Based on the class of complex gradient-Laplace operators, we show the design of a non-separable two-dimensional wavelet basis from a single and analytically defined generator wavelet function. The wavelet decomposition is implemented by an efficient FFT-based filterbank. By allowing for slight redundancy, we obtain the Marr wavelet pyramid decomposition that features improved translation-invariance and steerability. The link with Marr's theory of early vision is due to the replication of the essential processing steps (Gaussian smoothing, Laplacian, orientation detection). Finally, we show how to find a compact multiscale primal sketch of the image, and how to reconstruct an image from it.

Date Published: 4 September 2009
PDF: 8 pages
Proc. SPIE 7446, Wavelets XIII, 74460W (4 September 2009); doi: 10.1117/12.825972

Published in SPIE Proceedings Vol. 7446:
Wavelets XIII
Vivek K. Goyal; Manos Papadakis; Dimitri Van De Ville, Editor(s)