Bounded biharmonic blending of Möbius transformations for flexible omnidirectional image rectification
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.cag.2020.09.011 http://hdl.handle.net/11449/206689 |
Resumo: | We propose a new method to correct distortions in equirectangular images, i.e., images that use the longitude/latitude representation to describe the full spherical field of view around a given viewpoint. We show that Möbius transformations are the correct mathematical tool to deal with the conflicting distortions in this setting: they are conformal, are able to rectify lines, perform rotations, translations and scales on the sphere and are bijective. Multiple transformations are specified through points, lines and cages on the sphere. We associate three points that uniquely define a Möbius transformation to each one of these geometric handles. Linear blend skinning with bounded biharmonic weights combine the different transformations into a single full spherical modified image. We present a collection of results in challenging settings and show that our method is more flexible and produces higher quality results when compared to previous methods. |
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Repositório Institucional da UNESP |
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spelling |
Bounded biharmonic blending of Möbius transformations for flexible omnidirectional image rectificationlinear blend skinningMöbius transformationsWide-angle imagesWe propose a new method to correct distortions in equirectangular images, i.e., images that use the longitude/latitude representation to describe the full spherical field of view around a given viewpoint. We show that Möbius transformations are the correct mathematical tool to deal with the conflicting distortions in this setting: they are conformal, are able to rectify lines, perform rotations, translations and scales on the sphere and are bijective. Multiple transformations are specified through points, lines and cages on the sphere. We associate three points that uniquely define a Möbius transformation to each one of these geometric handles. Linear blend skinning with bounded biharmonic weights combine the different transformations into a single full spherical modified image. We present a collection of results in challenging settings and show that our method is more flexible and produces higher quality results when compared to previous methods.UFSC - Universidade Federal de Santa Catarina - Campus Universitário TrindadeUNESP - Universidade Estadual Paulista Júlio de Mesquita Filho IFT - Instituto de Física Teórica, Rua Dr. Bento Teobaldo Ferraz, 271 - Bloco II - Vórzea da Barra FundaUNESP - Universidade Estadual Paulista Júlio de Mesquita Filho IFT - Instituto de Física Teórica, Rua Dr. Bento Teobaldo Ferraz, 271 - Bloco II - Vórzea da Barra FundaUniversidade Federal de Santa Catarina (UFSC)Universidade Estadual Paulista (Unesp)Souto Ferreira, Leonardo [UNESP]Sacht, Leonardo2021-06-25T10:36:34Z2021-06-25T10:36:34Z2020-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article51-60http://dx.doi.org/10.1016/j.cag.2020.09.011Computers and Graphics (Pergamon), v. 93, p. 51-60.0097-8493http://hdl.handle.net/11449/20668910.1016/j.cag.2020.09.0112-s2.0-85092704443Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengComputers and Graphics (Pergamon)info:eu-repo/semantics/openAccess2021-10-23T10:18:14Zoai:repositorio.unesp.br:11449/206689Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T15:06:23.367761Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Bounded biharmonic blending of Möbius transformations for flexible omnidirectional image rectification |
title |
Bounded biharmonic blending of Möbius transformations for flexible omnidirectional image rectification |
spellingShingle |
Bounded biharmonic blending of Möbius transformations for flexible omnidirectional image rectification Souto Ferreira, Leonardo [UNESP] linear blend skinning Möbius transformations Wide-angle images |
title_short |
Bounded biharmonic blending of Möbius transformations for flexible omnidirectional image rectification |
title_full |
Bounded biharmonic blending of Möbius transformations for flexible omnidirectional image rectification |
title_fullStr |
Bounded biharmonic blending of Möbius transformations for flexible omnidirectional image rectification |
title_full_unstemmed |
Bounded biharmonic blending of Möbius transformations for flexible omnidirectional image rectification |
title_sort |
Bounded biharmonic blending of Möbius transformations for flexible omnidirectional image rectification |
author |
Souto Ferreira, Leonardo [UNESP] |
author_facet |
Souto Ferreira, Leonardo [UNESP] Sacht, Leonardo |
author_role |
author |
author2 |
Sacht, Leonardo |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Federal de Santa Catarina (UFSC) Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Souto Ferreira, Leonardo [UNESP] Sacht, Leonardo |
dc.subject.por.fl_str_mv |
linear blend skinning Möbius transformations Wide-angle images |
topic |
linear blend skinning Möbius transformations Wide-angle images |
description |
We propose a new method to correct distortions in equirectangular images, i.e., images that use the longitude/latitude representation to describe the full spherical field of view around a given viewpoint. We show that Möbius transformations are the correct mathematical tool to deal with the conflicting distortions in this setting: they are conformal, are able to rectify lines, perform rotations, translations and scales on the sphere and are bijective. Multiple transformations are specified through points, lines and cages on the sphere. We associate three points that uniquely define a Möbius transformation to each one of these geometric handles. Linear blend skinning with bounded biharmonic weights combine the different transformations into a single full spherical modified image. We present a collection of results in challenging settings and show that our method is more flexible and produces higher quality results when compared to previous methods. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-12-01 2021-06-25T10:36:34Z 2021-06-25T10:36:34Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1016/j.cag.2020.09.011 Computers and Graphics (Pergamon), v. 93, p. 51-60. 0097-8493 http://hdl.handle.net/11449/206689 10.1016/j.cag.2020.09.011 2-s2.0-85092704443 |
url |
http://dx.doi.org/10.1016/j.cag.2020.09.011 http://hdl.handle.net/11449/206689 |
identifier_str_mv |
Computers and Graphics (Pergamon), v. 93, p. 51-60. 0097-8493 10.1016/j.cag.2020.09.011 2-s2.0-85092704443 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Computers and Graphics (Pergamon) |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
51-60 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808128461616709632 |