en
Scientific article
English

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

Published inIEEE transactions on image processing, vol. 17, no. 11, p. 2063-2080
Publication date2008
Abstract

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.

Keywords
  • *Algorithms
  • *Artificial Intelligence
  • Image Enhancement/*methods
  • Image Interpretation, Computer-Assisted/*methods
  • Pattern Recognition, Automated/*methods
  • Reproducibility of Results
  • Sensitivity and Specificity
Citation (ISO format)
VAN DE VILLE, Dimitri, UNSER, Michael. Complex wavelet bases, steerability, and the marr-like pyramid. In: IEEE transactions on image processing, 2008, vol. 17, n° 11, p. 2063–2080. doi: 10.1109/tip.2008.2004797
Identifiers
ISSN of the journal1057-7149
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