• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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• pp.45-48
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• 2002

Consider the mean distance of Brownian motion on Riemannian manifolds. We obtain the first three terms of the asymptotic expansion of the mean distance by means of Stochastic Differential Equation(SDE) for Brownian motion on Riemannian manifold. This method proves to be much simpler for further expansion than the methods developed by Liao and Zheng(1995). Our expansion gives the same characterizations as the mean exit time from a small geodesic ball with regard to Euclidean space and the rank 1 symmetric spaces.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.37-42
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• 2003

We study the asymptotic expansion in small time of the mean distance of Brownian motion on Riemannian manifolds. We compute the first four terms of the asymptotic expansion of the mean distance by using the decomposition of Laplacian into homogeneous components. This expansion can he expressed in terms of the scalar valued curvature invariants of order 2, 4, 6.

• Journal of Internet Computing and Services
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• v.6 no.1
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• pp.85-93
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• 2005

This paper describes how to distribute high multi-dimensional facial expression data of vast quantity over a suitable space and produce facial expression animations by selecting expressions while animator navigates this space in real-time. We have constructed facial spaces by using about 2400 facial expression frames on this paper. These facial spaces are created by calculating of the shortest distance between two random expressions. The distance between two points In the space of expression, which is manifold space, is described approximately as following; When the linear distance of them is shorter than a decided value, if the two expressions are adjacent after defining the expression state vector of facial status using distance matrix expressing distance between two markers, this will be considered as the shortest distance (manifold distance) of the two expressions. Once the distance of those adjacent expressions was decided, We have taken a Floyd algorithm connecting these adjacent distances to yield the shortest distance of the two expressions. We have used CCA(Curvilinear Component Analysis) technique to visualize multi-dimensional spaces, the form of expressing space, into two dimensions. While the animators navigate this two dimensional spaces, they produce a facial animation by using user interface in real-time.

• Proceedings of the KSME Conference
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• 2001.06d
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• pp.945-949
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• 2001

This study is an experimental study on the characteristics of emission by changing catalytic converter position for cold-start. The measurements are done a changing of the distance between exhaust manifold and catalytic converter. It measured temperature of exhaust manifold, before and after catalytic converter at each position of experimental condition. and measured the characteristics of emission which is HC, CO, $CO_{2}$ and lambda at each position of experimental condition. The results show a few advantage about reduction of HC and CO as catalytic converter's temperature is raised quickly as closed exhaust manifold. but $CO_{2}$ has not the same trend of HC and CO. From measurement value of lambda, reduction effects of $NO_{x}$ are known a few advantage as increase of the distance between exhaust manifold and catalytic converter.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.6 no.1
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• pp.50-56
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• 2007

Exhaust manifold is generally subjected to thermal cycle loadings ; at hot condition, large compressive plastic deformations are generated, and at cold condition, tensile stresses are remained in highly deformed critical zones. These phenomena originate from the fact that thermal expansions of the runners are restricted by inlet flange clamped to the cylinder head, because the former is less stiff than the latter and, the temperature of the inlet flange is lower than that of the runners. Since the failure of an exhaust manifold is mainly caused by geometric constraints between the cylinder head and the manifold, the thermal stress can be controlled by geometric factors. The generic geometric factors include the inter distance (2R), the distance from the head to the outlet (L), the tube diameter(d) and the tube thickness (t). This criteria based on elastic analysis up to onset of yield apparently indicate that the pre-stress also reduces the factor; however, high temperature relaxation may reduce this effect at later operation stage.

