• Proceedings of the IEEK Conference
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• 2006.06a
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• pp.1031-1032
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• 2006

A 3D model based face recognition system is generally inefficient in computation time because 3D face model consists of a large number of vertices. In this paper, we propose a novel 3D face representation algorithm to reduce the number of vertices and optimize its computation time.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.5
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• pp.494-499
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• 1990

A new compact hierarchical representation method image is proposed. This method represents a binary image with the set of decimal numbers. Each decimal number represents the pattern of nonterminal node(gray node) in the quadtree. This pattern implies the combination of its four child nodes. The total number of gray nodes is one third of that terminal nodes. We show that gray tree method is efficient comparing with others which have been studied.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.4
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• pp.238-246
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• 2011

This paper proposes a new semantic representation and its associated similarity measure. The representation expresses textual context observed in a context of a certain term as a network where nodes are terms and edges are the number of cooccurrences between connected terms. To compare terms represented in networks, a graph kernel is adopted as a similarity measure. The proposed representation has two notable merits compared with previous semantic representations. First, it can process polysemous words in a better way than a vector representation. A network of a polysemous term is regarded as a combination of sub-networks that represent senses and the appropriate sub-network is identified by context before compared by the kernel. Second, the representation permits not only words but also senses or contexts to be represented directly from corresponding set of terms. The validity of the representation and its similarity measure is evaluated with two tasks: synonym test and unsupervised word sense disambiguation. The method performed well and could compete with the state-of-the-art unsupervised methods.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.583-592
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• 2017

The paper gives the regularity of dual quaternionic functions and the dual Cauchy-Riemann system in dual quaternions. Also, the paper researches the polar representation and properties of a dual quaternionic function and their regular quaternionic functions.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.2
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• pp.428-431
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• 2007

A floating-point number system is used to represent a wide range of real numbers using finite number of bits. The standard the IEEE adopted in 1987 divides the range of real numbers into intervals of [$2^E,2^{E+1}$), where E is an Integer represented with finite bits, and defines equally spaced equal counts of discrete numbers in each interval. Since the numbers are defined discretely, not only the number representation itself includes errors but in floating-point arithmetic some strange behaviors are observed which cannot be agreed with the real world arithmetic. In this paper errors with floating-point number representation, those with arithmetic operations, and those due to order of arithmetic operations are analyzed theoretically with help of and verification with the results of some MATLAB program executions.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.831-846
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• 2011

There are several methods, in the literature, for finding the fuzzy optimal solution of fully fuzzy transportation problems (transportation problems in which all the parameters are represented by fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, a new method (based on fuzzy linear programming formulation) is proposed to find the fuzzy optimal solution of unbalanced fuzzy transportation problems with a new representation of trapezoidal fuzzy numbers. The advantages of the proposed method over existing method are discussed. Also, it is shown that it is better to use the proposed representation of trapezoidal fuzzy numbers instead of existing representation of trapezoidal fuzzy numbers for finding the fuzzy optimal solution of fuzzy transportation problems. To illustrate the proposed method a fuzzy transportation problem (FTP) is solved by using the proposed method and the obtained results are discussed. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems occurring in real life situations.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.487-498
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• 2007

In this paper, we obtain important combinatorial identities of generalized harmonic numbers using symmetric polynomials. We also obtain the matrix representation for the generalized harmonic numbers whose inverse matrix can be computed recursively.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.7
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• pp.3172-3193
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• 2018

Recently, several studies have shown that linear representation based approaches are very effective and efficient for image classification. One of these linear-representation-based approaches is the Collaborative representation (CR) method. The existing algorithms based on CR have two major problems that degrade their classification performance. First problem arises due to the limited number of available training samples. The large variations, caused by illumintion and expression changes, among query and training samples leads to poor classification performance. Second problem occurs when an image is partially noised (contiguous occlusion), as some part of the given image become corrupt the classification performance also degrades. We aim to extend the collaborative representation framework under limited training samples face recognition problem. Our proposed solution will generate virtual samples and intra-class variations from training data to model the variations effectively between query and training samples. For robust classification, the image patches have been utilized to compute representation to address partial occlusion as it leads to more accurate classification results. The proposed method computes representation based on local regions in the images as opposed to CR, which computes representation based on global solution involving entire images. Furthermore, the proposed solution also integrates the locality structure into CR, using Euclidian distance between the query and training samples. Intuitively, if the query sample can be represented by selecting its nearest neighbours, lie on a same linear subspace then the resulting representation will be more discriminate and accurately classify the query sample. Hence our proposed framework model the limited sample face recognition problem into sufficient training samples problem using virtual samples and intra-class variations, generated from training samples that will result in improved classification accuracy as evident from experimental results. Moreover, it compute representation based on local image patches for robust classification and is expected to greatly increase the classification performance for face recognition task.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.5
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• pp.2346-2362
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• 2016

As one of the most important issues in computer vision and image processing, online object tracking plays a key role in numerous areas of research and in many real applications. In this study, we present a novel tracking method based on the proposed structured sparse representation model, in which the tracked object is assumed to be sparsely represented by a set of object and background templates. The contributions of this work are threefold. First, the structure information of all the candidate samples is utilized by a joint sparse representation model, where the representation coefficients of these candidates are promoted to share the same sparse patterns. This representation model can be effectively solved by the simultaneous orthogonal matching pursuit method. In addition, we develop a tracking algorithm based on the proposed representation model, a discriminative candidate selection scheme, and a simple model updating method. Finally, we conduct numerous experiments on several challenging video clips to evaluate the proposed tracker in comparison with various state-of-the-art tracking algorithms. Both qualitative and quantitative evaluations on a number of challenging video clips show that our tracker achieves better performance than the other state-of-the-art methods.

• Journal of Educational Research in Mathematics
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• v.24 no.4
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• pp.595-605
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• 2014

Infinite decimals have an infinite number of digits, chosen arbitrary and independently, to the right side of the decimal point. Since infinite decimals are ambiguous numbers impossible to write them down completely, the infinite decimal representation accompanies unavoidable opaqueness. This article focused the transparent aspect of infinite decimal representation with respect to the completeness axiom of real numbers. Long before the formalization of real number concept in $19^{th}$ century, many mathematicians were able to deal with real numbers relying on this transparency of infinite decimal representations. This analysis will contribute to overcome the double discontinuity caused by the different conceptualizations of real numbers in school and academic mathematics.