Fourier cross correlation and invariance transformations for an optimal recognition of functions deformed by affine groups
- 1 June 1992
- journal article
- Published by Optica Publishing Group in Journal of the Optical Society of America A
- Vol. 9 (6) , 895-902
- https://doi.org/10.1364/josaa.9.000895
Abstract
A framework for an optimal analysis of a large class of patterns deformed by affine transformation groups is presented. This approach is based on the properties of the Fourier cross correlation and Lie groups theory. Group properties such as homogeneity, symmetry, and isometry are utilized naturally. In particular, the important groups of similarities and rigid motion in plane and space are considered. The method is general to any object functions: picture, shape, curve, etc.Keywords
This publication has 10 references indexed in Scilit:
- Recognition of distorted patterns by invariance kernelsPattern Recognition, 1991
- Invariant pattern recognition, symmetry, and Radon transformsJournal of the Optical Society of America A, 1989
- On the minimum number of templates required for shift, rotation and size invariant pattern recognitionPattern Recognition, 1988
- Maximal matching of 3-D points for multiple-object motion estimationPattern Recognition, 1988
- Relationship between integral transform invariances and Lie group theoryJournal of the Optical Society of America A, 1988
- Cross-correlation model for pattern acuityJournal of the Optical Society of America A, 1986
- Subjective Lorentz transformations and the perception of motion*Journal of the Optical Society of America, 1978
- Position, rotation, and scale invariant optical correlationApplied Optics, 1976
- Scale invariant optical correlation using Mellin transformsOptics Communications, 1976
- The Lie algebra of visual perceptionJournal of Mathematical Psychology, 1966