2.50
Hdl Handle:
http://hdl.handle.net/10547/292552
Title:
Sparse image representation by directionlets
Authors:
Velisavljević, Vladan ( 0000-0001-9980-9368 ) ; Vetterli, Martin; Beferull-Lozano, Baltasar; Dragotti, Pier Luigi
Abstract:
Despite the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency and sparsity of its representation are limited by the spatial symmetry and separability of its basis functions built in the horizontal and vertical directions. One-dimensional discontinuities in images (edges or contours), which are important elements in visual perception, intersect too many wavelet basis functions and lead to a non-sparse representation. To capture efficiently these elongated structures characterized by geometrical regularity along different directions (not only the horizontal and vertical), a more complex multidirectional (M-DIR) and asymmetric transform is required. We present a lattice-based perfect reconstruction and critically sampled asymmetric M-DIR WT. The transform retains the separable filtering and subsampling and the simplicity of computations and filter design from the standard two-dimensional (2D) WT, unlike the case for some other directional transform constructions (e.g., curvelets, contourlets, or edgelets). The corresponding asymmetric basis functions, called direction-lets, have directional vanishing moments along any two directions with rational slopes, which allows for a sparser representation of elongated and oriented features. As a consequence of the improved sparsity, directionlets provide an efficient tool for nonlinear approximation of images, significantly outperforming the standard 2D WT. Furthermore, directionlets combined with wavelet-based image compression methods lead to a gain in performance in terms of both the mean square error and visual quality, especially at low bit-rate compression, while retaining the same complexity. Finally, a shift-invariant non-subsampled version of directionlets is successfully implemented in image interpolation, where critical sampling is not a key requirement.
Citation:
Velisavljevic, V., Vetterli, M., Beferull-Lozano, B. and Dragotti, P.L. (2010) 'Sparse image representation by directionlets', in Hawkes, P. (ed.) Advances in imaging and electron physics. Volume 161. Philadelphia: Elsevier, pp.147-209.
Publisher:
Elsevier
Issue Date:
2010
URI:
http://hdl.handle.net/10547/292552
DOI:
10.1016/S1076-5670(10)61004-X
Additional Links:
http://www.sciencedirect.com/science/article/pii/S107656701061004X
Type:
Book chapter
Language:
en
ISBN:
9780123813183
Appears in Collections:
Centre for Wireless Research (CWR)

Full metadata record

DC FieldValue Language
dc.contributor.authorVelisavljević, Vladanen_GB
dc.contributor.authorVetterli, Martinen_GB
dc.contributor.authorBeferull-Lozano, Baltasaren_GB
dc.contributor.authorDragotti, Pier Luigien_GB
dc.date.accessioned2013-05-21T13:28:09Zen
dc.date.available2013-05-21T13:28:09Zen
dc.date.issued2010en
dc.identifier.citationVelisavljevic, V., Vetterli, M., Beferull-Lozano, B. and Dragotti, P.L. (2010) 'Sparse image representation by directionlets', in Hawkes, P. (ed.) Advances in imaging and electron physics. Volume 161. Philadelphia: Elsevier, pp.147-209.en_GB
dc.identifier.isbn9780123813183en
dc.identifier.doi10.1016/S1076-5670(10)61004-Xen
dc.identifier.urihttp://hdl.handle.net/10547/292552en
dc.description.abstractDespite the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency and sparsity of its representation are limited by the spatial symmetry and separability of its basis functions built in the horizontal and vertical directions. One-dimensional discontinuities in images (edges or contours), which are important elements in visual perception, intersect too many wavelet basis functions and lead to a non-sparse representation. To capture efficiently these elongated structures characterized by geometrical regularity along different directions (not only the horizontal and vertical), a more complex multidirectional (M-DIR) and asymmetric transform is required. We present a lattice-based perfect reconstruction and critically sampled asymmetric M-DIR WT. The transform retains the separable filtering and subsampling and the simplicity of computations and filter design from the standard two-dimensional (2D) WT, unlike the case for some other directional transform constructions (e.g., curvelets, contourlets, or edgelets). The corresponding asymmetric basis functions, called direction-lets, have directional vanishing moments along any two directions with rational slopes, which allows for a sparser representation of elongated and oriented features. As a consequence of the improved sparsity, directionlets provide an efficient tool for nonlinear approximation of images, significantly outperforming the standard 2D WT. Furthermore, directionlets combined with wavelet-based image compression methods lead to a gain in performance in terms of both the mean square error and visual quality, especially at low bit-rate compression, while retaining the same complexity. Finally, a shift-invariant non-subsampled version of directionlets is successfully implemented in image interpolation, where critical sampling is not a key requirement.en_GB
dc.language.isoenen
dc.publisherElsevieren_GB
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S107656701061004Xen_GB
dc.subjectdirectional transformsen_GB
dc.subjectimage codingen_GB
dc.subjectimage interpolationen_GB
dc.subjectMultiresolution analysisen_GB
dc.subjectsparse representationen_GB
dc.titleSparse image representation by directionletsen
dc.typeBook chapteren
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