  A method is introduced to derive resolution criteria for various a priori
defined templates of brightness distribution fitted to represent structures and
objects in astronomical images. The method is used for deriving criteria for
the minimum and maximum resolvable sizes of a template. The minimum resolvable
size of a template is determined by the ratio of (SNR-1)/SNR, and the maximum
detectable size is determined by the ratio of 1/SNR. Application of these
criteria is discussed in connection to data from filled-aperture instruments
and interferometers, accounting for different aperture shapes and the effects
of Fourier sampling, tapering, apodization and visibility weighting. Specific
resolution limits are derived for four different templates of brightness
distribution: (1) two-dimensional Gaussian, (2) optically thin spherical shell,
(3) disk of uniform brightness, and (4) ring. The limiting resolution for these
templates changes with SNR similarly to the quantum limit on resolution.
Practical application of the resolution limits is discussed in two examples
dealing with measurements of maximum brightness temperature in compact
relativistic jets and assessments of morphology of young supernova remnants.
