• Title/Summary/Keyword: normal vector

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The Compression of Normal Vectors to Prevent Visulal Distortion in Shading 3D Mesh Models (3D 메쉬 모델의 쉐이딩 시 시각적 왜곡을 방지하는 법선 벡터 압축에 관한 연구)

  • Mun, Hyun-Sik;Jeong, Chae-Bong;Kim, Jay-Jung
    • Korean Journal of Computational Design and Engineering
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    • v.13 no.1
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    • pp.1-7
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    • 2008
  • Data compression becomes increasingly an important issue for reducing data storage spaces as well as transmis-sion time in network environments. In 3D geometric models, the normal vectors of faces or meshes take a major portion of the data so that the compression of the vectors, which involves the trade off between the distortion of the images and compression ratios, plays a key role in reducing the size of the models. So, raising the compression ratio when the normal vector is compressed and minimizing the visual distortion of shape model's shading after compression are important. According to the recent papers, normal vector compression is useful to heighten com-pression ratio and to improve memory efficiency. But, the study about distortion of shading when the normal vector is compressed is rare relatively. In this paper, new normal vector compression method which is clustering normal vectors and assigning Representative Normal Vector (RNV) to each cluster and using the angular deviation from actual normal vector is proposed. And, using this new method, Visually Undistinguishable Lossy Compression (VULC) algorithm which distortion of shape model's shading by angular deviation of normal vector cannot be identified visually has been developed. And, being applied to the complicated shape models, this algorithm gave a good effectiveness.

SCALED VISUAL CURVATURE AND VISUAL FRENET FRAME FOR SPACE CURVES

  • Jeon, Myungjin
    • Journal of the Chungcheong Mathematical Society
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    • v.34 no.1
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    • pp.37-53
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    • 2021
  • In this paper we define scaled visual curvature and visual Frenet frame that can be visually accepted for discrete space curves. Scaled visual curvature is relatively simple compared to multi-scale visual curvature and easy to control the influence of noise. We adopt scaled minimizing directions of height functions on each neighborhood. Minimizing direction at a point of a curve is a direction that makes the point a local minimum. Minimizing direction can be given by a small noise around the point. To reduce this kind of influence of noise we exmine the direction whether it makes the point minimum in a neighborhood of some size. If this happens we call the direction scaled minimizing direction of C at p ∈ C in a neighborhood Br(p). Normal vector of a space curve is a second derivative of the curve but we characterize the normal vector of a curve by an integration of minimizing directions. Since integration is more robust to noise, we can find more robust definition of discrete normal vector, visual normal vector. On the other hand, the set of minimizing directions span the normal plane in the case of smooth curve. So we can find the tangent vector from minimizing directions. This lead to the definition of visual tangent vector which is orthogonal to the visual normal vector. By the cross product of visual tangent vector and visual normal vector, we can define visual binormal vector and form a Frenet frame. We examine these concepts to some discrete curve with noise and can see that the scaled visual curvature and visual Frenet frame approximate the original geometric invariants.

Comonotonic Uncertain Vector and Its Properties

  • Li, Shengguo;Zhang, Bo;Peng, Jin
    • Industrial Engineering and Management Systems
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    • v.12 no.1
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    • pp.16-22
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    • 2013
  • This paper proposes a new concept of comonotonicity of uncertain vector based on the uncertainty theory. In order to understand the comonotonicity of uncertain vector, some equivalent definitions are presented. Following the proposed concept, some basic properties of comonotonic uncertain vector are investigated. In addition, the operational law is given for calculating the uncertainty distributions of monotone functions of comonotonic uncertain variables. With the help of operational law, the comonotonic uncertain vector is applied to the premium pricing problems. At last, some numerical examples are given to illustrate the application.

Superpixel-based Vehicle Detection using Plane Normal Vector in Dispar ity Space

  • Seo, Jeonghyun;Sohn, Kwanghoon
    • Journal of Korea Multimedia Society
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    • v.19 no.6
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    • pp.1003-1013
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    • 2016
  • This paper proposes a framework of superpixel-based vehicle detection method using plane normal vector in disparity space. We utilize two common factors for detecting vehicles: Hypothesis Generation (HG) and Hypothesis Verification (HV). At the stage of HG, we set the regions of interest (ROI) by estimating the lane, and track them to reduce computational cost of the overall processes. The image is then divided into compact superpixels, each of which is viewed as a plane composed of the normal vector in disparity space. After that, the representative normal vector is computed at a superpixel-level, which alleviates the well-known problems of conventional color-based and depth-based approaches. Based on the assumption that the central-bottom of the input image is always on the navigable region, the road and obstacle candidates are simultaneously extracted by the plane normal vectors obtained from K-means algorithm. At the stage of HV, the separated obstacle candidates are verified by employing HOG and SVM as for a feature and classifying function, respectively. To achieve this, we trained SVM classifier by HOG features of KITTI training dataset. The experimental results demonstrate that the proposed vehicle detection system outperforms the conventional HOG-based methods qualitatively and quantitatively.

