{"id":"https://openalex.org/W7161781428","doi":"https://doi.org/10.48550/arxiv.2605.19210","title":"D-Convexity: A Unified Differentiable Convex Shape Prior via Quasi-Concavity for Data-driven Image Segmentation","display_name":"D-Convexity: A Unified Differentiable Convex Shape Prior via Quasi-Concavity for Data-driven Image Segmentation","publication_year":2026,"publication_date":"2026-05-19","ids":{"openalex":"https://openalex.org/W7161781428","doi":"https://doi.org/10.48550/arxiv.2605.19210"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.19210","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.19210","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.19210","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136560277","display_name":"Shengzhe Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Shengzhe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136606163","display_name":"Hao Yan","orcid":"https://orcid.org/0000-0003-1531-3053"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yan, Hao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.39160001277923584,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.39160001277923584,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.2535000145435333,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.07750000059604645,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.733299970626831},{"id":"https://openalex.org/keywords/segmentation","display_name":"Segmentation","score":0.5936999917030334},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5300999879837036},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.46309998631477356},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4352000057697296},{"id":"https://openalex.org/keywords/image-segmentation","display_name":"Image segmentation","score":0.39809998869895935},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.3792000114917755},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.37400001287460327},{"id":"https://openalex.org/keywords/shape-analysis","display_name":"Shape analysis (program analysis)","score":0.3490999937057495}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.733299970626831},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6074000000953674},{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"score":0.5936999917030334},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5300999879837036},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.46309998631477356},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4352000057697296},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"score":0.39809998869895935},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39480000734329224},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.3792000114917755},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.37400001287460327},{"id":"https://openalex.org/C112604564","wikidata":"https://www.wikidata.org/wiki/Q7489226","display_name":"Shape analysis (program analysis)","level":3,"score":0.3490999937057495},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.34630000591278076},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.3395000100135803},{"id":"https://openalex.org/C65885262","wikidata":"https://www.wikidata.org/wiki/Q7429708","display_name":"Scale-space segmentation","level":4,"score":0.3353999853134155},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3273000121116638},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32659998536109924},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.3264000117778778},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.3224000036716461},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.31369999051094055},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30300000309944153},{"id":"https://openalex.org/C25694479","wikidata":"https://www.wikidata.org/wiki/Q7446278","display_name":"Segmentation-based object categorization","level":5,"score":0.29679998755455017},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.29280000925064087},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.2833999991416931},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.2542000114917755}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.19210","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.19210","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.19210","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.19210","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Convexity":[0],"is":[1],"a":[2,28,33,52,91,96,104,110,123,180,207],"fundamental":[3],"geometric":[4],"prior":[5,37],"that":[6,127],"underlies":[7],"many":[8],"natural":[9],"and":[10,31,76,86,103,119,158,171,193,210],"man-made":[11],"structures,":[12],"yet":[13],"remains":[14],"challenging":[15],"to":[16,63,100,197],"impose":[17],"effectively":[18],"in":[19],"end-to-end":[20],"trainable":[21],"segmentation":[22,144,170],"networks.":[23],"We":[24],"revisit":[25],"convexity":[26,36,157,195],"from":[27,188],"functional":[29],"perspective":[30],"propose":[32],"unified,":[34],"threshold-free":[35],"based":[38,203],"on":[39,74,113],"the":[40,43,114,133,147],"quasi-concavity":[41,138],"of":[42,50,61,183],"network's":[44],"output":[45],"mask":[46],"function":[47],"u.":[48],"Instead":[49],"constraining":[51],"single":[53,208],"binary":[54],"segmentation,":[55],"we":[56,82],"require":[57],"all":[58],"super-level":[59],"sets":[60],"u":[62,75],"be":[64,129],"convex,":[65],"transforming":[66],"global":[67],"shape":[68,160,186],"constraints":[69,192],"into":[70],"local,":[71],"differentiable":[72,211],"inequalities":[73],"its":[77],"derivatives.":[78],"From":[79],"this":[80],"principle,":[81],"derive":[83],"zero,":[84],"first,":[85],"second-order":[87,106,120],"characterizations,":[88],"yielding":[89],"respectively":[90],"local":[92],"midpoint":[93],"convexification":[94],"algorithm,":[95],"gradient-based":[97],"condition":[98],"linked":[99],"supporting":[101],"hyperplanes,":[102],"sufficient":[105],"inequality":[107],"expressed":[108],"as":[109],"quadratic":[111],"form":[112],"tangent":[115],"plane.":[116],"The":[117],"first":[118],"formulations":[121,196],"produce":[122],"compact":[124],"convolutional":[125],"loss":[126],"can":[128],"densely":[130],"applied":[131],"across":[132,162],"image":[134],"without":[135],"thresholding.":[136],"Our":[137],"losses":[139],"integrate":[140],"seamlessly":[141],"with":[142],"modern":[143],"networks":[145,166],"via":[146],"proposed":[148],"convex":[149,185],"gradient":[150],"projection":[151],"module":[152],"(CGPM).":[153],"They":[154],"consistently":[155],"enforce":[156],"improve":[159],"regularity":[161],"multiple":[163],"datasets,":[164],"outperforming":[165],"tailored":[167],"for":[168],"retinal":[169],"surpassing":[172],"previous":[173,184],"shape-aware":[174],"methods.":[175],"Remarkably,":[176],"our":[177],"analysis":[178],"unifies":[179],"wide":[181],"spectrum":[182],"models,":[187],"discrete":[189],"1-0-1":[190],"line":[191],"graph-cuts":[194],"curvature":[198],"or":[199],"signed":[200],"distance":[201],"Laplacian":[202],"level-set":[204],"priors,":[205],"within":[206],"continuous":[209],"framework.":[212]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-21T00:00:00"}
