Connections between binary, gray-scale and fuzzy mathematical morphologies

Nachtegael, Mike; Kerre, Etienne

doi:10.1016/s0165-0114(01)00013-6

Cited by 100 publications

(79 citation statements)

References 10 publications

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“…The average (mean) filter [20] smoothes images data, the eliminating noise. Using the gray level values in a square or rectangular window surrounding on each individual pixel, this filter performs spatial filtering.…”

Section: Filtering Techniques 31 Average Filteringmentioning

confidence: 99%

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A Comparative Study of Gaussian Noise Removal Methodologies for Gray Scale Images

Tulin¹

2017

IJCA

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Image filtering is a technique to preserve important signal elements such as edges, smoothing the details of the image to make images appear clear and sharpener. Among all the non linear concepts to suppress Gaussian noise the fuzzy logic based approaches are important as they are capable of reasoning with vague and uncertain information. In this study, have made comparative study with the existing noise reduction methods where the images contaminated with Gaussian noise and found the best result by using fuzzy image filter with the help of fuzzy rules which make use of membership functions. In this article, to perform fuzzy smoothing, fuzzy derivative concept is also applied. This method provides better input for further image processing techniques. It also increases the contrast of the images, fine details and sharpening the edges as well. This comparative study, is made by numerical measures and visual inspection.

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Section: Filtering Techniques 31 Average Filteringmentioning

confidence: 99%

“…Therefore, if two out of three derivative values are small, it is safe to assume that no edge is present in the considered direction. This observation will be taken into account when we formulate the fuzzy rule [20,21] …”

Section: Noise Estimationmentioning

confidence: 99%

A Comparative Study of Gaussian Noise Removal Methodologies for Gray Scale Images

Tulin¹

2017

IJCA

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“…For fuzzy inputs x ∈ [0, 1] n and fuzzy weights w ∈ [0, 1] n , the identity on the left-hand side of the first Equation in 32.5 describes a fuzzy morphological neuron because it corresponds to an operation of dilation in fuzzy mathematical morphology [43,66]. Note that the operation of multiplication represents a special case of fuzzy conjunction.…”

Section: Morphological Neural Networkmentioning

confidence: 99%

“…for some sets X and Y then we speak of a fuzzy erosion, a fuzzy dilation, a fuzzy anti-erosion, or a fuzzy anti-dilation [43,17,66]. The operators of erosion and dilation are often linked in terms of either one of the following relationships of duality: adjunction or negation.…”

Section: The Complete Lattice Framework Of Mathematical Morphologymentioning

confidence: 99%

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Fuzzy Associative Memories and Their Relationship to Mathematical Morphology

Sussner

Valle

2008

Handbook of Granular Computing

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Morphological Associative Memories

Valle

Sussner

Santos

2018

Wiley Encyclopedia of Electrical and Electronics Engineering

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Morphological associative memories (MAMs) belong to the class of morphological neural networks that – in contrast to classical models of artificial neural networks – employ operators of mathematical morphology in order to aggregate the synaptic weights and the incoming signal. The original and most widely known MAM model as well as some recent modifications of this model can be formulated using matrix operation of a lattice algebra called minimax algebra that is closely related to the umbra approach of grayscale mathematical morphology. Fuzzy MAM models execute basic operations of fuzzy mathematical morphology in the recall phase. In this article, we briefly review the aforementioned MAM models and discuss some applications in classification, hyperspectral image analysis, and prediction.

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Connections between binary, gray-scale and fuzzy mathematical morphologies

Cited by 100 publications

References 10 publications

A Comparative Study of Gaussian Noise Removal Methodologies for Gray Scale Images

A Comparative Study of Gaussian Noise Removal Methodologies for Gray Scale Images

Fuzzy Associative Memories and Their Relationship to Mathematical Morphology

Morphological Associative Memories

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