Refereed full papers (journals, book chapters, international conferences)

1988

@article{FeC1988,
	vgclass =	{refpap},
	vgproject =	{invariance},
	author =	{M. Ferraro and T. Caelli},
	title =	{The relationship between integral transform invariances
	and {L}ie group theory},
	journal =	{Journal of the Optical Society of America (A)},
	volume =	{5},
	pages =	{738--742},
	year =	{1988},
	abstract =	{We explore the relationships between two classical means
	of mathematically representing visual patterns that are invariant under
	geometric transformations. One, based on integral transforms, in
	particular Fourier transforms, produces transform magnitudes invariant
	to pairwise combinations of translations, rotations, and size changes.
	The second, based on the degree to which the pattern remains invariant
	to differential operators (which are the infinitesimal generators of
	the geometric transformations), results in algebraic relations between
	pattern structures and group theoretical properties of the transforms.
	Formal relationships are established between these representations,
	relating the kernel properties of the integral transforms to the
	associated Lie transformation groups.},
}