{"id":"https://openalex.org/W7152481759","doi":"https://doi.org/10.48550/arxiv.2604.07180","title":"Energy-based Tissue Manifolds for Longitudinal Multiparametric MRI Analysis","display_name":"Energy-based Tissue Manifolds for Longitudinal Multiparametric MRI Analysis","publication_year":2026,"publication_date":"2026-04-08","ids":{"openalex":"https://openalex.org/W7152481759","doi":"https://doi.org/10.48550/arxiv.2604.07180"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.07180","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07180","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.07180","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057801204","display_name":"Kartikay Tehlan","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tehlan, Kartikay","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5115729138","display_name":"Lukas F\u00f6rner","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"F\u00f6rner, Lukas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128834183","display_name":"Nico Schmutzenhofer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schmutzenhofer, Nico","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042661460","display_name":"Michael C. Fr\u00fchwald","orcid":"https://orcid.org/0000-0002-8237-1854"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fr\u00fchwald, Michael","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133240564","display_name":"Matthias Wagner","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wagner, Matthias","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133265068","display_name":"Nassir Navab","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Navab, Nassir","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5011729018","display_name":"Thomas Wendler","orcid":"https://orcid.org/0000-0002-0915-0510"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wendler, Thomas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5057801204"],"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.1534000039100647,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.1534000039100647,"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/T10241","display_name":"Functional Brain Connectivity Studies","score":0.10249999910593033,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.09529999643564224,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/level-set","display_name":"Level set (data structures)","score":0.6028000116348267},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.5619000196456909},{"id":"https://openalex.org/keywords/segmentation","display_name":"Segmentation","score":0.5065000057220459},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.4921000003814697},{"id":"https://openalex.org/keywords/voxel","display_name":"Voxel","score":0.49129998683929443},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.48739999532699585},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.40700000524520874},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.38580000400543213},{"id":"https://openalex.org/keywords/tracking","display_name":"Tracking (education)","score":0.38580000400543213},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.3783000111579895}],"concepts":[{"id":"https://openalex.org/C153008295","wikidata":"https://www.wikidata.org/wiki/Q6535093","display_name":"Level set (data structures)","level":2,"score":0.6028000116348267},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.5619000196456909},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5196999907493591},{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"score":0.5065000057220459},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.4921000003814697},{"id":"https://openalex.org/C54170458","wikidata":"https://www.wikidata.org/wiki/Q663554","display_name":"Voxel","level":2,"score":0.49129998683929443},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.48739999532699585},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48579999804496765},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.40700000524520874},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.38580000400543213},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.38580000400543213},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3783000111579895},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.3734999895095825},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.3686999976634979},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.35519999265670776},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.3547999858856201},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.34619998931884766},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32580000162124634},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.32510000467300415},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.32120001316070557},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.31700000166893005},{"id":"https://openalex.org/C12725497","wikidata":"https://www.wikidata.org/wiki/Q810247","display_name":"Baseline (sea)","level":2,"score":0.31290000677108765},{"id":"https://openalex.org/C125269122","wikidata":"https://www.wikidata.org/wiki/Q1751397","display_name":"Level