Morphological expressions for DTCNN functions

Brugge, M.H. ter; Krol, R.J.; Nijhuis, J.A.G.; Spaanenburg, Lambert

doi:10.1109/icnn.1996.548989

Cited by 3 publications

(5 citation statements)

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“…A DT-CNN is equivalent to a function of two variables in the morphological domain, if the input-output behavior of and is identical, i.e., if a certain image is applied to the input of and the output of is initialized by , then the output after iterations is equivalent to . Formally, this equivalence relation is defined by (8) where denotes the input of and the output at time as defined in (1) and (2). Notice the relation between the arguments of and the conceptual inputs of .…”

Section: The Dt-cnn Equivalence Of Morphologymentioning

confidence: 99%

“…The first argument of is associated with the input , while the second argument is associated with the initial output . To exemplify the functional equivalence relation, we will show that the morphological function is equivalent to the DT-CNN defined by (9) According to (8) this is proved by showing for each pair of images that if is initialized by an image and by , then after execution the output of corresponds to the image , or equivalently . Using (7), this is equivalent to showing for each :…”

Section: The Dt-cnn Equivalence Of Morphologymentioning

confidence: 99%

“…Formula (8) defines the equivalence between a binary morphological function and a DT-CNN. A unary function is implemented by either a DT-CNN with zero feedback or a DT-CNN with zero control.…”

Section: The Dt-cnn Equivalence Of Morphologymentioning

confidence: 99%

“…Similarly, the variable corresponds to the initial output . The correctness of each of the presented templates can be proved by (8), (12), or (13). As a representative example, we will do this for the function .…”

Section: The Dt-cnn Equivalence Of Morphologymentioning

confidence: 99%

“…The usage of these templates is demonstrated by solving a bank-note recognition problem. In [8]- [10], generic templates are given for a large number of elementary and compound operations. Instead of presenting them as solutions to dedicated image processing tasks, the templates are introduced as part of the translation scheme that maps general morphological expressions to efficient DT-CNN implementations.…”

Section: Introductionmentioning

confidence: 99%

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Transformational DT-CNN design from morphological specifications

Brugge

Nijhuis

Spaanenburg

1998

IEEE Trans. Circuits Syst. I

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Morphology provides the algebraic means to specify operations on images. Discrete-time cellular neural networks (DT-CNN's) mechanize the execution of operations on images. The paper first shows the equivalence between morphological functions and DT-CNN's. Then, the argument is extended to the synthesis of optimal DT-CNN structures from complex morphological expressions. It is shown that morphological specifications may be freely derived, to be subsequently transformed and adopted to the needs of a specific target technology. This process of technology mapping can be automated along the well-trodden path in CAD for microelectronics.

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Section: The Dt-cnn Equivalence Of Morphologymentioning

confidence: 99%

Section: The Dt-cnn Equivalence Of Morphologymentioning

confidence: 99%

Section: The Dt-cnn Equivalence Of Morphologymentioning

confidence: 99%