• Title/Summary/Keyword: mirror symmetry

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The Optimization Method of Symmetrical Building Plan Using Point Group Theory (포인트그룹 이론을 이용한 대칭적 건물 평면형태의 최적대안 결정방안)

  • 진경일
    • Korean Institute of Interior Design Journal
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    • no.38
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    • pp.75-82
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    • 2003
  • The symmetry is general geometric design principal in contemporary architecture shape. But, Symmetry sometimes easily causes unreasonable design. In some reason, two of symmetric units in the apartment, one side of unit have very reasonable plan and arrangement but opposite side unit nay not. For example, if the kitchen on right unit had right-handed arrangement, the symmetrical other would have left-handed kitchen arrangement. In addition to this, if each house unit has the same plan but different direction, each unit has different usage or affects the residents' life pattern. Nevertheless, Architects use only one unit plan to design public housing development by using symmetric operator (mirror, proper rotation, inversion center) at their option. This study suggests that using group theory and mathematical matrix rather than designer's discretion can solve this symmetry problem clearly. And, this study analysis the merits and demerits between each symmetrical pair of unit plan shapes by using mathematical point group theory and matrix.

EFFICIENTLY COMPUTING TORUS CHARTS IN LANDAU-GINZBURG MODELS OF COMPLETE INTERSECTIONS IN GRASSMANNIANS OF PLANES

  • Prince, Thomas
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.5
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    • pp.1719-1724
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    • 2017
  • In this note, companion to the paper [10], we describe an alternative method for finding Laurent polynomials mirror-dual to complete intersections in Grassmannians of planes, in the sense discussed in [10]. This calculation follows a general method for finding torus charts on Hori-Vafa mirrors to complete intersections in toric varieties, detailed in [5] generalising the method of [8].

On-Road Succeeding Vehicle Detection using Characteristic Visual Features (시각적 특징들을 이용한 도로 상의 후방 추종 차량 인식)

  • Adhikari, Shyam Prasad;Cho, Hi-Tek;Yoo, Hyeon-Joong;Yang, Chang-Ju;Kim, Hyong-Suk
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.59 no.3
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    • pp.636-644
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    • 2010
  • A method for the detection of on-road succeeding vehicles using visual characteristic features like horizontal edges, shadow, symmetry and intensity is proposed. The proposed method uses the prominent horizontal edges along with the shadow under the vehicle to generate an initial estimate of the vehicle-road surface contact. Fast symmetry detection, utilizing the edge pixels, is then performed to detect the presence of vertically symmetric object, possibly vehicle, in the region above the initially estimated vehicle-road surface contact. A window defined by the horizontal and the vertical line obtained from above along with local perspective information provides a narrow region for the final search of the vehicle. A bounding box around the vehicle is extracted from the horizontal edges, symmetry histogram and a proposed squared difference of intensity measure. Experiments have been performed on natural traffic scenes obtained from a camera mounted on the side view mirror of a host vehicle demonstrate good and reliable performance of the proposed method.

Posture Symmetry based Motion Capture System for Analysis of Lower -limbs Rehabilitation Training

  • Lee, Seok-Jun;Jung, Soon-Ki
    • Journal of Korea Multimedia Society
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    • v.14 no.12
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    • pp.1517-1527
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    • 2011
  • This paper presents a motion capture based rehabilitation training system for a lower-limb paretic patient. The system evaluates the rehabilitation status of the patient by using the bend posture of the knees and the weight balance of the body. The posture of both legs is captured with a single camera using the planar mirror. The weight distribution is obtained by the Wii Balance Board. Self-occlusion problem in the tracking of the legs is resolved by using k-nearest neighbor based clustering with body symmetry and local-linearity of the posture data. To do this, we present data normalization and its symmetric property in the normalized vector space.

Binary-phase Complex Spatial Light Modulators Driven by Mirror Symmetry

  • Choi, Minho;Choi, Jaewu
    • Current Optics and Photonics
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    • v.5 no.3
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    • pp.261-269
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    • 2021
  • Binary-phase complex spatial light modulators (BP-C-SLMs) are proposed and simulated. This study shows that bottom-top mirror-symmetrical uniaxial systems between two orthogonal polarizers allow one to construct BP-C-SLMs. BP-C-SLMs double the information-handling capacity per pixel, compared to the conventional amplitude-only spatial light modulators (A-SLMs), as well as being simply implemented with a single spatial light modulator (SLM), rather than a combination of an A-SLM and a binary-phase SLMs. Under limited conditions, BP-C-SLMs can control only the amplitude in single-phase space, and act as A-SLMs.

