Scale-Space Generation via Uncertainty Principles

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 twodimensional Weyl-Heisenberg groups, the one-dimensional Affine group, and the two-dimensional similitude group of IR2 , SIM(2) = IR2 ×(IR+ × 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.

• Type: Conference
• Year: 2005
• Where: SCALESPACE
• Authors: Chen Sagiv, Nir A. Sochen, Yehoshua Y. Zeevi
• Keywords: Affine Group, One-dimensional Affine Group, SCALESPACE 2005, Uncertainty Principles