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Directionlets: anisotropic multidirectional representation with separable filtering

Research Output: Contribution to journal Article Peer-review

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.

Publication Information

Output type

Research Output: Contribution to journal Article Peer-review

Original language

English

Pages from-to (Number of pages)

Pages 1916

Journal (Volume, Issue Number)

IEEE Transactions on Image Processing (Volume 15, Issue 7)

Publication milestones

  • Published - 01/07/2006

Publication status

Published - 01/07/2006

ISSN

1057-7149

External Publication IDs

  • handle.net: 10547/268212
  • Scopus: 33745728950

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