Software development for the visualization of brain fiber tract by using 24-bit color coding in diffusion tensor image

  • Oh, Jung-Su;Song, In-Chan;Ik hwan Cho;Kim, Jong-Hyo;Chang, Kee-Hyun;Park, Kwang-Suk
    • Proceedings of the KSMRM Conference
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    • 2002.11a
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    • pp.133-133
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    • 2002
  • Purpose: The purpose of paper is to implement software to visualize brain fiber tract using a 24-bit color coding scheme and to test its feasibility. Materials and Methods: MR imaging was performed on GE 1.5 T Signa scanner. For diffusion tensor image, we used a single shot spin-echo EPI sequence with 7 non-colinear pulsed-field gradient directions: (x, y, z):(1,1,0),(-1,1,0),(1,0,1),(-1,0,1),(0,1,1),(0,1,-1) and without diffusion gradient. B-factor was 500 sec/$\textrm{mm}^2$. Acquisition parameters are as follows: TUTE=10000ms/99ms, FOV=240mm, matrix=128${\times}$128, slice thickness/gap=6mm/0mm, total slice number=30. Subjects consisted of 10 normal young volunteers (age:21∼26 yrs, 5 men, 5 women). All DTI images were smoothed with Gaussian kernel with the FWHM of 2 pixels. Color coding schemes for visualization of directional information was as follows. HSV(Hue, Saturation, Value) color system is appropriate for assigning RGB(Red, Green, and Blue) value for every different directions because of its volumetric directional expression. Each of HSV are assigned due to (r,$\theta$,${\Phi}$) in spherical coordinate. HSV calculated by this way can be transformed into RGB color system by general HSV to RGB conversion formula. Symmetry schemes: It is natural to code the antipodal direction to be same color(antipodal symmetry). So even with no symmetry scheme, the antipodal symmetry must be included. With no symmetry scheme, we can assign every different colors for every different orientation.(H =${\Phi}$, S=2$\theta$/$\pi$, V=λw, where λw is anisotropy). But that may assign very discontinuous color even between adjacent yokels. On the other hand, Full symmetry or absolute value scheme includes symmetry for 180$^{\circ}$ rotation about xy-plane of color coordinate (rotational symmetry) and for both hemisphere (mirror symmetry). In absolute value scheme, each of RGB value can be expressed as follows. R=λw|Vx|, G=λw|Vy|, B=λw|Vz|, where (Vx, Vy, Vz) is eigenvector corresponding to the largest eigenvalue of diffusion tensor. With applying full symmetry or absolute value scheme, we can get more continuous color coding at the expense of coding same color for symmetric direction. For better visualization of fiber tract directions, Gamma and brightness correction had done. All of these implementations were done on the IDL 5.4 platform.

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ONE-POINTED GRAVITATIONAL GROMOV-WITTEN INVARIANTS FOR GRASSMANNIANS

  • Kim, Bum-Sig
    • Journal of the Korean Mathematical Society
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    • v.38 no.5
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    • pp.1061-1068
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    • 2001
  • We write down explicity a recursive formula of one-pointed gravitational Gromov-Witten invariants and reduce the computation of them to a combinatoric problem which is not solved yet. The one-pointed invariants were played important role in Givental’s program in mirror symmetry. In section 3, we describe the combinatoric problem which can be read independently.

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HYPERBOLICITY OF CHAIN TRANSITIVE SETS WITH LIMIT SHADOWING

  • Fakhari, Abbas;Lee, Seunghee;Tajbakhsh, Khosro
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.5
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    • pp.1259-1267
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    • 2014
  • In this paper we show that any chain transitive set of a diffeomorphism on a compact $C^{\infty}$-manifold which is $C^1$-stably limit shadowable is hyperbolic. Moreover, it is proved that a locally maximal chain transitive set of a $C^1$-generic diffeomorphism is hyperbolic if and only if it is limit shadowable.

Pre-processing Method for Face Recognition Robust to Lightness Variation; Facial Symmetry (조명 변화에 강건한 얼굴 인식의 전처리 기법; 얼굴의 대칭성)

  • Kwon Heak-Bong;Kim Young-Gil;Chang Un-Dong;Song Young-Jun
    • The Journal of the Korea Contents Association
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    • v.4 no.4
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    • pp.163-169
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    • 2004
  • In this paper. we propose a shaded recognition method using symmetric feature. When the existing PCA is applied to shaded face images, the recognition rate is decreased. To improve the recognition rate, we use facial symmetry. If the difference of light and shade is greater than a threshold value, we make a mirror image by replacing the dark side with the bright side symmetrically Then the mirror image is compared with a query image. We compare the performance of the proposed algorithm with the existing algorithms such as PCA, PCA without three eigenfaces and histogram equalization methods. The recognition rate of our method shows $98.889\%$ with the excellent result.

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Design of Two-Dimensional Robust Face Recognition System Realized with the Aid of Facial Symmetry with Illumination Variation (얼굴의 대칭성을 이용하여 조명 변화에 강인한 2차원 얼굴 인식 시스템 설계)

  • Kim, Jong-Bum;Oh, Sung-Kwun
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.64 no.7
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    • pp.1104-1113
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    • 2015
  • In this paper, we propose Two-Dimensional Robust Face Recognition System Realized with the Aid of Facial Symmetry with Illumination Variation. Preprocessing process is carried out to obtain mirror image which means new image rearranged by using difference between light and shade of right and left face based on a vertical axis of original face image. After image preprocessing, high dimensional image data is transformed to low-dimensional feature data through 2-directional and 2-dimensional Principal Component Analysis (2D)2PCA, which is one of dimensional reduction techniques. Polynomial-based Radial Basis Function Neural Network pattern classifier is used for face recognition. While FCM clustering is applied in the hidden layer, connection weights are defined as a linear polynomial function. In addition, the coefficients of linear function are learned through Weighted Least Square Estimation(WLSE). The Structural as well as parametric factors of the proposed classifier are optimized by using Particle Swarm Optimization(PSO). In the experiment, Yale B data is employed in order to confirm the advantage of the proposed methodology designed in the diverse illumination variation