The theory of an image decomposition that we refer to as a sieve is de
veloped for images defined in any finite number of dimensions. The dec
omposition has many desirable properties including the preservation of
scale-space causality and the localization of sharp-edged objects in
the transformation domain. The decomposition has the additional proper
ties of manipulability, which means that it is easy to construct patte
rn recognition systems, and scale-calibration, which means that it may
be used for accurate measurement. (C) 1996 SPIE and IS&T.