• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.121-126
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• 1985

D.K. Harrison [5] has shown that if R and S are fields of characteristic different from 2, then two Witt rings W(R) and W(S) are isomorphic if and only if W(R)/I(R)$^{3}$ and W(S)/I(S)$^{3}$ are isomorphic where I(R) and I(S) denote the fundamental ideals of W(R) and W(S) respectively. In [1], J.K. Arason and A. Pfister proved a corresponding result when the characteristics of R and S are 2, and, in [9], K.I. Mandelberg proved the result when R and S are commutative semi-local rings having 2 a unit. In this paper, we prove the result when R and S are 2-fold full rings. Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is nondegenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$ (V, R) induced by B is an isomorphism), and with a quadratic mapping .phi.:V.rarw.R such that B(x,y)=(.phi.(x+y)-.phi.(x)-.phi.(y))/2 and .phi.(rx)= $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U(R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$, .., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2, we reserve the notation [ $a_{11}$, $a_{22}$] for the space.the space.e.e.e.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.9
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• pp.3856-3863
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• 2012

A 3D reconstruction technique from stereo images that requires minimal intervention from the user has been developed. The reconstruction problem consists of three steps of estimating specific geometry groups. The first step is estimating the epipolar geometry that exists between the stereo image pairs which includes feature matching in both images. The second is estimating the affine geometry, a process to find a special plane in the projective space by means of vanishing points. The third step, which includes camera self-calibration, is obtaining a metric geometry from which a 3D model of the scene could be obtained. The major advantage of this method is that the stereo images do not need to be calibrated for reconstruction. The results of camera calibration and reconstruction have shown the possibility of obtaining a 3D model directly from features in the images.

• Journal of Korean Society of Transportation
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• v.34 no.3
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• pp.248-262
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• 2016

The study documents the analysis on characters and symbols shown in the pavement markings in the perspective of mathematics educators. The purpose of this study is to propose a pavement marking method that can enhance readability from the driver's eye position. To this end, this study analyzed the figure of the pavement markings that can be actually recognized by the projective geometry perspective. As a result, it proposed alternatives to the current pavement markings by introducing the concept of the compression ratio. Results of the study are as follows. First, the rule was established to obtain the compression ratio. If the observation of two viewing angles are x and y, then the compression ratio S is ${\sin}y/{\cos}\(\frac{x-y}{2}\)$. Second, we presented two alternatives to the pavement marking method for the displayed information. One is a method for improving the pavement markings in terms of the compression ratio, the other is a method by varying vertical length of the pavement markings while holding its width constant. Based on the outcomes from this study, a mathematical analysis can be further studied for the perception of speed according to the types of pavement marking line.

• Journal of Korea Multimedia Society
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• v.9 no.4
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• pp.421-433
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• 2006

This paper proposes a method to insert virtual objects into a real video stream based on feature tracking and camera pose estimation from a set of single-camera video frames. To insert or modify 3D shapes to target video frames, the transformation from the 3D objects to the projection of the objects onto the video frames should be revealed. It is shown that, without a camera calibration process, the 3D reconstruction is possible using multiple images from a single camera under the fixed internal camera parameters. The proposed approach is based on the simplification of the camera matrix of intrinsic parameters and the use of projective geometry. The method is particularly useful for augmented reality applications to insert or modify models to a real video stream. The proposed method is based on a linear parameter estimation approach for the auto-calibration step and it enhances the stability and reduces the execution time. Several experimental results are presented on real-world video streams, demonstrating the usefulness of our method for the augmented reality applications.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.223-234
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• 2003

This note contains the following results for a ring A : (1) A is simple Artinian if and only if A is a prime right YJ-injective, right and left V-ring with a maximal right annihilator ; (2) if A is a left quasi-duo ring with Jacobson radical J such that $_{A}$A/J is p-injective, then the ring A/J is strongly regular ; (3) A is von Neumann regular with non-zero socle if and only if A is a left p.p.ring containing a finitely generated p-injective maximal left ideal satisfying the following condition : if e is an idempotent in A, then eA is a minimal right ideal if and only if Ae is a minimal left ideal ; (4) If A is left non-singular, left YJ-injective such that each maximal left ideal of A is either injective or a two-sided ideal of A, then A is either left self-injective regular or strongly regular : (5) A is left continuous regular if and only if A is right p-injective such that for every cyclic left A-module M, $_{A}$M/Z(M) is projective. ((5) remains valid if 《continuous》 is replaced by 《self-injective》 and 《cyclic》 is replaced by 《finitely generated》. Finally, we have the following two equivalent properties for A to be von Neumann regula. : (a) A is left non-singular such that every finitely generated left ideal is the left annihilator of an element of A and every principal right ideal of A is the right annihilator of an element of A ; (b) Change 《left non-singular》 into 《right non-singular》in (a).(a).

