The Generalized Gabor Scheme of Image Representation in Biological and Machine Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multichannel Texture Analysis Using Localized Spatial Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Unsupervised texture segmentation using Gabor filters
Pattern Recognition
Journal of Mathematical Imaging and Vision
Image Representation Using 2D Gabor Wavelets
IEEE Transactions on Pattern Analysis and Machine Intelligence
Gabor-Space Geodesic Active Contours
AFPAC '00 Proceedings of the Second International Workshop on Algebraic Frames for the Perception-Action Cycle
Geodesic Active Contours Applied to Texture Feature Space
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
On the Axioms of Scale Space Theory
Journal of Mathematical Imaging and Vision
α scale spaces on a bounded domain
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Scale-space generation via uncertainty principles
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Image enhancement and denoising by complex diffusion processes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Integrated active contours for texture segmentation
IEEE Transactions on Image Processing
Coherent States, Wavelets and Their Generalizations
Coherent States, Wavelets and Their Generalizations
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The uncertainty principle is a fundamental concept in the context of signal and image processing, just as much as it has been in the framework of physics and more recently in harmonic analysis. Uncertainty principles can be derived by using a group theoretic approach. This approach yields also a formalism for finding functions which are the minimizers of the uncertainty principles. A general theorem which associates an uncertainty principle with a pair of self-adjoint operators is used in finding the minimizers of the uncertainty related to various groups.This study is concerned with the uncertainty principle in the context of the Weyl-Heisenberg, the SIM(2), the Affine and the Affine-Weyl-Heisenberg groups. We explore the relationship between the two-dimensional affine group and the SIM (2) group in terms of the uncertainty minimizers. The uncertainty principle is also extended to the Affine-Weyl-Heisenberg group in one dimension. Possible minimizers related to these groups are also presented and the scale-space properties of some of the minimizers are explored.