NDLI: Directionlets: anisotropic multidirectional representation with separable filtering

Content Provider	IEEE Xplore Digital Library
Author	Velisavljevic, V. Beferull-Lozano, B. Vetterli, M. Dragotti, P.L.
Copyright Year	1992
Abstract	In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensional (1-D) discontinuities in images (edges and contours) that are very important elements in visual perception, intersect too many wavelet basis functions and lead to a nonsparse representation. To efficiently capture these anisotropic geometrical structures characterized by many more than the horizontal and vertical directions, a more complex multidirectional (M-DIR) and anisotropic transform is required. We present a new lattice-based perfect reconstruction and critically sampled anisotropic M-DIR WT. The transform retains the separable filtering and subsampling and the simplicity of computations and filter design from the standard two-dimensional WT, unlike in the case of some other directional transform constructions (e.g., curvelets, contourlets, or edgelets). The corresponding anisotropic basis functions (directionlets) have directional vanishing moments along any two directions with rational slopes. Furthermore, we show that this novel transform provides an efficient tool for nonlinear approximation of images, achieving the approximation power O(N/sup -1.55/), which, while slower than the optimal rate O(N/sup -2/), is much better than O(N/sup -1/) achieved with wavelets, but at similar complexity.
Sponsorship	IEEE Signal Processing Society
Page Count	18
File Size	3130538
Starting Page	1916
Ending Page	1933
File Format	PDF
ISSN	10577149
Volume Number	15
Issue Number	7
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-07-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Anisotropic magnetoresistance Filtering Channel bank filters Image processing Wavelet transforms Filter bank Image coding Visual perception Image reconstruction Geometry wavelets Directional vanishing moments directionlets filter banks geometry multidirection multiresolution separable filtering sparse image representation
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Software

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