• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.695-704
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• 2018

In this paper we derive some basic inequalities connecting the Minkowski measure of symmetry, the Minkowski symmetral and the Banach-Mazur distance. We then explore the geometric contents of these inequalities and shed light on the structure of the quotient 𝔅/Aff of the space of convex bodies modulo the affine transformations.

• Journal of Internet Computing and Services
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• v.10 no.4
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• pp.1-11
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• 2009

Recently there has arisen concern in both the database community and the graphics society about data retrieval from large motion databases because the high dimensionality of motion data implies high costs. In this circumstance, finding an effective distance measure and an efficient query processing method for such data is a challenging problem. This paper presents an elaborate motion query processing system, SMoFinder (Similar Motion Finder), which incorporates a novel kinematic distance measure and an efficient indexing strategy via adaptive frame segmentation. To this end, we regard human motions as multi-linkage kinematics and propose the weighted Minkowski distance metric. For efficient indexing, we devise a new adaptive segmentation method that chooses representative frames among similar frames and stores chosen frames instead of all frames. For efficient search, we propose a new search method that processes k-nearest neighbors queries over only representative frames. Our experimental results show that the size of motion databases is reduced greatly (${\times}1/25$) but the search capability of SMoFinder is equal to or superior to that of other systems.

• Journal of Science Education
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• v.47 no.3
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• pp.263-272
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• 2023

We consider how a pre-service teacher can understand and utilize various concepts of Euclidean geometry by learning conic sections using mathematical definitions in non-Euclidean geometry. In a third-grade class of D University, we used mathematical definitions to demonstrate that learning conic sections in non-Euclidean space, such as taxicab geometry and Minkowski distance space, can aid pre-service teachers by enhancing their ability to acquire and accept new geometric concepts. As a result, learning conic sections using mathematical definitions in taxicab geometry and Minkowski distance space is expected to contribute to enhancing the education of pre-service teachers for Euclidean geometry expertise by fostering creative and flexible thinking.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.628-631
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• 1996

This paper proposes a surface recognition algorithm which determines the types of contact surfaces by fusing the information collected by the multisensor system, consisted of the optical tactile and force/torque sensors. Since the image shape measured by the optical tactile sensor system, which is used for determining the surface type, varies depending on the forces provided at the measuring moment, the force information measured by the f/t sensor takes an important role. In this paper, an image contour is represented by the long and short axes and they are fuzzified individually by the membership function formulated by observing the variation of the lengths of the long and short axes depending on the provided force. The fuzzified values of the long and short axes are fused using the average Minkowski's distance. Compared to the case where only the contour information is used, the proposed algorithm has shown about 14% of enhancement in the recognition ratio. Especially, when imposing the optimal force determined by the experiments, the recognition ratio has been measured over 91%.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.659-689
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• 2010

Taxicab distance function is a practical distance notion which gives us information of real world pathway distance that really taxi can go through. As one of the non-Euclidean geometry, this study of an ideal city with all roads running horizontal or vertical, was introduced by the Russian Mathematician H. Minkowski and synthetically reported by the E. F. Kraus in 1986. After that, there were many reports and papers on this topic and still being researched. At this point of view, our research about taxicab geometry provides its differences from Euclidean plane geometry, and considers about several theorems on plane geometry using the taxicab distance function.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.8
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• pp.1272-1277
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• 2017

To assist radiologists for the characterization of breast masses, Computer-aided Diagnosis(CADx) system has been studied. The CADx system can improve the diagnostic accuracy of radiologists by providing objective information about breast masses. Morphological and texture features were extracted from the breast ultrasound images. Based on extracted features, the CADx system retrieves masses that are similar to a query mass from a reference library using a k-nearest neighbor (k-NN) approach. Eight similarity measures of distance, Euclidean, Chebyshev(Minkowski family), Canberra, Lorentzian($F_2$ family), Wave Hedges, Motyka(Intersection family), and Cosine, Dice(Inner Product family) are evaluated by ROC(Receiver Operating Characteristic) analysis. The Inner Product family measure used with the k-NN classifier provided slightly higher performance for classification of malignant and benign masses than those with the Minkowski, $F_2$, and Intersection family measures.