Tessellation-independent Approximation of Normal Vectors (Tessellation에 독립적인 법선 벡터 근사에 대한 연구)

  • Ahn, Jaewoo;Kim, Woongsoon
    • Journal of the Korea Computer Graphics Society
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    • v.4 no.2
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    • pp.29-32
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    • 1998
  • When rendering polyhedral models, normal vectors at polygon vertices are necessary for smooth shading. The most commonly used technique of approximating a vertex normal vector by averaging normal vectors of faces around the vertex yields, however, different results on different tessellations Further, continuous deformation of models may cause abrupt discontinuous changes in normal vector directions. In this paper, a variation of the above technique is proposed to avoid these problems. Specifically, it uses a weighted average of normal vectors of faces around the vertex, where the weight of a face being the angular span of the two edges incident on the vertex.

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An Empiricla Bayes Estimation of Multivariate nNormal Mean Vector

  • Kim, Hea-Jung
    • Journal of the Korean Statistical Society
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    • v.15 no.2
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    • pp.97-106
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    • 1986
  • Assume that $X_1, X_2, \cdots, X_N$ are iid p-dimensional normal random vectors ($p \geq 3$) with unknown covariance matrix. The problem of estimating multivariate normal mean vector in an empirical Bayes situation is considered. Empirical Bayes estimators, obtained by Bayes treatmetn of the covariance matrix, are presented. It is shown that the estimators are minimax, each of which domainates teh maximum likelihood estimator (MLE), when the loss is nonsingular quadratic loss. We also derive approximate credibility region for the mean vector that takes advantage of the fact that the MLE is not the best estimator.

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The Gentan Probability, A Model for the Improvement of the Normal Wood Concept and for the Forest Planning

  • Suzuki, Tasiti
    • Journal of Korean Society of Forest Science
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    • v.67 no.1
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    • pp.52-59
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    • 1984
  • A Gentan probability q(j) is the probability that a newly planted forest will be felled at age-class j. A future change in growing stock and yield of the forests can be predicted by means of this probability. On the other hand a state of the forests is described in terms of an n-vector whose components are the areas of each age-class. This vector, called age-class vector, flows in a n-1 dimensional simplex by means of $n{\times}n$ matrices, whose components are the age-class transition probabilities derived from the Gentan probabilities. In the simplex there exists a fixed point, into which an arbitrary forest age vector sinks. Theoretically this point means a normal state of the forest. To each age-class-transition matrix there corresponds a single normal state; this means that there are infinitely many normal states of the forests.

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On the Robustness of Chi-square Test Procedure for a Compounded Multivariate Normal Mean

  • Kim, Hea-Jung
    • Communications for Statistical Applications and Methods
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    • v.2 no.2
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    • pp.330-335
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    • 1995
  • The rebustness of one sample Chi-square test for multivariate normal mean vector is investigated when the multivariate normal population is mixed with another multivariate normal population with differing in the mean vector. Explicit expressions for the level of significance and power of the test are derived. Some numerical results indicate that the Chi-square test procedure is quite robust against slight mixtures of multivariate normal populations differing in location parameters.

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NOTE ON NORMAL EMBEDDING

  • Yi, Seung-Hun
    • Bulletin of the Korean Mathematical Society
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    • v.39 no.2
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    • pp.289-297
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    • 2002
  • It was shown by L. Polterovich ([3]) that if L is a totally real submanifold of a symplectic manifold $(M,\omega)$ and L is parallelizable then L is normal. So we try to find an answer to the question of whether there is a compatible almost complex structure J on the symplectic vector bundle $TM$\mid$_{L}$ such that $TL{\cap}JTL=0$ assuming L is normal and parallelizable. Although we could not reach an answer, we observed that the claim holds at the vector space level. And related to the question, we showed that for a symplectic vector bundle $(M,\omega)$ of rank 2n and $E=E_1{\bigoplus}E_2$, where $E=E_1,E_2$are Lagrangian subbundles of E, there is an almost complex structure J on E compatible with ${\omega}$ and $JE_1=E_2$. And finally we provide a necessary and sufficient condition for a given embedding into a symplectic manifold to be normal.

Real-Time Image-Based Relighting for Tangible Video Teleconference (실감화상통신을 위한 실시간 재조명 기술)

  • Ryu, Sae-Woon;Parka, Jong-Il
    • Journal of Broadcast Engineering
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    • v.14 no.6
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    • pp.807-810
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    • 2009
  • This paper deals with a real-time image based relighting system for tangible video teleconference. The proposed image based relighting system renders the extracted human object using the virtual environmental images. The proposed system can homogenize virtually the lighting environments of remote users on the video teleconference, or render the humans like they are in the virtual places. To realize the video teleconference, the paper obtains the 3D object models of users in real-time using the controlled lighting system. In this paper, we use single color camera and synchronized two directional flash lights. Proposed system generates pure shading images using on and off flash images subtraction. One pure shading reflectance map generates a directional normal map from multiplication of each reflectance map and basic normal vector map. Each directional basic normal map is generated by inner vector calculation of incident light vector and camera viewing vector. And the basic normal vector means a basis component of real surface normal vector. The proposed system enables the users to immerse video teleconference just as they are in the virtual environments.