Distances between fuzzy sets representing grey level images

Löwen, R.; Peeters, Werner

doi:10.1016/s0165-0114(96)00399-5

Cited by 30 publications

(11 citation statements)

References 2 publications

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“…Let U = {u 1 , · · · , u n } be a finite universe of discourse. The following presents three instances of strong similarity measures [16,22,23,24]. …”

Section: Recurrent Exponential Fuzzy Associative Memories Based On Simentioning

confidence: 99%

Generalized Recurrent Exponential Fuzzy Associative Memories Based on Similarity Measures

Souza¹,

Valle²,

Sussner³

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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The recurrent exponential fuzzy associative memory (RE-FAM) can be viewed as a recurrent neural network that employs a fuzzy similarity measure in its hidden layer. This paper introduces the generalized recurrent exponential fuzzy associative memory (GRE-FAM). In contrast to the RE-FAM, the GRE-FAM is equipped with a second hidden layer that is geared to avoiding crosstalk. Apart from theoretical results, this paper includes some computational experiments concerning the reconstruction of corrupted gray-scale images.

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“…Let U = {u 1 , · · · , u n } be a finite universe of discourse. The following presents three instances of strong similarity measures [16,22,23,24]. …”

Section: Recurrent Exponential Fuzzy Associative Memories Based On Simentioning

confidence: 99%

Generalized Recurrent Exponential Fuzzy Associative Memories Based on Similarity Measures

Souza¹,

Valle²,

Sussner³

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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“…It relies on a L p norm between m and n, leading to the following generic definition [32,40,41]: ; (38) d N ðm; nÞ Z sup x2S jmðxÞ K nðxÞj:…”

Section: Comparison Of Membership Functionsmentioning

confidence: 99%

“…[41]. The basic idea is to combine spatial information and membership values by assuming a tolerance value t, indicating the differences that can occur without saying that the objects are no more similar.…”

Section: Combination Of Spatial and Membership Comparisonsmentioning

confidence: 99%

Fuzzy spatial relationships for image processing and interpretation: a review

Bloch

2005

Image and Vision Computing

186

129

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“…Zwick et al (1987) reviews many early proposals of such distances, which they test along with set-theoretic equality indices, for their psychological plausibility. Lowen and Peeters (1998) provide an extensive study of a class of distances between fuzzy sets for which the triangle inequality is not fulfilled.…”

Section: Fuzzy Algebraic Structuresmentioning

confidence: 99%

Fuzzy Sets: History and Basic Notions

Dubois¹,

Ostasiewicz

Prade³

2000

The Handbooks of Fuzzy Sets Series

139

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Abstract. This paper is an introduction to fuzzy set theory. It has several purposes. First, it tries to explain the emergence of fuzzy sets from an historical perspective. Looking back to the history of sciences, it seems that fuzzy sets were bound to appear at some point in the 20th century. Indeed, Zadeh's works have cristalized and popularized a concern that has appeared in the first half of the century, mainly in philosophical circles. Another purpose of the paper is to scan the basic definitions in the field, that are required for a proper reading of the rest of the volume, as well as the other volumes of the Handbooks of Fuzzy Sets Series. This Chapter also contains a discussion on operational semantics of the generally too abstract notion of membership function. Lastly, a survey of variants of fuzzy sets and related matters is provided.

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Distances between fuzzy sets representing grey level images

Cited by 30 publications

References 2 publications

Generalized Recurrent Exponential Fuzzy Associative Memories Based on Similarity Measures

Generalized Recurrent Exponential Fuzzy Associative Memories Based on Similarity Measures

Fuzzy spatial relationships for image processing and interpretation: a review

Fuzzy Sets: History and Basic Notions

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