Abstract

Scaled transforms have recently been introduced as a powerful mathematical tool for processing (e.g., detecting) images that are arbitrarily scaled or rotated. It will be shown that the scaled transforms are equivalent to a subclass of the linear shift-variant, “form-invariant” filters. The equivalence holds in the sense that, given any scaled transform and any input signal, a linear shift-variant filter can be found such that the outputs of the filter and of the scaled transform are Fourier-transform pairs. The relevance of this result is briefly discussed.

© 1983 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Image processing with the radial Hilbert transform: theory and experiments

Jeffrey A. Davis, Dylan E. McNamara, Don M. Cottrell, and Juan Campos
Opt. Lett. 25(2) 99-101 (2000)

Shift-and-scale-invariant pattern recognition using an elliptic coordinate-transformed phase-only filter

Javier García, Tomasz Szoplik, and Carlos Ferreira
Appl. Opt. 31(23) 4823-4828 (1992)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (2)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (21)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription