• Honam Mathematical Journal
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• v.32 no.1
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• pp.53-60
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• 2010

The concept of discrete curvature is a discretization of the curvature. Many literatures introduce discrete curvatures derived from arc length of circular arcs. We propose a new concept of discrete curvature of a polygon at each vertex, which is derived from area of fan shapes. We estimate the error of the discrete curvature and compare the discrete curvature with old one.

• Journal of Korea Multimedia Society
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• v.20 no.12
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• pp.1951-1959
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• 2017

Due to the fact that 3D printing is applied to many areas of life, 3D printing models are often used illegally without any permission from the original providers. This paper presents a novel watermarking algorithm for the copyright protection and ownership identification for 3D printing based on the radius curvature of 3D triangle. 3D triangles are extracted and classified into groups based on radius curvature by the clustering algorithm, and then the mean radius curvature of each group will be computed for watermark embedding. The watermark data is embedded to the groups of 3D triangle by changing the mean radius curvature of each group. In each group, we select a 3D triangle which has the nearest radius curvature with the changed mean radius curvature. Finally, we change the vertices of the selected facet according to the changed radius curvature has been embedded watermark. In experiments, the distance error between the original 3D printing model and the watermarked 3D printing model is approximate zero, and the Bit Error Rate is also very low. From experimental results, we verify that the proposed algorithm is invisible and robustness with geometric attacks rotation, scaling and translation.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.2
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• pp.145-153
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• 2006

An optimal capturing trajectory for a moving object is proposed in this paper based on the observation that a single-curvature path is more accurate than double-or triple-curvature paths. Moving distance, moving time, and trajectory error are major factors considered in deciding an optimal path for capturing the moving object. That is, the moving time and distance are minimized while the trajectory error is maintained as small as possible. The three major factors are compared for the single and the double curvature trajectories to show superiority of the single curvature trajectory. Based upon the single curvature trajectory, a kinematics model of a mobile robot is proposed to follow and capture the moving object, in this paper. A capturing scenario can be summarized as follows: 1. Motion of the moving object has been captured by a CCD camera., 2. Position of the moving object has been estimated using the image frames, and 3. The mobile robot tries to follow the moving object along the single curvature trajectory which matches positions and orientations of the moving object and the mobile robot at the final moment. Effectiveness of the single curvature trajectory modeling and capturing algorithm has been proved, through simulations and real experiments using a 2-DOF wheel-based mobile robot.

• Proceedings of the Korea Concrete Institute Conference
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• 1991.04a
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• pp.81-85
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• 1991

The object of this study is to propose the bending moment-curvature relationships based on the bond properties between concrete and steel for noncraking zone, and evaluate the flexural displacement of reinforced concrete members. The bond-slip relationship and the strain hardening effect of steel were taken into account in order to evaluate the spacing of the cracks and the curvature distribution. Calculated curvature distribution along the longitudinal axis was transformed into equivalent curvature distribution. The flexural displacement was calculated by means of double intergral of the equivalent curvature. Calculated values are in good agreement with the experimental data.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.355-379
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• 2024

In this paper, we establish the curvature estimates for a class of curvature equations with general right hand sides depending on the gradient. We show an existence result by using the continuity method based on a priori estimates. We also derive interior curvature bounds for solutions of a class of curvature equations subject to affine Dirichlet data.

• Proceedings of the IEEK Conference
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• 2000.11d
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• pp.211-214
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• 2000

In this paper, we propose a regular-texture image retrieval approach relating In curvature. Maximum curvature and minimum curvature are computed from the query and each regular-texture image in the database. Seven features are computed from curvature characterizing statistical properties of the corresponding image. Each regular-texture image in the database is then represented as the seven CM (curvature measurement)-features. Query comparison and matching can be done using the corresponding CM-features. Experimental results on Brodatz texture show that the proposed approach is effective.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.461-477
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• 2016

This work considers a particular type of swept surface named canal surfaces in Euclidean 3-space. For such a kind of surfaces, some interesting and important relations about the Gaussian curvature, the mean curvature and the second Gaussian curvature are found. Based on these relations, some canal surfaces are characterized.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.113-125
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• 2019

In this paper, we consider the Ricci curvature of a directed graph, based on Lin-Lu-Yau's definition. We give some properties of the Ricci curvature, including conditions for a directed regular graph to be Ricci-flat. Moreover, we calculate the Ricci curvature of the cartesian product of directed graphs.

• Journal of Auto-vehicle Safety Association
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• v.3 no.2
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• pp.28-33
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• 2011

This paper presents driving path estimation algorithm for adaptive cruise control system and advanced emergency braking system using multi-sensor fusion. Through data collection, yaw rate filtering based road curvature and vision sensor road curvature characteristics are analyzed. Yaw rate filtering based road curvature and vision sensor road curvature are fused into the one curvature by weighting factor which are considering characteristics of each curvature data. The proposed driving path estimation algorithm has been investigated via simulation performed on a vehicle package Carsim and Matlab/Simulink. It has been shown via simulation that the proposed driving path estimation algorithm improves primary target detection rate.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2009.01a
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• pp.482-486
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• 2009

Scale-invariant feature is an effective method for retrieving and classifying images. In this study, we analyze a scale-invariant planar curve features for developing 2D shapes. Scale-space filtering is used to determine contour structures on different scales. However, it is difficult to track significant points on different scales. In mathematics, curvature is considered to be fundamental feature of a planar curve. However, the curvature of a digitized planar curve depends on a scale. Therefore, automatic scale detection for curvature analysis is required for practical use. We propose a technique for achieving automatic scale detection based on difference of curvature. Once the curvature values are normalized with regard to the scale, we can calculate difference in the curvature values for different scales. Further, an appropriate scale and its position are detected simultaneously, thereby avoiding tracking problem. Appropriate scales and their positions can be detected with high accuracy. An advantage of the proposed method is that the detected significant points do not need to be located in the same contour. The validity of the proposed method is confirmed by experimental results.