Cellular Computers and Biomedical Image Processing

Sternberg, S.

doi:10.1007/978-3-642-93218-2_27

Cited by 39 publications

(12 citation statements)

References 8 publications

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“…In addition, they can be implemented using simple and fast software or hardware; examples include various digital [58,61] and analog, i.e., optical or hybrid optical-electronic implementations [46,63]. Their wide applicability and ease of implementation poses the question which signal processing systems can be represented by using dilations and erosions as the basic building blocks.…”

Section: Universality Of Morphological Operatorsmentioning

confidence: 99%

Morphological Signal and Image Processing

Maragos¹

2009

Wireless, Networking, Radar, Sensor Array Processing, and Nonlinear Signal Processing

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Section: Universality Of Morphological Operatorsmentioning

confidence: 99%

Morphological Signal and Image Processing

Maragos¹

2009

Wireless, Networking, Radar, Sensor Array Processing, and Nonlinear Signal Processing

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“…Following the publication of [14] and [23], and also the work of Sternberg in the USA [25,26], this discipline gained an increasing popularity inside the image processing community, as is witnessed by a special issue of the journal Computer Vision, Graphics, and Image Processing devoted to mathematical morphology [27], and the increasing number of articles in technical journals referring to it (for example the tutorial [6]). …”

Section: What Is Mathematical Morphology?mentioning

confidence: 99%

The algebraic basis of mathematical morphology

Ronse

Heijmans²

1991

CVGIP: Image Understanding

132

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Mathematical morphology is a theory of image transformations and functionals deriving its tools from set theory and integral geometry. This paper deals with a general algebraic approach which both reveals the mathematical structure of morphological operations and unifies several examples into one framework. The main assumption is that the object space is a complete lattice and that the transformations of interest are invariant under a given abelian group of automorphisms on that lattice. It turns out that the basic operations called dilation and erosion are adjoints of each other in a very specific lattice sense and can be completely characterized if the automorphism group is assumed to be transitive on a sup-generating subset of the complete lattice. The abstract theory is illustrated by a large variety of examples and applications.

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“…Another set representation off is its umbra [4], [5] point-wise minimum (maximum). By using (l), (5), and the properties of sup/inf, the next results follow easily and establish that, intersection (union) of threshold sets or umbrae corresponds to A (V) of functions:…”

Section: Introductionmentioning

confidence: 99%

A representation theory for morphological image and signal processing

Maragos

1989

IEEE Trans. Pattern Anal. Machine Intell.

204

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Abstract-This paper presents a unifying theory for many concepts and operations encountered in or related to morphological image and signal analysis. This unification requires a set-theoretic melhodology, where signals are modeled as sets, systems (signal transformations) are viewed as set mappings, and translation-invariant systems are uniquely characterized by special collections of input signals. This approach leads to a general representation theory, in which any translation-invariant, increasing, upper semicontinuous system can be represented exactly as a minimal nonlinear superposition of morphological erosions or dilations.In this representation, many similarities and a few differences are observed between systems processing binary or multilevel signals, and continuous-domain or discrete-domain signals.The theory is used to analyze some special cases of image/signal analysis systems, such as morphological filters, median and order-statistic filters, linear filters, and shape recognition transforms.Although the developed theory is algebraic, its prototype operations are well suitable for shape analysis; hence, the results of this study also apply to systems that extract information about the geometrical structure of signals.Zndex Terms--Image/signal processing, mathematical morphology, nonlinear/linear filtering, shape analysis, systems representation.

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Cellular Computers and Biomedical Image Processing

Cited by 39 publications

References 8 publications

Morphological Signal and Image Processing

Morphological Signal and Image Processing

The algebraic basis of mathematical morphology

A representation theory for morphological image and signal processing

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