Wavelets provide a sparse representation for piecewise smooth signals in 1-D; however, separable extensions of wavelets to multiple dimensions do not achieve the same level of sparseness. Recently proposed directional lifting offers transforms sensitive to edges that are not aligned with the coordinate axes, yet the concatenation of separate 1-D slices implicitly assumes independent directional slices and could create large or isotropic support. True 2-D filters and lifting schemes will avoid both of these problems. By aligning the support of the filters with the expected edge, the filters will create fewer non-zero coefficients. Because these filters correspond to interpolation, the theory of Neville filters can automatically determine the coefficients. For images that consist of two bilinear functions divided by a line, geometric lifting demonstrates a 2-4 times reduction of the number of non-zero coefficients compared with the Daubechies order 2 wavelet. In addition, there is a gain of 2.4 dB in nonlinear approximation.

Original languageEnglish (US)
Title of host publication2009 IEEE International Conference on Image Processing, ICIP 2009 - Proceedings
PublisherIEEE Computer Society
Number of pages4
ISBN (Print)9781424456543
StatePublished - 2009
Event2009 IEEE International Conference on Image Processing, ICIP 2009 - Cairo, Egypt
Duration: Nov 7 2009Nov 10 2009

Publication series

NameProceedings - International Conference on Image Processing, ICIP
ISSN (Print)1522-4880


Other2009 IEEE International Conference on Image Processing, ICIP 2009


  • Adaptive transforms
  • Geometric regularity
  • Lifting
  • Wavelet transforms

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Signal Processing


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