Full affine wavelets are scale-space with a twist

Yossi Ferdman; Chen Sagiv; Nir Sochen

doi:10.1007/978-3-540-72823-8_1

Full affine wavelets are scale-space with a twist

Yossi Ferdman^*, Chen Sagiv, Nir Sochen

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	English
Title of host publication	Scale Space and Variational Methods in Computer Vision, First International Conference, SSVM 2007, Proceedings
Publisher	Springer Verlag
Pages	1-12
Number of pages	12
ISBN (Print)	9783540728221
DOIs	https://doi.org/10.1007/978-3-540-72823-8_1
State	Published - 2007
Event	1st International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2007 - Ischia, Italy Duration: 30 May 2007 → 2 Jun 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4485 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	1st International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2007
Country/Territory	Italy
City	Ischia
Period	30/05/07 → 2/06/07

Access to Document

10.1007/978-3-540-72823-8_1

Cite this

Ferdman, Y., Sagiv, C., & Sochen, N. (2007). Full affine wavelets are scale-space with a twist. In Scale Space and Variational Methods in Computer Vision, First International Conference, SSVM 2007, Proceedings (pp. 1-12). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4485 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-72823-8_1

Ferdman, Yossi ; Sagiv, Chen ; Sochen, Nir. / Full affine wavelets are scale-space with a twist. Scale Space and Variational Methods in Computer Vision, First International Conference, SSVM 2007, Proceedings. Springer Verlag, 2007. pp. 1-12 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Ferdman, Y, Sagiv, C & Sochen, N 2007, Full affine wavelets are scale-space with a twist. in Scale Space and Variational Methods in Computer Vision, First International Conference, SSVM 2007, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4485 LNCS, Springer Verlag, pp. 1-12, 1st International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2007, Ischia, Italy, 30/05/07. https://doi.org/10.1007/978-3-540-72823-8_1

Full affine wavelets are scale-space with a twist. / Ferdman, Yossi; Sagiv, Chen; Sochen, Nir.
Scale Space and Variational Methods in Computer Vision, First International Conference, SSVM 2007, Proceedings. Springer Verlag, 2007. p. 1-12 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4485 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Ferdman Y, Sagiv C, Sochen N. Full affine wavelets are scale-space with a twist. In Scale Space and Variational Methods in Computer Vision, First International Conference, SSVM 2007, Proceedings. Springer Verlag. 2007. p. 1-12. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-72823-8_1

Full affine wavelets are scale-space with a twist

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