set method","level":4,"score":0.3109999895095825},{"id":"https://openalex.org/C118317068","wikidata":"https://www.wikidata.org/wiki/Q2100760","display_name":"Point distribution model","level":2,"score":0.3066999912261963},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.30390000343322754},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.30059999227523804},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.3003000020980835},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"score":0.2994999885559082},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27900001406669617},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.27559998631477356},{"id":"https://openalex.org/C112353826","wikidata":"https://www.wikidata.org/wiki/Q127313","display_name":"Active contour model","level":4,"score":0.27459999918937683},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2732999920845032},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26809999346733093},{"id":"https://openalex.org/C32209215","wikidata":"https://www.wikidata.org/wiki/Q5535483","display_name":"Geometric flow","level":3,"score":0.26750001311302185},{"id":"https://openalex.org/C71169176","wikidata":"https://www.wikidata.org/wiki/Q7512907","display_name":"Signed distance function","level":2,"score":0.26350000500679016},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.2547999918460846},{"id":"https://openalex.org/C202286095","wikidata":"https://www.wikidata.org/wiki/Q579262","display_name":"Error function","level":2,"score":0.2531999945640564}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.07180","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07180","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.07180","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07180","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":"article"},"sustainable_development_goals":[{"score":0.8594135046005249,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,41,61,70,106,162,191,234],"geometric":[3,108,220],"framework":[4],"for":[5,223,236],"longitudinal":[6,224],"multi-parametric":[7],"MRI":[8,152],"analysis":[9,226],"based":[10],"on":[11,21],"patient-specific":[12,214],"energy":[13,55,67,101,159,174,215],"modelling":[14],"in":[15,173,178,243],"sequence":[16,153,179],"space.":[17],"Rather":[18,141],"than":[19,142],"operating":[20],"images":[22],"with":[23,165,193],"spatial":[24],"networks,":[25],"each":[26],"voxel":[27,196],"is":[28,46,103,121,128],"represented":[29],"by":[30],"its":[31],"multi-sequence":[32],"intensity":[33],"vector":[34],"($T1$,":[35],"$T1c$,":[36],"$T2$,":[37],"FLAIR,":[38],"ADC),":[39],"and":[40,91,120,175],"compact":[42],"implicit":[43],"neural":[44],"representation":[45],"trained":[47],"via":[48],"denoising":[49],"score":[50],"matching":[51],"to":[52,88,137,200],"learn":[53],"an":[54],"function":[56,218],"$E_\u03b8(\\mathbf{u})$":[57],"over":[58],"$\\mathbb{R}^d$":[59],"from":[60],"single":[62],"baseline":[63,100,139,158,183],"scan.":[64],"The":[65,207],"learned":[66],"landscape":[68],"provides":[69],"differential-geometric":[71],"description":[72],"of":[73,114,133,151,239],"tissue":[74,82],"regimes":[75],"without":[76,204,227],"segmentation":[77,229],"labels.":[78],"Local":[79],"minima":[80],"define":[81],"basins,":[83],"gradient":[84],"magnitude":[85],"reflects":[86],"proximity":[87],"regime":[89,185],"boundaries,":[90],"Laplacian":[92],"curvature":[93],"characterises":[94],"local":[95],"constraint":[96],"structure.":[97],"Importantly,":[98],"this":[99,138],"manifold":[102],"treated":[104],"as":[105,131,211,219],"fixed":[107],"reference:":[109],"it":[110],"encodes":[111],"the":[112,149,157,182],"set":[113],"contrast":[115],"combinations":[116],"observed":[117],"at":[118,124],"diagnosis":[119],"not":[122],"retrained":[123],"follow-up.":[125],"Longitudinal":[126],"assessment":[127],"therefore":[129],"formulated":[130],"evaluation":[132],"subsequent":[134],"scans":[135,169],"relative":[136],"geometry.":[140],"comparing":[143],"anatomical":[144],"segmentations,":[145],"we":[146],"analyse":[147],"how":[148],"distribution":[150],"vectors":[154],"evolves":[155],"under":[156],"function.":[160],"In":[161,190],"paediatric":[163],"case":[164,192],"later":[166],"recurrence,":[167],"follow-up":[168],"show":[170],"progressive":[171],"deviation":[172],"directional":[176],"displacement":[177],"space":[180],"toward":[181],"tumour-associated":[184],"before":[186],"clear":[187],"radiological":[188],"reappearance.":[189],"stable":[194],"disease,":[195],"distributions":[197],"remain":[198],"confined":[199],"established":[201],"low-energy":[202],"basins":[203],"systematic":[205],"drift.":[206],"presented":[208],"cases":[209],"serve":[210],"proof-of-concept":[212],"that":[213],"manifolds":[216],"can":[217],"reference":[221],"systems":[222],"mpMRI":[225],"explicit":[228],"or":[230],"supervised":[231],"classification,":[232],"providing":[233],"foundation":[235],"further":[237],"investigation":[238],"manifold-based":[240],"tissue-at-risk":[241],"tracking":[242],"neuro-oncology.":[244]},"counts_by_year":[],"updated_date":"2026-05-03T08:25:01.440150","created_date":"2026-04-10T00:00:00"}