Electronic Resource
Springer
Set-valued analysis
3 (1995), S. 33-50
ISSN:
1572-932X
Keywords:
47H04
;
68U10
;
mathematical morphology
;
Minkowski sum
;
Minkowski subtraction
;
set-convolution
;
internal set-convolution
;
Steiner selection
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Mathematical morphology started as a set of tools for analysing images by the use of transformations based on set-theoretical operations which are the Minkowski sum and subtraction. It was first developed for the analysis of binary images. Its extension to grey-level images was a later development with the extension of the Minkowski operations to real-valued functions in terms of sup-convolution and inf-convolution. The purpose of this paper is to define a type of convolution between set-valued maps, to study its properties, and to establish some associated differential relations. This set-convolution map allows us to extend the Minkowski sum and substraction to multivalued functions and to functions with vectorial values.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01033640
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