Metric free nearness measure using description-based neighbourhoods

Preprint versionThe focus of this paper is on a metric free nearness measure for quantifying the descriptive nearness of digital images. Regions of Interest (ROI) play an important role in discerning perceptual similarity within a single image, or between a pair of images. In terms of pixels, closeness between ROIs can be assessed in light of the traditional closeness between points and sets and closeness between sets using topology or proximity theory. A metric free nearness measure is introduced in this paper by finding common patterns among disjoint description based neighbourhoods obtained from these spatially defined sets. The contribution of this article is a metric free nearness measure implemented within the Proximity System, an application used to demonstrate near set concepts using digital images.https://link.springer.com/article/10.1007/s11786-013-0141-

Descriptive Topological Spaces for Performing Visual Search

Accepted versionThis article presents an approach to performing the task of visual search in the context of descriptive topological spaces. The presented algorithm forms the basis of a descriptive visual search system (DVSS) that is based on the guided search model (GSM) that is motivated by human visual search. This model, in turn, consists of the bottom-up and top-down attention models and is implemented within the DVSS in three distinct stages. First, the bottom-up activation process is used to generate saliency maps and to identify salient objects. Second, perceptual objects, defined in the context of descriptive topological spaces, are identified and associated with feature vectors obtained from a VGG deep learning convolutional neural network. Lastly, the top-down activation process makes decisions on whether the object of interest is present in a given image through the use of descriptive patterns within the context of a descriptive topological space. The presented approach is tested with images from the ImageNet ILSVRC2012 and SIMPLIcity datasets. The contribution of this article is a descriptive pattern-based visual search algorithm."This research has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant 418413, and the Faculty of Graduate Studies at the University of Winnipeg."https://link.springer.com/chapter/10.1007/978-3-662-58768-3_

A Descriptive Tolerance Nearness Measure for Performing Graph Comparison

Accepted versionThis article proposes the tolerance nearness measure (TNM) as a computationally reduced alternative to the graph edit distance (GED) for performing graph comparisons. The TNM is defined within the context of near set theory, where the central idea is that determining similarity between sets of disjoint objects is at once intuitive and practically applicable. The TNM between two graphs is produced using the Bron-Kerbosh maximal clique enumeration algorithm. The result is that the TNM approach is less computationally complex than the bipartite-based GED algorithm. The contribution of this paper is the application of TNM to the problem of quantifying the similarity of disjoint graphs and that the maximal clique enumeration-based TNM produces comparable results to the GED when applied to the problem of content-based image processing, which becomes important as the number of nodes in a graph increases."This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant 418413."https://content.iospress.com/articles/fundamenta-informaticae/fi174

Interval Type-2 Beta Fuzzy Near Sets Approach to Content-Based Image Retrieval

In computer-based search systems, similarity plays a key role in replicating the human search process. Indeed, the human search process underlies many natural abilities such as image recovery, language comprehension, decision making, or pattern recognition. The search for images consists of establishing a correspondence between the available image and that sought by the user, by measuring the similarity between the images. Image search by content is generaly based on the similarity of the visual characteristics of the images. The distance function used to evaluate the similarity between images depends notonly on the criteria of the search but also on the representation of the characteristics of the image. This is the main idea of a content-based image retrieval (CBIR) system. In this article, first, we constructed type-2 beta fuzzy membership of descriptor vectors to help manage inaccuracy and uncertainty of characteristics extracted the feature of images. Subsequently, the retrieved images are ranked according to the novel similarity measure, noted type-2 fuzzy nearness measure (IT2FNM). By analogy to Type-2 Fuzzy Logic and motivated by near sets theory, we advanced a new fuzzy similarity measure (FSM) noted interval type-2 fuzzy nearness measure (IT-2 FNM). Then, we proposed three new IT-2 FSMs and we have provided mathematical justification to demonstrate that the proposed FSMs satisfy proximity properties (i.e. reflexivity, transitivity, symmetry, and overlapping). Experimental results generated using three image databases showing consistent and significant results

A geometry of information, I: Nerves, posets and differential forms

The main theme of this workshop (Dagstuhl seminar 04351) is `Spatial Representation: Continuous vs. Discrete'. Spatial representation has two contrasting but interacting aspects (i) representation of spaces' and (ii) representation by spaces. In this paper, we will examine two aspects that are common to both interpretations of the theme, namely nerve constructions and refinement. Representations change, data changes, spaces change. We will examine the possibility of a `differential geometry' of spatial representations of both types, and in the sequel give an algebra of differential forms that has the potential to handle the dynamical aspect of such a geometry. We will discuss briefly a conjectured class of spaces, generalising the Cantor set which would seem ideal as a test-bed for the set of tools we are developing.Comment: 28 pages. A version of this paper appears also on the Dagstuhl seminar portal http://drops.dagstuhl.de/portals/04351