?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Affine+Registration+of+label+maps+in+Label+Space&rft.creator=Rathi%2C+Yogesh&rft.creator=Malcolm%2C+James&rft.creator=Bouix%2C+Sylvain&rft.creator=Tannenbaum%2C+Allen&rft.creator=Shenton%2C+Martha+E&rft.subject=Machine+Vision&rft.description=Two+key+aspects+of+coupled+multi-object+shape%0D%0Aanalysis+and+atlas+generation+are+the+choice+of+representation%0D%0Aand+subsequent+registration+methods+used+to+align+the+sample%0D%0Aset.+For+example%2C+a+typical+brain+image+can+be+labeled+into%0D%0Athree+structures%3A+grey+matter%2C+white+matter+and+cerebrospinal%0D%0Afluid.+Many+manipulations+such+as+interpolation%2C+transformation%2C%0D%0Asmoothing%2C+or+registration+need+to+be+performed+on+these+images%0D%0Abefore+they+can+be+used+in+further+analysis.+Current+techniques%0D%0Afor+such+analysis+tend+to+trade+off+performance+between+the+two%0D%0Atasks%2C+performing+well+for+one+task+but+developing+problems+when%0D%0Aused+for+the+other.%0D%0AThis+article+proposes+to+use+a+representation+that+is+both%0D%0Aflexible+and+well+suited+for+both+tasks.+We+propose+to+map+object%0D%0Alabels+to+vertices+of+a+regular+simplex%2C+e.g.+the+unit+interval+for%0D%0Atwo+labels%2C+a+triangle+for+three+labels%2C+a+tetrahedron+for+four%0D%0Alabels%2C+etc.+This+representation%2C+which+is+routinely+used+in+fuzzy%0D%0Aclassification%2C+is+ideally+suited+for+representing+and+registering%0D%0Amultiple+shapes.+On+closer+examination%2C+this+representation%0D%0Areveals+several+desirable+properties%3A+algebraic+operations+may%0D%0Abe+done+directly%2C+label+uncertainty+is+expressed+as+a+weighted%0D%0Amixture+of+labels+(probabilistic+interpretation)%2C+interpolation+is%0D%0Aunbiased+toward+any+label+or+the+background%2C+and+registration%0D%0Amay+be+performed+directly.%0D%0AWe+demonstrate+these+properties+by+using+label+space+in+a+gradient%0D%0Adescent+based+registration+scheme+to+obtain+a+probabilistic%0D%0Aatlas.+While+straightforward%2C+this+iterative+method+is+very+slow%2C%0D%0Acould+get+stuck+in+local+minima%2C+and+depends+heavily+on+the+initial%0D%0Aconditions.+To+address+these+issues%2C+two+fast+methods+are+proposed%0D%0Awhich+serve+as+coarse+registration+schemes+following+which+the%0D%0Aiterative+descent+method+can+be+used+to+refine+the+results.+Further%2C%0D%0Awe+derive+an+analytical+formulation+for+direct+computation+of+the%0D%0A%22group+mean%22+from+the+parameters+of+pairwise+registration+of+all%0D%0Athe+images+in+the+sample+set.+We+show+results+on+richly+labeled%0D%0A2D+and+3D+data+sets.&rft.publisher=Journal+of+Computing%2C+https%3A%2F%2Fsites.google.com%2Fsite%2Fjournalofcomputing%2F&rft.date=2010-06-06&rft.type=Journal+(Paginated)&rft.type=PeerReviewed&rft.format=application%2Fpdf&rft.identifier=http%3A%2F%2Fcogprints.org%2F6843%2F1%2FRegistrationLabelSpace.pdf&rft.identifier=++Rathi%2C+Yogesh+and+Malcolm%2C+James+and+Bouix%2C+Sylvain+and+Tannenbaum%2C+Allen+and+Shenton%2C+Martha+E++(2010)+Affine+Registration+of+label+maps+in+Label+Space.++%5BJournal+(Paginated)%5D+++++&rft.relation=http%3A%2F%2Fcogprints.org%2F6843%2F