• The Pure and Applied Mathematics
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• v.21 no.4
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• pp.257-270
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• 2014

In this article, we consider a homogeneous function of degree four in quaternionic vector spaces and $S^{4n+3}$ which is invariant under $S^3$ and U(n + 1)-action. We show it is an isoparametric function providing isoparametric hypersurfaces in $S^{4n+3}$ with g = 4 distinct principal curvatures and isoparametric hypersurfaces in quaternionic projective spaces with g = 5. This extends study of Nomizu on isoparametric function on complex vector spaces and complex projective spaces.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.48 no.6
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• pp.115-123
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• 2011

Most of cameras being used in practice induce lens distortion; the amount of distortion depends on the specific applications as well as the camera cost. Up to now, many methods of lens distortion correction have relied on invariant properties of projective geometry to find distortion parameters. A common property is "the straight line in scene is straight line in image". However, if the straight lines are also parallel together, the previous works have missed this restriction in determining lens distortion parameters. In this paper, we propose a method that leads to guarantee of the restrictions simultaneously for the determination. Therefore, corrected image will close to an ideal image taken by the pinhole camera model. The effectiveness of the proposed method is verified by our experiments on both synthetic images and real images.

• Journal of the Korea Society of Computer and Information
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• v.10 no.3 s.35
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• pp.173-182
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• 2005

In this paper, we propose a landmark recognition method which is irrelevant to the camera viewpoint on the navigation for localization. Features in previous research is variable to camera viewpoint, therefore due to the wealth of information, extraction of visual landmarks for positioning is not an easy task. The proposed method in this paper, has the three following stages; first, extraction of features, second, learning and recognition, third, matching. In the feature extraction stage, we set the interest areas of the image. where we extract the corner points. And then, we extract features more accurate and resistant to noise through statistical analysis of a small eigenvalue. In learning and recognition stage, we form robust feature models by testing whether the feature model consisted of five corner points is an invariant feature irrelevant to viewpoint. In the matching stage, we reduce time complexity and find correspondence accurately by matching method using similarity evaluation function and Graham search method. In the experiments, we compare and analyse the proposed method with existing methods by using various indoor images to demonstrate the superiority of the proposed methods.

• The Transactions of the Korea Information Processing Society
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• v.6 no.9
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• pp.2540-2547
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• 1999

Chromakey method is one of key technologies for realizing virtual studio, and the blue portions of a captured image in virtual studio, are replaced with a computer generated or real image. The replaced image must be changed according to the camera parameter of studio for natural merging with the non-blue portions of a captured image. This paper proposes a novel method to extract camera parameters using the recognition of pentagonal patterns that are painted on a blue screen. We extract corresponding points between a blue screen. We extract corresponding points between a blue screen and a captured image using the projective invariant features of a pentagon. Then, calculate camera parameters using corresponding points by the modification of Tsai's method. Experimental results indicate that the proposed method is more accurate compared to conventional method and can process about twelve frames of video per a second in Pentium-MMX processor with CPU clock of 166MHz.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.46 no.4
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• pp.97-107
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• 2009

In image-based gait recognition systems, physical factors, such as the camera angle and the lens distortion, and environmental factors such as illumination determines the performance of recognition. In this paper we present a robust gait recognition method by compensating various types of image distortions. The proposed method is compared with existing gait recognition algorithm with consideration of both physical and environmental distortion factors in the input image. More specifically, we first present an efficient compensation algorithm of image distortion by using the projective transform, and test the feasibility of the proposed algorithm by comparing the recognition performances with and without the compensation process. Proposed method gives universal gait data which is invariant to both distance and environment. Gained data improved gait recognition rate about 41.5% in indoor image and about 55.5% in outdoor image. Proposed method can be used effectively in database(DB) construction, searching and tracking of specific objects.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.43 no.2 s.308
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• pp.11-19
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• 2006

In this paper, we propose a method to estimate camera extrinsic parameter based on projective and permutation invariance point features. Because feature informations in previous research is variant to c.:men viewpoint, extraction of correspondent point is difficult. Therefore, in this paper, we propose the extracting method of invariant point features, and new matching method using similarity evaluation function and Graham search method for reducing time complexity and finding correspondent points accurately. In the calculation of camera extrinsic parameter stage, we also propose two-stage motion parameter estimation method for enhancing convergent degree of LM algorithm. In the experiment, we compare and analyse the proposed method with existing method by using various indoor images to demonstrate the superiority of the proposed algorithms.

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.11-15
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• 1985

Manddelberg [9] has shown that a Clifford algebra of a free quadratic space over an arbitrary semi-local ring R in Brawer-Wall group BW(R) is determined by its rank, determinant, and Hasse invariant. In this paper, we prove a corresponding result when R is a full ring.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 non-degenerate (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)=1/2(.phi.(x+y)-.phi.(x)-.phi.(y)) 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 U9R). 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 $a_{11}$, $a_{22}$] for the space. A commutative ring R having 2 a unit is called full [10] if for every triple $a_{1}$, $a_{2}$, $a_{3}$ of elements in R with ( $a_{1}$, $a_{2}$, $a_{3}$)=R, there is an element w in R such that $a_{1}$+ $a_{2}$w+ $a_{3}$ $w^{2}$=unit.TEX>=unit.t.t.t.