Full affine wavelets are scale-space with a twist

Authors:
Yossi Ferdman;Chen Sagiv;Nir Sochen
Affiliations:
Department of Applied Mathematics, University of Tel Aviv, Tel-Aviv, Israel;-;Department of Applied Mathematics, University of Tel Aviv, Tel-Aviv, Israel
Venue:
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Year:
2007

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Abstract

In this work we study the relation between the Gabor-Morlet wavelet transform and scale-space theory. It is shown that the usual wavelet transform is a projection of scale-space on a specific frequency component. This result is then generalized to the full two-dimensional affine group. A close relation between this generalized wavelet transform and a family of scale-spaces of images that are related by SL(2) is established. Using frame theory we show that sampling from different images in this family, and from different scales enables a complete reconstruction of the image.