Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid

@article{Ville2008ComplexWB,
  title={Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid},
  author={Dimitri Van De Ville and Michael Unser},
  journal={IEEE Transactions on Image Processing},
  year={2008},
  volume={17},
  pages={2063-2080}
}
Our aim in this paper is to tighten the link between wavelets, some classical image-processing operators, and David Marr's theory of early vision. The cornerstone of our approach is a new complex wavelet basis that behaves like a smoothed version of the Gradient-Laplace operator. Starting from first principles, we show that a single-generator wavelet can be defined analytically and that it yields a semi-orthogonal complex basis of L 2(R2), irrespective of the dilation matrix used. We also… CONTINUE READING
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