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

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Date
2011
Link to item file
http://arxiv.org/abs/1101.5320v2
Dewey
Sciences connexes (physique, astrophysique)
Sujet
Review; Multiscale; Geometric representations; Oriented decompositions; Scale-space; Wavelets; Atoms; Sparsity; Redundancy; Bases; Frames; Edges; Textures; Image processing; Haar wavelet; Non-Euclidean wavelets
Journal issue
Signal Processing
Volume
91
Number
12
Publication date
2011
Article pages
2699-2730
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.sigpro.2011.04.025
URI
https://basepub.dauphine.fr/handle/123456789/11672
Collections
  • CEREMADE : Publications
Metadata
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Author
Jacques, Laurent
Duval, Laurent
Chaux, Caroline
Peyré, Gabriel
Type
Article accepté pour publication ou publié
Abstract (EN)
The 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.

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