TY - JOUR
T1 - Scale-space generation via uncertainty principles
AU - Sagiv, Chen
AU - Sochen, Nir A.
AU - Zeevi, Yehoshua Y.
PY - 2005
Y1 - 2005
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=24644499602&partnerID=8YFLogxK
U2 - 10.1007/11408031_30
DO - 10.1007/11408031_30
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AN - SCOPUS:24644499602
SN - 0302-9743
VL - 3459
SP - 351
EP - 362
JO - Lecture Notes in Computer Science
JF - Lecture Notes in Computer Science
T2 - 5th International Conference on Scale Space and PDE Methods in Computer Vision, Scale-Space 2005
Y2 - 7 April 2005 through 9 April 2005
ER -