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Complex wavelet bases, steerability, and the marr-like pyramid.
Journal article

Complex wavelet bases, steerability, and the marr-like pyramid.

  • Van De Ville D Biomedical Imaging Group (BIG), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland. dimitri.vandeville@epfl.ch
  • Unser M
  • 2008-11-01
Published in:
  • IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. - 2008
Algorithms
Artificial Intelligence
Image Enhancement
Image Interpretation, Computer-Assisted
Pattern Recognition, Automated
Reproducibility of Results
Sensitivity and Specificity
English 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 L2 (R2), irrespective of the dilation matrix used. We also provide an efficient FFT-based filterbank implementation. We then propose a slightly redundant version of the transform that is nearly translation-invariant and that is optimized for better steerability (Gaussian-like smoothing kernel).We call it the Marr-like wavelet pyramid because it essentially replicates the processing steps in Marr's theory of early vision.We use it to derive a primal wavelet sketch which is a compact description of the image by a multiscale, subsampled edge map. Finally, we provide an efficient iterative algorithm for the reconstruction of an image from its primal wavelet sketch.
Language
  • English
Open access status
green
Identifiers
Persistent URL
https://sonar.ch/global/documents/176742
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