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

1984

@article{AlR1984,
	vgclass =	{refpap},
	vgproject =	{invariance},
	author =	{J\"{u}rgen Altmann and Herbert J.P. Reitb\"{o}ck},
	title =	{A Fast Correlation Method for Scale- and
	Translation-Invariant Pattern Recognition},
	journal =	{IEEE Transactions on Pattern Analysis and Machine Intelligence},
	volume =	{6},
	number =	{1},
	pages =	{46--57},
	month =	{January},
	year =	{1984},
	abstract =	{A size- and position-invariant description of an image
	function can be obtained via the absolute value of the Mellin transform
	of its Fourier amplitude spectrum. If the transform is implemented on a
	digital computer via a discrete Fourier-Mellin transform, these exact
	invariances are not preserved due to sampling- and border-effects. In
	this paper these effects are discussed, and an alternative correlation
	method is proposed. The method  consists of calculating the normalized
	absolute magnitude of the discrete Fourier transform (DFT) of the image
	function (which gives invariance to translation and multiplicative
	amplitude changes) and a subsequent logarithmic distortion in $x$- and
	$y$-direction, which converts scaling to translation. Two such
	transforms are compared by calculating the normalized Euclidean
	distances between both for all possible relative shifts along the main
	diagonal. If, for some shift, the distance has a minimum below a
	similarity threshold, the underlying image functions will probably
	differ only by translation and scaling. The magnitude of this shift is
	related to the scale factor between the objects.  Good separation
	between similar and nonsimilar objects is possible if two size criteria
	imposed by the DFT are met: the total object size must not exceed
	$\frac{N}{4}$ ($N$ is the number of image points in each dimension),
	and object details have to be larger than about 4 image points. As a
	consequence, $N$ increases with object complexity and desired scale
	range.  With $N = 64$, only a limited object manifold can be handled;
	with $N = 256$, useful results are found for quite complicated forms.

	The method described has the additional advantage that the
	magnification factor is accessible. Its disadvantage, the requirement
	that two transforms have to be compared at many relative positions, can
	be avoided by an independent evaluation of the scale factor via the
	normalized central second moments of the image functions. These moments
	can be calculated from the normalized absolute magnitude of the
	discrete Fourier transform. If the size ratio of image and sample is
	thus known, the relative position can be estimated, where the
	logarithmically distorted spectra would coincide in case of similarity.
	Correct scale factors are obtained if the object size is between 4 and
	about $\frac{N}{2}$ image points. Since one comparison suffices for
	every stored sample, the proposed method is even faster than a discrete
	Fourier-Mellin transform.},
}