Bipolar Fuzzy Spatial Information: Geometry, Morphology, Spatial Reasoning

Bloch, Isabelle

doi:10.1007/978-3-642-14755-5_4

Cited by 8 publications

(5 citation statements)

References 56 publications

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“…This can be considered as an extension to the bipolar case of attention focusing approaches. Illustrations of this idea on the problem of recognition of brain structures from magnetic resonance imaging are presented in [16,18], and the integration of bipolar fuzzy mathematical morphology into descriptions logics for spatial reasoning has been proposed in [63].…”

Section: Resultsmentioning

confidence: 99%

“…Here we assume that this consistency constraint hold. A discussion on how to achieve it can be found in [18].…”

Section: Illustrative Example In the Spatial Domainmentioning

confidence: 99%

“…A direct application of Definition 10 is the computation of the perimeter of a bipolar fuzzy set, defined as a bipolar fuzzy number 4 |∇(μ, ν)| where the cardinality |.| is defined as proposed in [18] 5 :…”

Section: Morphological Gradientmentioning

confidence: 99%

“…In the following, we will detail the case of bipolar fuzzy sets, extending our previous work in [15,16,18,19] to any partial ordering. This case includes the other examples described above: the case of sets corresponds to the case where only bipolarity should be taken into account, without fuzziness (hence the membership function takes only values 0 and 1).…”

Section: Introductionmentioning

confidence: 98%

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Mathematical morphology on bipolar fuzzy sets: general algebraic framework

Bloch

2012

International Journal of Approximate Reasoning

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In many domains of information processing, bipolarity is a core feature to be considered: positive information represents what is possible or preferred, while negative information represents what is forbidden or surely false. If the information is moreover endowed with vagueness and imprecision, as is the case for instance in spatial information processing, then bipolar fuzzy sets constitute an appropriate knowledge representation framework. In this paper, we focus on mathematical morphology as a tool to handle such information and reason on it. Applying mathematical morphology to bipolar fuzzy sets requires defining an appropriate lattice. We extend previous work based on specific partial orderings to any partial ordering leading to a complete lattice. We address the case of algebraic operations and of operations based on a structuring element, and show that they have good properties for any partial ordering, and that they can be useful for processing in particular spatial information, but also other types of bipolar information such as preferences and constraints. Particular cases using Pareto and lexicographic orderings are illustrated. Operations derived from fuzzy bipolar erosion and dilation are proposed as well.

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Section: Resultsmentioning

confidence: 99%

“…Here we assume that this consistency constraint hold. A discussion on how to achieve it can be found in [18].…”

Section: Illustrative Example In the Spatial Domainmentioning

confidence: 99%

Section: Morphological Gradientmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Mathematical morphology on bipolar fuzzy sets: general algebraic framework

Bloch

2012

International Journal of Approximate Reasoning

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“…For the relations “close” and “far,” the second function β dist that evaluates Euclidean distance is used:After iterating over the image two times, each point P ϵ S has an (approximately) optimal reference point Q ϵ R attached and the respective value x of β( P , Q ). In the second stage of the algorithm, this value is mapped onto an acceptability value between 0 and 1 by using the appropriate mapping for the relative directions and distances: f α for direction, f close for nearness, and f far for farnessBloch (2010) describes how to extend the fuzzy spatial framework to include bipolar information. The notion of having a fuzzy set μ: S → [0, 1] is extended to a bipolar fuzzy set, which is a pair of membership functions (μ, v ).…”

Section: How Path Perceives Physical Scenesmentioning

confidence: 99%

Perception and simulation during concept learning.

Weitnauer

Goldstone

Ritter

2023

Psychological Review

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A key component of humans' striking creativity in solving problems is our ability to construct novel descriptions to help us characterize novel concepts. Bongard problems (BPs), which challenge the problem solver to come up with a rule for distinguishing visual scenes that fall into two categories, provide an elegant test of this ability. BPs are challenging for both human and machine category learners because only a handful of example scenes are presented for each category, and they often require the open-ended creation of new descriptions. A new type of BP called physical Bongard problems (PBPs) is introduced, which requires solvers to perceive and predict the physical spatial dynamics implicit in the depicted scenes. The perceiving and testing hypotheses on structures (PATHS) computational model, which can solve many PBPs, is presented and compared to human performance on the same problems. PATHS and humans are similarly affected by the ordering of scenes within a PBP. Spatially or temporally juxtaposing similar (relative to dissimilar) scenes promotes category learning when the scenes belong to different categories but hinders learning when the similar scenes belong to the same category. The core theoretical commitments of PATHS, which we believe to also exemplify open-ended human category learning, are (a) the continual perception of new scene descriptions over the course of category learning; (b) the context-dependent nature of that perceptual process, in which the perceived scenes establish the context for the perception of subsequent scenes; (c) hypothesis construction by combining descriptions into explicit rules; and (d) bidirectional interactions between perceiving new aspects of scenes and constructing hypotheses for the rule that distinguishes categories.

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Introduction

Bloch

Ralescu

2022

Fuzzy Sets Methods in Image Processing and Understanding

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Bipolar Fuzzy Spatial Information: Geometry, Morphology, Spatial Reasoning

Cited by 8 publications

References 56 publications

Mathematical morphology on bipolar fuzzy sets: general algebraic framework

Mathematical morphology on bipolar fuzzy sets: general algebraic framework

Perception and simulation during concept learning.

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