DocumentCode :
981378
Title :
Directionlets: anisotropic multidirectional representation with separable filtering
Author :
Velisavljevic, Vladan ; Beferull-Lozano, Baltasar ; Vetterli, Martin ; Dragotti, Pier Luigi
Author_Institution :
Sch. of Comput. & Commun. Sci., Swiss Fed. Inst. of Technol. Lausanne, Switzerland
Volume :
15
Issue :
7
fYear :
2006
fDate :
7/1/2006 12:00:00 AM
Firstpage :
1916
Lastpage :
1933
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-1.55), which, while slower than the optimal rate O(N-2), is much better than O(N-1) achieved with wavelets, but at similar complexity.
Keywords :
filtering theory; image representation; wavelet transforms; anisotropic basis functions; anisotropic geometrical structures; anisotropic multidirectional representation; anisotropic transform; critically sampled anisotropic M-DIR WT; directional transform; directional vanishing moments; directionlets; image processing; lattice-based perfect reconstruction; nonlinear image approximation; nonsparse representation; one-dimensional discontinuities; rational slopes; separable filtering; spatial isotropy; standard wavelet transform; visual perception; wavelet basis functions; Anisotropic magnetoresistance; Channel bank filters; Filter bank; Filtering; Geometry; Image coding; Image processing; Image reconstruction; Visual perception; Wavelet transforms; Directional vanishing moments; directionlets; filter banks; geometry; multidirection; multiresolution; separable filtering; sparse image representation; wavelets; Algorithms; Anisotropy; Artifacts; Computer Graphics; Computer Simulation; Filtration; Image Enhancement; Image Interpretation, Computer-Assisted; Information Storage and Retrieval; Models, Statistical; Numerical Analysis, Computer-Assisted; Signal Processing, Computer-Assisted; Stochastic Processes;
fLanguage :
English
Journal_Title :
Image Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1057-7149
Type :
jour
DOI :
10.1109/TIP.2006.877076
Filename :
1643699
Link To Document :
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