Sufficiently Near Sets of Neighbourhoods

Peters, James F.

doi:10.1007/978-3-642-24425-4_4

Cited by 10 publications

(5 citation statements)

References 9 publications

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“…The approach to CBIR in this paper, however, is tolerance space-based that is directly related to recent work on near neighbourhoods (Peters, 2011;Peters and Borkowski, 2011), tolerance near sets (Pal et al, 2010), perception-based computing (Skowron and Wasilewski, 2010; and the topology of digital images (Peters and Naimpally, 2011;Peters and Tiwari, 2011;Naimpally and Peters, 2012). The key concept in a tolerance space-based approach is the limitation of the human visual perception in differentiating between visual stimuli that are different but close to each other within a tolerable level of error.…”

Section: Introduction and Related Workmentioning

confidence: 97%

Perceptual tolerance neighborhood‐based similarity in content‐based image retrieval and classification

Meghdadi

Peters

2012

International Journal of Intelligent Computing and Cybernetics

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Purpose -The purpose of this paper is to demonstrate the effectiveness and advantages of using perceptual tolerance neighbourhoods in tolerance space-based image similarity measures and its application in content-based image classification and retrieval. Design/methodology/approach -The proposed method in this paper is based on a set-theoretic approach, where an image is viewed as a set of local visual elements. The method also includes a tolerance relation that detects the similarity between pairs of elements, if the difference between corresponding feature vectors is less than a threshold 2 (0,1). Findings -It is shown that tolerance space-based methods can be successfully used in a complete content-based image retrieval (CBIR) system. Also, it is shown that perceptual tolerance neighbourhoods can replace tolerance classes in CBIR, resulting in more accuracy and less computations. Originality/value -The main contribution of this paper is the introduction of perceptual tolerance neighbourhoods instead of tolerance classes in a new form of the Henry-Peters tolerance-based nearness measure (tNM) and a new neighbourhood-based tolerance-covering nearness measure (tcNM). Moreover, this paper presents a side -by -side comparison of the tolerance space based methods with other published methods on a test dataset of images.

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Section: Introduction and Related Workmentioning

confidence: 97%

Perceptual tolerance neighborhood‐based similarity in content‐based image retrieval and classification

Meghdadi

Peters

2012

International Journal of Intelligent Computing and Cybernetics

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“…This section introduces an application of local admissible covers in a descriptive EF-space, stemming from a recent study of applications of near sets in proximity spaces [25,19] and a number of studies of nearness in digital images [11,12,9,13,10,21,22,23].…”

Section: Descriptive Admissible Covers In Micropalaeontologymentioning

confidence: 99%

“…The motivation for this approach stems from the need to consider fine-grained neighbourhoods of points in admissible covers that facilitate highly accurate measures of nearness of tiny parts of sets of objects of interest. The study of descriptively near sets in admissible covers stems from recent work on near sets (see, e.g., [24,19,10,25,21,22,8,26,23,28,30,6,16,27]). …”

Section: Introductionmentioning

confidence: 99%

Nearness of Sets in Local Admissible Covers. Theory and Application in Micropalaeontology

Peters

2013

Fundamenta Informaticae

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This paper considers the nearness of sets in local descriptive admissible covers of nonempty sets and the problem of quantifying the nearness of such sets. A brief review of descriptive Efremovič spaces as well descriptive intersection and union provides a foundation for the study of descriptive admissible covers. Descriptively near sets in admissible covers contain sequences of points with members having similar descriptions. The motivation for this approach stems from the need to consider fine-grained neighbourhoods of points in admissible covers that facilitate highly accurate measures of nearness of tiny parts of sets of objects of interest. A practical application of local admissible covers is given in terms of micropalaeontology and the detection of minute similarities and differences in microfossils, useful in the study of climate change, mineral and fossil fuel exploration.

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“…Kuroki and Wang [9] gave some properties of the lower and upper approximations with respect to normal subgroups, and Davvaz [2], introduced the notion of rough subring (respectively ideal) with respect to an ideal of a ring. In recent years, there has been a fast growing interest in this new emerging theory, ranging from work in pure theory such as topological and algebraic foundations [3,4,15,26,24,25,11,19,20] and [21], to diverse areas of applications [5,6].…”

Section: Introductionmentioning

confidence: 99%

“…The concept of near set theory was motivated by image analysis and inspired by a study of the perception of the nearness of familiar physical objects was carried out in cooperation with Pawlak in a purely philosophical manner in a poem entitled "How Near" written in 2002 and published in 2007 [14]. More recent work considers a generalized approach theory in the study of the nearness of nonempty sets that resemble each other [20,21] and a topological framework for the study of nearness and apartness of sets (see, e.g., [11,19]).…”

Section: Introductionmentioning

confidence: 99%