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A panorama on multiscale geometric representations, intertwining spatial, directional and frequency selectivity

dc.contributor.authorJacques, Laurent
dc.contributor.authorDuval, Laurent
HAL ID: 8914
ORCID: 0000-0002-7732-4666
dc.contributor.authorChaux, Caroline
HAL ID: 7515
dc.contributor.authorPeyré, Gabriel
HAL ID: 1211
dc.date.accessioned2013-09-13T11:14:16Z
dc.date.available2013-09-13T11:14:16Z
dc.date.issued2011
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/11672
dc.language.isoenen
dc.subjectReviewen
dc.subjectMultiscaleen
dc.subjectGeometric representationsen
dc.subjectOriented decompositionsen
dc.subjectScale-spaceen
dc.subjectWaveletsen
dc.subjectAtomsen
dc.subjectSparsityen
dc.subjectRedundancyen
dc.subjectBasesen
dc.subjectFramesen
dc.subjectEdgesen
dc.subjectTexturesen
dc.subjectImage processingen
dc.subjectHaar waveleten
dc.subjectNon-Euclidean waveletsen
dc.subject.ddc520en
dc.titleA panorama on multiscale geometric representations, intertwining spatial, directional and frequency selectivityen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThe richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share a hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping “pictures”. We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.en
dc.relation.isversionofjnlnameSignal Processing
dc.relation.isversionofjnlvol91en
dc.relation.isversionofjnlissue12en
dc.relation.isversionofjnldate2011
dc.relation.isversionofjnlpages2699-2730en
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.sigpro.2011.04.025en
dc.identifier.urlsitehttp://arxiv.org/abs/1101.5320v2en
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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