Abstract The extraction of copies of a template appearing in a figure can be defined as the composition of a hit-or-miss transform by a pair of structuring elements, followed by a dilation by the first structuring element. On the other hand, the operation of template extraction can be abstractly characterized by the three requirements of antiextensivity, idempotence, and a new property that we call “overcondensation”; we designate by “open-overcondensation” an operator having these three properties. Examples include digital contour extraction, or the above-mentioned composition of a hit-or-miss transform by a dilation. Decompositions formulas of open-overcondensations in terms of such operators are given; they parallel the well-known decomposition formulas for openings. Generalizations of “rank-max” openings and inf-overfilters are also given. These results hold not only for sets or gray-level images, they are valid in the framework of complete lattices.
[1]
Henk J. A. M. Heijmans,et al.
The algebraic basis of mathematical morphology. I Dilations and erosions
,
1990,
Comput. Vis. Graph. Image Process..
[2]
Edward R. Dougherty,et al.
Morphological methods in image and signal processing
,
1988
.
[3]
Junior Barrera,et al.
Set Operator Decomposition and Conditionally Translation Invariant Elementary Operators
,
1994,
ISMM.
[4]
Junior Barrera,et al.
Decomposition of mappings between complete lattices by mathematical morphology, Part I. General lattices
,
1993,
Signal Process..
[5]
Xinhua Zhuang,et al.
Image Analysis Using Mathematical Morphology
,
1987,
IEEE Transactions on Pattern Analysis and Machine Intelligence.
[6]
G. Banon,et al.
Minimal representations for translation-invariant set mappings by mathematical morphology
,
1991
.