• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.793-806
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• 2002

Feature-based similarity retrieval become an important research issue in image database systems. The features of image data are useful to discrimination of images. In this paper, we propose the highspeed k-Nearest Neighbor search algorithm based on Self-Organizing Maps. Self-Organizing Maps (SOM) provides a mapping from high dimensional feature vectors onto a two-dimensional space. The mapping preserves the topology of the feature vectors. The map is called topological feature map. A topological feature map preserves the mutual relations (similarity) in feature spaces of input data. and clusters mutually similar feature vectors in a neighboring nodes. Each node of the topological feature map holds a node vector and similar images that is closest to each node vector. In topological feature map, there are empty nodes in which no image is classified. We experiment on the performance of our algorithm using color feature vectors extracted from images. Promising results have been obtained in experiments.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.85-98
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• 2022

The purpose of this paper is to introduce the notion of Fermatean fuzzy topological space by motivating from the notion of intuitionistic fuzzy topological space, and define Fermatean fuzzy continuity of a function defined between Fermatean fuzzy topological spaces. For this purpose, we define the notions of image and the pre-image of a Fermatean fuzzy subset with respect to a function and we investigate some basic properties of these notions. We also construct the coarsest Fermatean fuzzy topology on a non-empty set X which makes a given function f from X into Y a Fermatean fuzzy continuous where Y is a Fermatean fuzzy topological space. Finally, we introduce the concept of Fermatean fuzzy points and study some types of separation axioms in Fermatean fuzzy topological space.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.18 no.1
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• pp.223-229
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• 2018

This paper proposes a robust technique of image segmentation, which can be obtained if the topological persistence of each connected component is used as the feature vector for the graph-based image segmentation. The topological persistence of the components, which are obtained from the super-level set of the image, is computed from the morse function which is associated with the gray-level or color value of each pixel of the image. The procedure for the components to be born and be merged with the other components is presented in terms of zero-dimensional homology group. Extensive experiments are conducted with a variety of images to show the more correct image segmentation can be obtained by merging the components of small persistence into the adjacent components of large persistence.

• Journal of KIISE
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• v.43 no.7
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• pp.812-819
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• 2016

This paper introduces and analyzes the theoretical basis and method of the conventional initial-value assignment problem and feasibility of image segmentation. The paper presents topological evidence and a method of appropriate initial-value assignment based on topology theory. Subsequently, the paper shows minimum conditions for feasibility of image segmentation based on separation axiom theory of topology and a validation method of effectiveness for image modeling. As a summary, this paper shows image segmentation with its mathematical validity based on topological analysis rather than statistical analysis. Finally, the paper applies the theory and methods to conventional Gaussian random field model and examines effectiveness of GRF modeling.

• Journal of Korea Multimedia Society
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• v.20 no.1
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• pp.10-16
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• 2017

This paper proposes efficient schemes for image segmentation using the region-based active contour model. The developed methods can approach the boundaries of the desired objects by evolving the curves through minimization of the Mumford-Shah energy functionals, given arbitrary curves as initial conditions. Topological changes such as splitting or merging of curves should be handled for the methods to work properly without prior knowledge of the number of objects to be segmented. This paper introduces how to change topological structure of the curves and shows experimental results by applying the methods to the images.

• Journal of KIISE:Databases
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• v.29 no.5
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• pp.358-366
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• 2002

Feature-based similarity retrieval become an important research issue in image database systems. The features of image data are useful to discrimination of images. In this paper, we propose the high speed k-Nearest Neighbor search algorithm based on Self-Organizing Maps. Self-Organizing Maps(SOM) provides a mapping from high dimensional feature vectors onto a two-dimensional space and generates a topological feature map. A topological feature map preserves the mutual relations (similarities) in feature spaces of input data, and clusters mutually similar feature vectors in a neighboring nodes. Therefore each node of the topological feature map holds a node vector and similar images that is closest to each node vector. We implemented a k-NN search for similar image classification as to (1) access to topological feature map, and (2) apply to pruning strategy of high speed search. We experiment on the performance of our algorithm using color feature vectors extracted from images. Promising results have been obtained in experiments.

