging and remote sensing requires topological correctness [1]–[3] . Studies on vessel and road segmentation show that this requirement holds across different network structures [4], [5] .  \nThis work was supported by the Fundamental Research Funds for the Central Universities, China (N26GFZ006) . (Corresponding author: Runda Jia.)  \nYoucheng Zong, Runda Jia, Minxuan Hu, and Dakuo He are with the College of Information Science and Engineering, Northeastern University, Shenyang 110004, China (e-mail: [zongyc@mails.neu.edu.cn](zongyc@mails.neu.edu.cn); [jiarunda@ise.neu.edu.cn](jiarunda@ise.neu.edu.cn); humingx  \n[uan@mails.neu.edu.cn](uan@mails.neu.edu.cn); [hedakuo@ise.neu.edu.cn](hedakuo@ise.neu.edu.cn)) .  \nWeilan Su is with the Changsha Stomatological Hospital, Changsha 410005, China (e-mail: [suweilan@zsskqyy1.wecom.work](suweilan@zsskqyy1.wecom.work)).  \nThe source code is available at [https://github.com/mituan-ai/WPRF](https://github.com/mituan-ai/WPRF) open.  \nWork on context modeling and structure distillation in remotesensing semantic segmentation addresses the same structurepreservation issue beyond medical images [6], [7] . Even promptable foundation models such as SAM2 exhibit frequent topological breaks in zero-shot capillary segmentation [8],[9] . A single micro-break fragments a continuous tree into disconnected pieces, invalidating downstream tasks such as bifurcation analysis or route planning. Annotations are often union-only binary regions without reliable instance-level definitions, making connectivity and topological quality more important than simple region overlap [10],[11] . Even when the final output is a single semantic mask, breaks or false links are amplified by downstream processing such as s","cbCaioX3Nja2AIpL","https://ap.wps.com/l/cbCaioX3Nja2AIpL","pdf",25482251,1,14,"English","en",105,"# Introduction\n## Topological correctness and connectivity failures\n## Topological Gradient Starvation (TGS)\n## Proposed Widest-Path Reachability Fields (WPRF)","[{\"question\":\"Why do standard pixel-wise segmentation losses often fail on slender structure connectivity?\",\"answer\":\"They distribute gradients uniformly across pixels, but connectivity depends on an extremely sparse set of bottleneck pixels. As a result, bottleneck pixels receive negligible gradient contribution compared with easy thick structures and background, leading to topological breaks.\"},{\"question\":\"What is Topological Gradient Starvation (TGS)?\",\"answer\":\"TGS describes the mismatch under sum-based losses (e.g., Dice, BCE) where connectivity-critical bottleneck pixels get disproportionately weak updates due to their scarcity. This makes connectivity breaks more likely even when overall pixel accuracy is high.\"},{\"question\":\"How does Widest-Path Reachability Fields (WPRF) address the connectivity problem?\",\"answer\":\"WPRF introduces a differentiable Max-Min reachability objective that reroutes gradient flow toward connectivity bottlenecks. It is plug-and-play, backbone-agnostic, and adds no inference overhead, enabling end-to-end optimization of reachability.\"}]",1784193852,35,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"widest-path-reachability-fields-for-connectivity-preserving-slender-structure-segmentation","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/widest-path-reachability-fields-for-connectivity-preserving-slender-structure-segmentation/84194/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why do standard pixel-wise segmentation losses often fail on slender structure connectivity?","Question",{"text":75,"@type":76},"They distribute gradients uniformly across pixels, but connectivity depends on an extremely sparse set of bottleneck pixels. As a result, bottleneck pixels receive negligible gradient contribution compared with easy thick structures and background, leading to topological breaks.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is Topological Gradient Starvation (TGS)?",{"text":80,"@type":76},"TGS describes the mismatch under sum-based losses (e.g., Dice, BCE) where connectivity-critical bottleneck pixels get disproportionately weak updates due to their scarcity. This makes connectivity breaks more likely even when overall pixel accuracy is high.",{"name":82,"@type":73,"acceptedAnswer":83},"How does Widest-Path Reachability Fields (WPRF) address the connectivity problem?",{"text":84,"@type":76},"WPRF introduces a differentiable Max-Min reachability objective that reroutes gradient flow toward connectivity bottlenecks. 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