Axiomatic quantification of multidimensional image resolution

Author

O´Sullivan, Joseph A. ; Jiang, Ming ; Ma, Xiao-ming ; Wang, Ge

Author_Institution

Dept. of Electr. Eng., Washington Univ., St. Louis, MO, USA

Volume

9

Issue

4

fYear

2002

fDate

4/1/2002 12:00:00 AM

Firstpage

120

Lastpage

122

Abstract

We generalize the axiomatic quantification of one-dimensional (1-D) image resolution to the multidimensional case. The imaging system of interest is characterized by a nonnegative spatially invariant point spread function. The axioms extended from the 1-D counterparts include nonnegativity, continuity, translation invariance, rotation invariance, luminance invariance, homogeneous scaling, and serial combination properties. It is proved that the only resolution measure consistent with the axioms is proportional to the square root of the trace of the covariance matrix of the point spread function.

Keywords

covariance matrices; image resolution; matrix algebra; optical transfer function; axiomatic quantification; continuity; covariance matrix; homogeneous scaling; imaging system; luminance invariance; multidimensional image resolution; nonnegative spatially invariant point spread function; resolution measure; rotation invariance; serial combination properties; translation invariance; Cities and towns; Convolution; Covariance matrix; Density measurement; Image resolution; Layout; Measurement standards; Multidimensional systems; Radiology; Spatial resolution;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/97.1001647

Filename

1001647