• Proceedings of the KAIS Fall Conference
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• 2003.11a
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• pp.223-230
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• 2003

Feature-based similarity retrieval has become an important research issue in multimedia database systems. The features of multimedia data are useful for discriminating between multimedia objects (e 'g', documents, images, video, music score, etc.). For example, images are represented by their color histograms, texture vectors, and shape descriptors, and are usually high-dimensional data. The performance of conventional multidimensional data structures(e'g', R- Tree family, K-D-B tree, grid file, TV-tree) tends to deteriorate as the number of dimensions of feature vectors increases. The R＊-tree is the most successful variant of the R-tree. In this paper, we propose a SOM-based R＊-tree as a new indexing method for high-dimensional feature vectors.The SOM-based R＊-tree combines SOM and R＊-tree to achieve search performance more scalable to high dimensionalities. Self-Organizing Maps (SOMs) provide mapping from high-dimensional feature vectors onto a two dimensional space. The mapping preserves the topology of the feature vectors. The map is called a topological of the feature map, and preserves the mutual relationship (similarity) in the feature spaces of input data, clustering mutually similar feature vectors in neighboring nodes. Each node of the topological feature map holds a codebook vector. A best-matching-image-list. (BMIL) holds similar images that are closest to each codebook vector. In a topological feature map, there are empty nodes in which no image is classified. When we build an R＊-tree, we use codebook vectors of topological feature map which eliminates the empty nodes that cause unnecessary disk access and degrade retrieval performance. We experimentally compare the retrieval time cost of a SOM-based R＊-tree with that of an SOM and an R＊-tree using color feature vectors extracted from 40, 000 images. The result show that the SOM-based R＊-tree outperforms both the SOM and R＊-tree due to the reduction of the number of nodes required to build R＊-tree and retrieval time cost.

• The Mathematical Education
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• v.13 no.2
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• pp.29-31
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• 1974

P.Zenor에 의해서 Monotonically Normal space가 정의되었으며 그후 R. Health와 D. Lutzer에 의해서 Linearly ordered topological space가 Monotonically Normal 임을 증명했다. 한편 Zenor는 Monotonically Normal Space의 hereditary에 관한 것을 question으로 남겼는데 Health와 Lutzer가 증명했고 또 그 증명보다 더 간단한 증명을 Calos R. Boyers가 증명했다[3]. 뿐만 아니라 그 결과로서 Linearly ordered topological space와 Elastic space 가 Monotonically Normal space임을 밝혔다. 또 [4]에서 Gary Gruenhage가 Monotonically Normal space가 Elastic space가 안됨을 counterexample을 들어서 증명했다. 결론적으로 Monotonically Normal spare와 Elastic space는 완전히 분리되었다. 또 Elastic space의 closed continuous image는 paracompact이고 Monotonically Normal 임을 증명했다. 이 논문에서는 본인이 밝힌 것은 Monotonically Normal space의 closed continuous image가 Mono tonically Normal임을 밝혔다.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.5
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• pp.450-456
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• 2006

Monte Carlo localization is known to be one of the most reliable methods for pose estimation of a mobile robot. Although MCL is capable of estimating the robot pose even for a completely unknown initial pose in the known environment, it takes considerable time to give an initial pose estimate because the number of random samples is usually very large especially for a large-scale environment. For practical implementation of MCL, therefore, a reduction in sample size is desirable. This paper presents a novel approach to reducing the number of samples used in the particle filter for efficient implementation of MCL. To this end, the topological information generated through the thinning technique, which is commonly used in image processing, is employed. The global topological map is first created from the given grid map for the environment. The robot then scans the local environment using a laser rangefinder and generates a local topological map. The robot then navigates only on this local topological edge, which is likely to be similar to the one obtained off-line from the given grid map. Random samples are drawn near the topological edge instead of being taken with uniform distribution all over the environment, since the robot traverses along the edge. Experimental results using the proposed method show that the number of samples can be reduced considerably, and the time required for robot pose estimation can also be substantially decreased without adverse effects on the performance of MCL.

• The Pure and Applied Mathematics
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• v.30 no.4
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• pp.357-375
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• 2023

In this paper, we introduce the concept of bipolar soft supra topological space and provide a characterization of the related concepts of bipolar soft supra closure and bipolar soft supra interior. We also establish a connection between bipolar soft supra topology and bipolar soft topology. Additionally, we present the concept of bipolar soft supra continuous mapping and examine the concept of bipolar soft supra compact topological space. A related result concerning the image of the bipolar soft supra compact space is proved. Finally, we identify the concepts of disconnected (connected) and strongly disconnected (strongly connected) space and derive several results linking them together. Relationships among these concepts are clarified with the aid of examples.