• The KIPS Transactions:PartD
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• v.19D no.2
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• pp.147-150
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• 2012

While LDA is a supervised dimension reduction method which finds projective directions to maximize separability between classes, the performance of LDA is severely degraded when the number of labeled data is small. Recently semi-supervised dimension reduction methods have been proposed which utilize abundant unlabeled data and overcome the shortage of labeled data. However, matrix computation usually used in statistical dimension reduction methods becomes hindrance to make the utilization of a large number of unlabeled data difficult, and moreover too much information from unlabeled data may not so helpful compared to the increase of its processing time. In order to solve these problems, we propose an ensemble approach for semi-supervised dimension reduction. Extensive experimental results in text classification demonstrates the effectiveness of the proposed method.

• Journal of Broadcast Engineering
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• v.11 no.4 s.33
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• pp.495-506
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• 2006

In this paper, we propose a self-calibration of a multi-camera system using factorization techniques for realistic contents generation. The traditional self-calibration algorithms for multi-camera systems have been focused on stereo(-rig) camera systems or multiple camera systems with a fixed configuration. Thus, it is required to exploit them in 3D reconstruction with a mobile multi-camera system and another general applications. For those reasons, we suggest the robust algorithm for general structured multi-camera systems including the algorithm for a plane-structured multi-camera system. In our paper, we explain the theoretical background and practical usages based on a projective factorization and the proposed affine factorization. We show experimental results with simulated data and real images as well. The proposed algorithm can be used for a 3D reconstruction and a mobile Augmented Reality.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.48 no.5
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• pp.13-24
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• 2011

This paper deals with a 3D-pose (orientation and position) estimation problem of a circular object in 3D-space. Circular features can be found with many objects in real world, and provide crucial cues in vision-based object recognition and location. In general, as a circular feature in 3D space is perspectively projected when imaged by a camera, it is difficult to recover fully three-dimensional orientation and position parameters from the projected curve information. This paper therefore proposes a 3D pose estimation method of a circular feature using a coplanar point. We first interpret a circular feature with a coplanar point in both the projective space and 3D space. A procedure for estimating 3D orientation/position parameters is then described. The proposed method is verified by a numerical example, and evaluated by a series of experiments for analyzing accuracy and sensitivity.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.38 no.4
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• pp.381-391
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• 2001

This paper presents an efficient approach to build an image mosaics from image sequences. Unlike general panoramic stitching methods, which usually require some geometrical feature points or solve the iterative nonlinear equations, our algorithm can directly recover the 8-parameter planar perspective transforms. We use four quasi-feature points in order to compute the projective transform between two images. This feature is based on the graylevel distribution and defined in the overlap area between two images. Therefore the proposed algorithm can reduce the total amount of the computation. We also present an algorithm lot efficiently matching the correspondence of the extracted feature. The proposed algorithm is applied to various images to estimate its performance and. the simulation results present that our algorithm can find the correct correspondence and build an image mosaics.

• Journal of Korean Academy of Nursing
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• v.22 no.2
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• pp.143-156
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• 1992

This descriptive study explored the health and illness concepts of preschoolers to provide understanding on which to build research. The subjects were convenience sample three to six year of age attending one art institute in Cheju city. Data were collected through semistructured interviews by author, Children were asked to draw two figures, one healthy and one ill persons. The drawings were not analysed to grasp the meaning as in a projective technique, but only to relate to their response. Data were coded and categorized by content analysis. The results of this study are summarized as follows : 1) Three year olds responded with some unrelated answers but well to questions related to their experiences of illness ; older participants answered questions related health and illness concepts more easily. Generally the levels of subjects' responses did not differ according to age and sex. 2) Preschoolers' answers about the cause, treatment and prevention of illness, and the meaning and promotion of health were coded and then classificated to 9 categories, (food, obedience to authoritys physical function, presence or absence of illness or symptoms, hygiene. treatment, traumatic injury, rest and germs). Food and obeidence to authority categories were most frequent responses the food category was associated with obeidence to authority because it seemed that the children follow the orders of their parents or other authority figures to eat or not to eat something This result was compatible with that of previous studies that preschoolers perceived illness as possible punishment for misbehavior. Participants except for one four year old boy did not suggest that germs cause illness. The children perceived themselves and their families as healthy even though they had symptoms of illness. 3) Preschoolers' health and illness concepts were. influenced by their experiences and related to their development that rules derived from authority and if not complied with, will bring punishment. These oonceptualizations may be the disparity that they perceived themselves and their families as healthy even though they were ill. A previous study by Perrin and Gerrity suggested that the level of children's illness concepts correlated with that of their physical causality and was lower than it. But the levels of health and illness concepts in this sample higher than those of the physical causality.