• Journal of the Korean Institute of Intelligent Systems
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• v.8 no.3
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• pp.95-103
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• 1998

This paper deals with a problem occuring in recognition of tactile images due to the effects of imposed force at a me urement moment. Tactile image of a contact surface, used for recognition of the surface type, varies depending on the forces imposed so that a false recognition may result in. This paper fuzzifies two parameters of the contour of a tactile image with the membership function formed by considering the imposed force. Two fuzzifed paramenters are fused by the average Minkowski's dist; lnce. The proposed algorithm was implemented on the multisensor system cnmposed of an optical tact le sensor and a 6 axes forceltorque sensor. By the experiments, the proposed algorithm has shown average recognition ratio greater than 869% over all imposed force ranges and object models which is about 14% enhancement comparing to the case where only the contour information is used. The pro- ~oseda lgorithm can be used for end-effectors manipulating a deformable or fragile objects or for recognition of 3D objects by implementing on multi-fingered robot hand.

• The Bulletin of The Korean Astronomical Society
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• v.43 no.2
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• pp.41.2-41.2
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• 2018

The Minkowski Functionals of the matter densityeld, as traced by galaxies, contain information regarding the nature of dark energy and the fraction of dark matter in the Universe. In particular, the genus is a statistic that provides a clean measurement of the shape of the linear matter power spectrum. As the genus is a topological quantity, it is insensitive to galaxy bias and gravitational collapse. Furthermore, as it traces the linear matter power spectrum, it is a conserved quantity with redshift. Hence the genus amplitude is a standard population that can be used to test the distance-redshift relation. In this talk, I show how we can extract the genus from galaxy catalogs, and how we can use its properties to constrain the equation of state of dark energy and the energy content of the Universe.

• Journal of the Korea Computer Industry Society
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• v.7 no.5
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• pp.537-544
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• 2006

Image Search is one of the most exciting and fast growing research areas in the filed of multimedia technology. This paper conducts an empirical evaluation of color descriptor that uses the information of color distribution in color images, which is the most basic element for image search. With the experimental results, we observe that in the top 10% of precision, HSV, Daubechies 9/7 and 2 level decomposition have little better than others. Also histogram quadratic metrics outperform the Minkowski form distance metrics in similarity measurements, but spend more than 20 in computational times.

• Journal of the Korean earth science society
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• v.40 no.4
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• pp.353-381
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• 2019

The general world model for homogeneous and isotropic universe has been proposed. For this purpose, we introduce a global and fiducial system of reference (world reference frame) constructed on a (4+1)-dimensional space-time, and assume that the universe is spatially a 3-dimensional hypersurface embedded in the 4-dimensional space. The simultaneity for the entire universe has been specified by the global time coordinate. We define the line element as the separation between two neighboring events on the expanding universe that are distinct in space and time, as viewed in the world reference frame. The information that determines the kinematics of the geometry of the universe such as size and expansion rate has been included in the new metric. The Einstein's field equations with the new metric imply that closed, flat, and open universes are filled with positive, zero, and negative energy, respectively. The curvature of the universe is determined by the sign of mean energy density. We have demonstrated that the flat universe is empty and stationary, equivalent to the Minkowski space-time, and that the universe with positive energy density is always spatially closed and finite. In the closed universe, the proper time of a comoving observer does not elapse uniformly as judged in the world reference frame, in which both cosmic expansion and time-varying light speeds cannot exceed the limiting speed of the special relativity. We have also reconstructed cosmic evolution histories of the closed world models that are consistent with recent astronomical observations, and derived useful formulas such as energy-momentum relation of particles, redshift, total energy in the universe, cosmic distance and time scales, and so forth. The notable feature of the spatially closed universe is that the universe started from a non-singular point in the sense that physical quantities have finite values at the initial time as judged in the world reference frame. It has also been shown that the inflation with positive acceleration at the earliest epoch is improbable.