Paper Info
Title
A Morphological View on Traditional Signal Processing.
Abstract
We argue that the fundamentals of mathematical morphology (partial ordered sets, openings, erosions etc.) could provide a, theoretical foundation for signal processing in general. The main observation is that signal processing addresses simpler versions of signals (of a given set S), and tills actually determines a partial ordering on S. Another observation, made ill the past by Serra, is that ideal filters are in fact algebraic openings. In this paper, these and other ideas are addressed and developed. In the first part of this paper, we show that several key signal processing tasks (linear filtering, quantization, and decimation) call be seen as particular cases of morphological operators. Specifically, for each of these operators, we show a complete inf-semilattice in which the operator is an erosion. This serves as a background and motivation for investigating the relationship between mathematical morphology and general signal processing. In the second part, we revisit the foundations of signal processing from the point of view of mathematical morphology. We show that, to every function. one can associate a partial ordering and an ideal filter (algebraic opening ill the resulting partial ordered set), which provide a characterization of the "simplification" (information loss) performed by the function. Then, links between classes of signal processing tasks and basic morphological operators are established.
Year
DOI
Venue
2000
10.1007/0-306-47025-X_2
Computational Imaging and Vision
Keywords
Field
DocType
mathematical morphology,complete semilattices,signal processing,image processing
Ordered set,Signal processing,Algebraic number,Mathematical morphology,Computer science,Parallel computing,Algorithm,Image processing,Partially ordered set
Conference
Volume
Citations 
PageRank 
18
2
0.39
References 
Authors
4
1
Name
Order
Citations
PageRank
Renato Keshet133827.26