Generic neighborhood operators
- 1 June 1992
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 14 (6) , 597-605
- https://doi.org/10.1109/34.141551
Abstract
A method that treats linear neighborhood operators within a unified framework that enables linear combinations, concatenations, resolution changes, or rotations of operators to be treated in a canonical manner is presented. Various families of operators with special kinds of symmetries (such as translation, rotation, magnification) are explicitly constructed in 1-D, 2-D, and 3-D. A concept of 'order' is defined, and finite orthonormal bases of functions closely connected with the operators of various orders are constructed. Linear transformations between the various representations are considered. The method is based on two fundamental assumptions: a decrease of resolution should not introduce spurious detail, and the local operators should be self-similar under changes of resolution. These assumptions merely sum up the even more general need for homogeneity isotropy, scale invariance, and separability of independent dimensions of front-end processing in the absence of a priori information.Keywords
This publication has 14 references indexed in Scilit:
- Visibility of blobs with a gaussian luminance profileVision Research, 1989
- A hitherto unnoticed singularity of scale-spacePublished by Institute of Electrical and Electronics Engineers (IEEE) ,1989
- Two-dimensional curvature operatorsJournal of the Optical Society of America A, 1988
- Operational significance of receptive field assembliesBiological Cybernetics, 1988
- Efficiency of a model human image codeJournal of the Optical Society of America A, 1987
- Deblurring Gaussian blurComputer Vision, Graphics, and Image Processing, 1987
- Representation of local geometry in the visual systemBiological Cybernetics, 1987
- A spatial filtering approach to texture analysisPattern Recognition Letters, 1985
- Fingerprints theorems for zero crossingsJournal of the Optical Society of America A, 1985
- The structure of imagesBiological Cybernetics, 1984