• The KIPS Transactions:PartA
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• v.11A no.2
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• pp.189-194
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• 2004

This paper describes method to distribute much high-dimensional facial expression motion data to 2 dimensional space, and method to create facial expression animation by select expressions that want by realtime as animator navigates this space. In this paper composed expression space using about 2400 facial expression frames. The creation of facial space is ended by decision of shortest distance between any two expressions. The expression space as manifold space expresses approximately distance between two points as following. After define expression state vector that express state of each expression using distance matrix which represent distance between any markers, if two expression adjoin, regard this as approximate about shortest distance between two expressions. So, if adjacency distance is decided between adjacency expressions, connect these adjacency distances and yield shortest distance between any two expression states, use Floyd algorithm for this. To materialize expression space that is high-dimensional space, project on 2 dimensions using Sammon's Mapping. Facial animation create by realtime with animators navigating 2 dimensional space using user interface.

• Korean Journal of Computational Design and Engineering
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• v.3 no.1
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• pp.1-14
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• 1998

This paper introduces non-manifold offsetting operations, which add or remove a uniform thickness from a given non-manifold model. Since these operations can be applied to not only solids but also wireframe or sheet objects, they are potentially useful for pipeline modeling, sheet metal and plastic part modeling, tolerance analysis, clearance checking, constant-radius rounding and filleting of solids, converting of abstracted models to solids, HC too1 path generation and so on. This paper describes mathematical properties and algorithms for non-manifold offsetting. In this algorithm, a sufficient set of tentative faces are generated first by offsetting all or a subset of the vertices, edges and faces of the non-manifold model. And then they are merged into a model using the Boolean operations. Finally topological entities which are within offset distance are removed. The partially modified offsetting algorithms for wireframes or sheets are also discussed in order to provide more practical offset models.

• Journal of the Korea Computer Industry Society
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• v.4 no.4
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• pp.569-578
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• 2003

This paper presents a method in which the user produces a real-time facial animation by navigating in the space of facial expressions created from a great number of captured facial expressions. The core of the method is define the distance between each facial expressions and how to distribute into suitable intuitive space using it and user interface to generate realtime facial expression animation in this space. We created the search space from about 2,400 raptured facial expression frames. And, when the user free travels through the space, facial expressions located on the path are displayed in sequence. To visually distribute about 2,400 captured racial expressions in the space, we need to calculate distance between each frames. And we use Floyd's algorithm to get all-pairs shortest path between each frames, then get the manifold distance using it. The distribution of frames in intuitive space apply a multi-dimensional scaling using manifold distance of facial expression frames, and distributed in 2D space. We distributed into intuitive space with keep distance between facial expression frames in the original form. So, The method presented at this paper has large advantage that free navigate and not limited into intuitive space to generate facial expression animation because of always existing the facial expression frames to navigate by user. Also, It is very efficient that confirm and regenerate nth realtime generation using user interface easy to use for facial expression animation user want.

• Journal of KIISE:Software and Applications
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• v.36 no.11
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• pp.960-966
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• 2009

A manifold is used to represent a relationship between high-dimensional data samples in low-dimensional space. In human pose estimation, it is created in low-dimensional space for processing image and 3D body configuration data. Manifold learning is to build a manifold. But it is vulnerable to silhouette variations. Such silhouette variations are occurred due to view-change, person-change, distance-change, and noises. Representing silhouette variations in a single manifold is impossible. In this paper, we focus a silhouette variation problem occurred by view-change. In previous view invariant pose estimation methods based on manifold learning, there were two ways. One is modeling manifolds for all view points. The other is to extract view factors from mapping functions. But these methods do not support one by one mapping for silhouettes and corresponding body configurations because of unsupervised learning. Modeling manifold and extracting view factors are very complex. So we propose a method based on triple manifolds. These are view manifold, pose manifold, and body configuration manifold. In order to build manifolds, we employ biased manifold learning. After building manifolds, we learn mapping functions among spaces (2D image space, pose manifold space, view manifold space, body configuration manifold space, 3D body configuration space). In our experiments, we could estimate various body poses from 24 view points.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.735-740
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• 2015

Tomova [8] gave an upper bound for the distance of a bridge surface for a knot with two different bridge positions in a 3-manifold. In this paper, we show that the result of Tomova [8, Theorem 10.3] can be improved in the case when there are two different bridge spheres for a link in $S^3$.