Share Email Print

Proceedings Paper

Properties of multiscale morphological filters, namely, the morphology decomposition theorem
Author(s): Pierre Chardaire; J. Andrew Bangham; C. Jeremy Pye; DeQuan Wu
Format Member Price Non-Member Price
PDF $17.00 $21.00

Paper Abstract

Sieves decompose 1D bounded functions, e.g., f to a set of increasing scale granule functions {dm, m equals 1 ...R}, that represent the information in a manner that is analogous to the pyramid of wavelets obtained by linear decomposition. Sieves based on sequences of increasing scale open-closings with flat structuring elements (M and N filters) map f to {d} and the inverse process maps {d} to f. Experiments show that a more general inverse exists such that {d} maps to f and back to {d}, where the granule functions {d}, are a subset of {d} in which granules may have changed amplitudes, that may include zero but not a change of sign. An analytical proof of this inverse is presented. This key property could prove important for feature recognition and opens the way for an analysis of the noise resistance of these sieves. The resulting theorems neither apply to parallel open-closing filters nor to median based sieves, although root median sieves do `nearly' invert and offer better statistical properties.

Paper Details

Date Published: 1 May 1994
PDF: 7 pages
Proc. SPIE 2180, Nonlinear Image Processing V, (1 May 1994); doi: 10.1117/12.172552
Show Author Affiliations
Pierre Chardaire, Univ. of East Anglia (United Kingdom)
J. Andrew Bangham, Univ. of East Anglia (United Kingdom)
C. Jeremy Pye, Univ. of East Anglia (United Kingdom)
DeQuan Wu, Oxford Univ. (United Kingdom)

Published in SPIE Proceedings Vol. 2180:
Nonlinear Image Processing V
Edward R. Dougherty; Jaakko Astola; Harold G. Longbotham, Editor(s)

© SPIE. Terms of Use
Back to Top
Sign in to read the full article
Create a free SPIE account to get access to
premium articles and original research
Forgot your username?