{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-IOI1VN6B/d4f55a54-eb33-440b-87b1-ab7eb608f4ce/PDF","dcterms:extent":"380 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-IOI1VN6B/79a5c2a1-3450-4f1b-bd86-7e8aee95a7ce/TEXT","dcterms:extent":"44 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-IOI1VN6B","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2017","dc:creator":["Kaszanitzky, Viktória E.","Schulze, Bernd"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:13"},{"@xml:lang":"sl","#text":"str. 31-47"}],"dc:identifier":["COBISSID:18173529","ISSN:1855-3966","URN:URN:NBN:SI:doc-IOI1VN6B"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"sl","#text":"dvig"},{"@xml:lang":"sl","#text":"incidenčna struktura"},{"@xml:lang":"sl","#text":"poliedrski sestav"},{"@xml:lang":"sl","#text":"simetrija"},{"@xml:lang":"sl","#text":"slika"},{"@xml:lang":"sl","#text":"stožčenje"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Lifting symmetric pictures to polyhedral scenes|"},"dc:description":[{"@xml:lang":"sl","#text":"Scene analysis is concerned with the reconstruction of ?$d$?-dimensional objects, such as polyhedral surfaces, from ?$(d-1)$?-dimensional pictures (i.e., projections of the objects onto a hyperplane). In this paper we study the impact of symmetry on the lifting properties of pictures. We first use methods from group representation theory to show that the lifting matrix of a symmetric picture can be transformed into a block-diagonalized form. Using this result we then derive new symmetry-extended counting conditions for a picture with a nontrivial symmetry group in an arbitrary dimension to be minimally flat (i.e., \"non-liftable\"). These conditions imply very simply stated restrictions on the number of those structural components of the picture that are fixed by the various symmetry operations of the picture. We then also transfer lifting results for symmetric pictures from Euclidean ?$(d-1)$?-space to Euclidean ?$d$?-space via the technique of coning. Finally, we offer some conjectures regarding sufficient conditions for a picture realized generically for a symmetry group to be minimally flat"},{"@xml:lang":"sl","#text":"Sestavna analiza se ukvarja z rekonstrukcijo ?$d$?-dimenzionalnih objektov, kot so poledrske ploskve, iz ?$(d-1)$?-dimenzionalnih slik (t.j. projekcij objektov na hiperravnino). V tem članku raziskujemo vpliv simetrije na dvižne lastnosti slik. Najprej z metodami teorije reprezentacij grup pokažemo, da se da dvižno matriko simetrične slike transformirati v bločno diagonalno obliko. S pomočjo tega rezultata nato izpeljemo nove preštevalne pogoje za razširitev simetrije slike z netrivialno simetrijsko grupo v poljubni dimenziji, pri katerih je slika kar se da ploska (t.j. \"ne-dvižna\"). Ti pogoji implicirajo zelo enostavno izražene omejitve glede števila tistih strukturnih komponent slike, ki se ohranjajo pri različnih simetrijskih operacijah, izvršenih na sliki. Nato s pomočjo tehnike stožčenja prenesemo dvižne rezultate o simetričnih slikah v evklidskem ?$(d-1)$?-prostoru na evklidski ?$d$?-prostor. Na koncu formuliramo nekaj domnev o zadostnih pogojih za to, da je pri generični realizaciji slike simetrijska grupa kar se da ploska"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-IOI1VN6B","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-IOI1VN6B"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-IOI1VN6B/d4f55a54-eb33-440b-87b1-ab7eb608f4ce/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-IOI1VN6B/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-IOI1VN6B"}}}}