BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Wavelet Primal Sketch Representation Using Marr Wavelet Pyramid and Its Reconstruction

D. Van De Ville, M. Unser

Proceedings of the SPIE Optics and Photonics 2009 Conference on Mathematical Methods: Wavelet XIII, San Diego CA, USA, August 2-6, 2009, vol. 7446, pp. 74460W-1–74460W-8.

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. 

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/vandeville0902.html,
AUTHOR="Van De Ville, D. and Unser, M.",
TITLE="Wavelet Primal Sketch Representation Using {M}arr Wavelet Pyramid
	and Its Reconstruction",
BOOKTITLE="Proceedings of the {SPIE} Conference on Mathematical Imaging:
	{W}avelet {XIII}",
YEAR="2009",
editor="",
volume="7446",
series="",
pages="74460W-1--74460W-8",
address="San Diego CA, USA",
month="August 2-6,",
organization="",
publisher="",
note="")

© 2009 SPIE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from SPIE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.