The Generalized Gabor Scheme of Image Representation in Biological and Machine Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Coherent States, Wavelets and Their Generalizations
Coherent States, Wavelets and Their Generalizations
The Uncertainty Principle: Group Theoretic Approach, Possible Minimizers and Scale-Space Properties
Journal of Mathematical Imaging and Vision
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
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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.