Scale-Space Generation via Uncertainty Principles | Zendy

Chen Sagiv | Zendy; Nir Sochen | Zendy; Yehoshua Y. Zeevi | Zendy

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Scale-Space Generation via Uncertainty Principles

Author(s) -

Chen Sagiv,

Nir Sochen,

Yehoshua Y. Zeevi

Publication year - 2005

Publication title -

lecture notes in computer science

Language(s) - English

Resource type - Book series

SCImago Journal Rank - 0.249

H-Index - 400

eISSN - 1611-3349

pISSN - 0302-9743

ISBN - 3-540-25547-8

DOI - 10.1007/11408031_30

Subject(s) - affine transformation , affine group , uncertainty principle , group (periodic table) , heisenberg group , space (punctuation) , similitude , mathematics , scale (ratio) , algebra over a field , pure mathematics , computer science , physics , artificial intelligence , quantum mechanics , quantum , operating system

This study is concerned with the uncertainty principles which are related to the Weyl-Heisenberg, the SIM(2) and the Affine groups. A general theorem which associates an uncertainty principle to a pair of self-adjoint operators was previously used in finding the minimizers of the uncertainty principles related to various groups, e.g., the one and two-dimensional Weyl-Heisenberg groups, the one-dimensional Affine group, and the two-dimensional similitude group of ℝ2, SIM(2) = ℝ2 ×(ℝ+ × SO(2)). In this study the relationship between the affine group in two dimensions and the SIM(2) group is investigated in terms of the uncertainty minimizers. Moreover, we present scale space properties of a minimizer of the SIM(2) group.

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