DocumentCode :
1555733
Title :
Annular filters for binary images
Author :
Heijmans, Henk J A M ; Ronse, Christian
Author_Institution :
Centre for Math. & Comput. Sci., Amsterdam, Netherlands
Volume :
8
Issue :
10
fYear :
1999
fDate :
10/1/1999 12:00:00 AM
Firstpage :
1330
Lastpage :
1340
Abstract :
A binary annular filter removes isolated points in the foreground and the background of an image. Here, the adjective “isolated” refers to an underlying adjacency relation between pixels, which may be different for foreground and background pixels. In this paper, annular filters are represented in terms of switch pairs. A switch pair consists of two operators which govern the removal of points from foreground and background, respectively. In the case of annular filters, switch pairs are completely determined by foreground and background adjacency. It is shown that a specific triangular condition in terms of both adjacencies is required to establish idempotence of the resulting annular filter. In the case of translation-invariant operators, an annular filter takes the form X→(X⊕A)∩X∪(X⊖B), where A and B are structuring elements satisfying some further conditions: when A∩B∩(A⊕B)≠Ø, it is an (idempotent) morphological filter; when A∪B⊂A⊕B, it is a strong filter and in this case it can be obtained by composing in either order the annular opening X→(X⊕A)∩X and the annular closing X→∪(X⊕B)
Keywords :
filtering theory; image processing; mathematical morphology; set theory; adjacency relation; annular closing; annular opening; background pixels; binary annular filter; binary images; foreground pixels; image background; image foreground; morphological filter; operators; switch pairs; translation-invariant operators; triangular condition; Computer science; Euclidean distance; Filters; Mathematics; Switches;
fLanguage :
English
Journal_Title :
Image Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1057-7149
Type :
jour
DOI :
10.1109/83.791959
Filename :
791959
Link To Document :
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