Journal
IEEE TRANSACTIONS ON IMAGE PROCESSING
Volume 17, Issue 11, Pages 2063-2080Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2008.2004797
Keywords
Feature extraction; primal sketch; steerable filters; wavelet design
Funding
- Swiss National Science Foundation [200020-109415]
- Center for Biomedical Imaging of the Geneva-Lausanne Universities
- EPFL
- foundations Leenaards and Louis-Jeantet
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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 (R-2), 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.
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