• 제목/요약/키워드: topological map

검색결과 159건 처리시간 0.028초

TOPOLOGY FIELDS, TOPOLOGICAL FLOWS AND TOPOLOGICAL ORGANISMS

  • Kim, Jae-Ryong
    • 충청수학회지
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    • 제26권1호
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    • pp.53-69
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    • 2013
  • Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a topology on X and regard ${\tau}(X)$ a topological space. A topology ${\tau}$ on X can be regarded a map from X to ${\tau}(X)$ naturally. Such a map will be called topology field. Similarly we can also define pe-topology field. If X is a topological flow group with acting group T, then naturally we can get a another topological flow ${\tau}(X)$ with same acting group T. If the topological flow X is minimal, we can prove ${\tau}(X)$ is also minimal. The disjoint unions of the topological spaces can describe some topological systems (topological organisms). Here we will give a definition of topological organism. Our purpose of this study is to describe some properties concerning patterns of relationship between topology fields and topological organisms.

A METHOD OF IMAGE DATA RETRIEVAL BASED ON SELF-ORGANIZING MAPS

  • Lee, Mal-Rey;Oh, Jong-Chul
    • Journal of applied mathematics & informatics
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    • 제9권2호
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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.

Some Properties of Product Smooth Fuzzy Topological Spaces

  • Park, Jin-Won
    • 한국지능시스템학회논문지
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    • 제9권6호
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    • pp.615-620
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    • 1999
  • We will investigate some properties of product smooth fuzzy topological spaces. We will show that a projection map in product smooth fuzzy topological spaces need not be a fuzzy open map. Furthermore a slice need not be homeomorphic to the coordinate spance which is parallel to it.

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Topological SLAM Based on Voronoi Diagram and Extended Kalman Filter

  • Choi, Chang-Hyuk;Song, Jae-Bok;Kim, Mun-Sang;Chung, Woo-Jin
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 2003년도 ICCAS
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    • pp.174-179
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    • 2003
  • Through the simultaneous localization and map building (SLAM) technique, a robot can create maps about its unknown environment while it continuously localizes its position. Grid maps and feature maps have been widely used for SLAM together with application of probability methods and POMDP (partially observed Markov decision process). But this approach based on grid maps suffers from enormous computational burden. Topological maps, however, have drawn more attention these days because they are compact, provide natural interfaces, and are easily applicable to path planning in comparison with grid maps. Some topological SLAM techniques like GVG (generalized Voronoi diagram) were introduced, but it enables the robot to decide only whether the current position is part of GVG branch or not in the GVG algorithm. In this paper, therefore, to overcome these problems, we present a method for updating a global topological map from the local topological maps. These local topological maps are created through a labeled Voronoi diagram algorithm from the local grid map built based on the sensor information at the current robot position. And the nodes of a local topological map can be utilized as the features of the environment because it is robust in light of visibility problem. The geometric information of the feature is applied to the extended Kalman filter and the SLAM in the indoor environment is accomplished. A series of simulations have been conducted using a two-wheeled mobile robot equipped with a laser scanner. It is shown that the proposed scheme can be applied relatively well.

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위상수학을 활용한 고려 평양부 고지도 분석 (Topological Geometry Education and its Application to the Analysis of the Map of West Capital Pyongyangbu of Old Korea)

  • 정택선;최규홍
    • East Asian mathematical journal
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    • 제34권4호
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    • pp.487-509
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    • 2018
  • We analyse the map of the west capital Pyongyangbu of Old Korea(AD 920) by topological method and geometrical method and compare it with the map of North Korea Pyongyang. By the analyse of the map we find the real place of the old map. The analysing and finding the real place of the old map is a very good example of geometry education. Many Koreans had learned and recognized that Old Korea(AD 920) was a small country located in the south part of Ablok river. But, after reading this paper they change their old recognitions and they take prides in Great Old Korea.

Reduction in Sample Size Using Topological Information for Monte Carlo Localization

  • Yang, Ju-Ho;Song, Jae-Bok;Chung, Woo-Jin
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 2005년도 ICCAS
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    • pp.901-905
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    • 2005
  • Monte Carlo localization is known to be one of the most reliable methods for pose estimation of a mobile robot. Much research has been done to improve performance of MCL so far. 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 estimate because the number of random samples is usually very large especially for a large-scale environment. For practical implementation of the 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 off- line using a thinning method, which is commonly used in image processing, is employed. The topological map is first created from the given grid map for the environment. The robot 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 the same as the one obtained off- line from the given grid map. Random samples are drawn near the off-line topological edge instead of being taken with uniform distribution, since the robot traverses along the edge. In this way, the sample size required for MCL can be drastically reduced, thus leading to reduced initial operation time. 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.

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ON COVERING AND QUOTIENT MAPS FOR 𝓘𝒦-CONVERGENCE IN TOPOLOGICAL SPACES

  • Debajit Hazarika;Ankur Sharmah
    • 대한수학회논문집
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    • 제38권1호
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    • pp.267-280
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    • 2023
  • In this article, we show that the family of all 𝓘𝒦-open subsets in a topological space forms a topology if 𝒦 is a maximal ideal. We introduce the notion of 𝓘𝒦-covering map and investigate some basic properties. The notion of quotient map is studied in the context of 𝓘𝒦-convergence and the relationship between 𝓘𝒦-continuity and 𝓘𝒦-quotient map is established. We show that for a maximal ideal 𝒦, the properties of continuity and preserving 𝓘𝒦-convergence of a function defined on X coincide if and only if X is an 𝓘𝒦-sequential space.

가정환경에서의 분류된 지역정보를 통한 계층적 시맨틱 지도 작성 (Building of a Hierarchical Semantic Map with Classified Area Information in Home Environments)

  • 박중태;송재복
    • 로봇학회논문지
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    • 제7권4호
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    • pp.252-258
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    • 2012
  • This paper describes hierarchical semantic map building using the classified area information in home environments. The hierarchical semantic map consists of a grid, CAIG (Classified Area Information in Grid), and topological map. The grid and CAIG maps are used for navigation and motion selection, respectively. The topological map provides the intuitive information on the environment, which can be used for the communication between robots and users. The proposed semantic map building algorithm can greatly improve the capabilities of a mobile robot in various domains, including localization, path-planning and HRI (Human-Robot Interaction). In the home environment, a door can be used to divide an area into various sections, such as a room, a kitchen, and so on. Therefore, we used not only the grid map of the home environment, but also the door information as a main clue to classify the area and to build the hierarchical semantic map. The proposed method was verified through various experiments and it was found that the algorithm guarantees autonomous map building in the home environment.

A UNIFIED FIXED POINT THEORY OF MULTIMAPS ON TOPOLOGICAL VECTOR SPACES

  • Park, Seh-Ie
    • 대한수학회지
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    • 제35권4호
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    • pp.803-829
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    • 1998
  • We give general fixed point theorems for compact multimaps in the "better" admissible class $B^{K}$ defined on admissible convex subsets (in the sense of Klee) of a topological vector space not necessarily locally convex. Those theorems are used to obtain results for $\Phi$-condensing maps. Our new theorems subsume more than seventy known or possible particular forms, and generalize them in terms of the involving spaces and the multimaps as well. Further topics closely related to our new theorems are discussed and some related problems are given in the last section.n.

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