• 대한전자공학회논문지
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• 제27권9호
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• pp.1448-1455
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• 1990

In this paper, a range image segmentation method is proposed. This method consists of an initial segmentation stage by discontinuous edge detection and surface type labeling based on the sign of the principal curvatures. Initially type labeled image is oversegmented, this image is merged via stepwise optimal region merging stage based on polynomial function approxiamtion. The successful segmentation results are presented for two synthetic range images with noise and a real-world ERIM range image.

• 대한수학회보
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• 제59권3호
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• pp.789-799
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• 2022

We establish a sharp integral inequality related to compact (without boundary) linear Weingarten hypersurfaces (immersed) in a locally symmetric Einstein manifold and we apply it to characterize totally umbilical hypersurfaces and isoparametric hypersurfaces with two distinct principal curvatures, one which is simple, in such an ambient space. Our approach is based on the ideas and techniques introduced by Alías and Meléndez in [4] for the case of hypersurfaces with constant scalar curvature in an Euclidean round sphere.

• Kyungpook Mathematical Journal
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• 제62권3호
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• pp.509-531
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• 2022

In this paper we define a new family of ruled surfaces using an othonormal Sannia frame defined on a base consisting of the striction curve of the tangent, the principal normal, the binormal and the Darboux ruled surface. We examine characterizations of these surfaces by first and second fundamental forms, and mean and Gaussian curvatures. Based on these characterizations, we provide conditions under which these ruled surfaces are developable and minimal. Finally, we present some examples and pictures of each of the corresponding ruled surfaces.

• 한국통신학회논문지
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• 제40권12호
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• pp.2363-2371
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• 2015

본 논문에서는 FAST(Features from Accelerated Segment Test) 특징점 검출기와 SIFT(Scale Invariant Feature Transform) 특징점 서술자(descriptor)를 사용하여 시점 변화에 강인한 특징점 정합 기법을 제안한다. 기존의 FAST 기법은 영상의 에지 부분을 따라서 불필요하게 특징점을 많이 추출하게 되는데 이러한 단점을 주곡률(principal curvatures)을 적용하여 개선한다. 추출된 특징점을 SIFT 서술자를 통해 기술하고 시점이 다른 두 영상으부터 구해진 정합쌍에 RANSAC(RANdom SAmple Consensus) 기법을 통하여 호모그래피(homography)를 계산한다. 시점 변화에 강인한 특징점 정합을 위해서 기준 영상의 특징점들을 호모그래피 변환을 통해 변경된 좌표와 시점이 다른 영상의 특징점 좌표간의 유클리디언(Euclidean) 거리를 통해 정합쌍을 분류한다. 같은 물체나 장소에 대해 시점이 변화된 여러 영상에 대한 실험을 통해서 제안하는 정합 기법이 적은 계산량으로 기존의 특징점 정합 기법보다 우수한 성능을 보여주는 것을 확인하였다.

• 소성∙가공
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• 제13권2호
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• pp.122-128
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• 2004

In order to make a doubly-curved sheet metal effectively, a sheet metal forming process has been developed by adopting the flexibility of the incremental forming process and the principle of bending deformation which causes slight deformation in thickness. The developed process is an unconstrained forming process with no holder. For this study, the experimental equipment is set up with the roll set which consists of two pairs of support rolls and one center roll. In the experiments using aluminum sheets, it is found that the curvature of the formed sheet metal is determined by controlling the distance between supporting rolls in pairs and the forming depth of the center roll and it also depends on the thickness of the sheet metal. In order to check the effect of process parameters on the generation of sheet metal curvatures in this process, the orthogonal array is adopted. From the experimental results, among the process parameters, the distance between supporting rolls in pairs along the direction of one principal radius of curvature as well as the forming depth and the thickness of the material is shown to influence the generation of curvature in the same direction significantly. That is, the other distance between supporting rolls in pairs which are not located in the same direction of one principal radius of curvature, does not have an significant effect on the generation of the curvature in that direction. It mainly affects the generation of curvature in its own direction with the forming depth and the thickness of the material.

• 대한수학회보
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• 제44권3호
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• pp.429-438
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• 2007

In this paper, we study the position vectors of a spacelike W-curve (or a helix), i.e., curve with constant curvatures, with spacelike, timelike and null principal normal in the Minkowski 3-space $\mathbb{E}_1^3$. We give some characterizations for spacelike W - curves whose image lies on the pseudohyperbolical space $\mathbb{H}_0^2$ and Lorentzian sphere $\mathbb{S}_1^2$ by using the positions vectors of the curve.

• 호남수학학술지
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• 제39권4호
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• pp.603-616
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• 2017

In this paper, we give some relations related with a spacelike principal-direction curve and a spacelike binormal-direction curve of a timelike Frenet curve. The Darboux-direction curve and the Darboux-rectifying curve of a timelike Frenet curve in Minkowski 3-space $E^3_1$ are introduced and some characterizations related with these associated curves are given. Later we define the spacelike V-direction curve which is associated with a timelike curve lying on a timelike oriented surface in $E^3_1$ and present some results together with the relationships between the curvatures of this associated curve.

• 한국CDE학회논문집
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• 제6권1호
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• pp.40-47
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• 2001

In reverse engineering, existing products are digitized fur the computer modeling. Using the digitized data, surfaces are modeled for new products. However, in the digitizing process measuring errors or deviations can be happened often in practice. Thus, it is important to adjust such errors or deviations during the computer modeling. To adjust the errors, fairing of the modeled surfaces is performed. In this paper, we present a surface fairing algorithm based on various fairness metrics. Fairness metrics can be discrete. We adopt discrete metrics for fairing given 3D point set. The fairness metrics include discrete principal curvatures. In this paper, automatic fairing process is proposed for fairing given 3D point sets for surfaces. The process uses various fairness criteria so that it is adequate to adopt designers'intents.

• 대한수학회보
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• 제53권3호
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• pp.875-884
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• 2016

Let x : $^{Mn-1}{\rightarrow}{\mathbb{R}}^n$ ($n{\geq}4$) be an umbilical free hyper-surface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and a Laguerre second fundamental form B, which are invariants of x under Laguerre transformation group. We denote the Laguerre scalar curvature by R and the trace-free Laguerre tensor by ${\tilde{L}}:=L-{\frac{1}{n-1}}tr(L)g$. In this paper, we prove a local classification result under the assumption of parallel Laguerre form and an inequality of the type $${\parallel}{\tilde{L}}{\parallel}{\leq}cR$$ where $c={\frac{1}{(n-3){\sqrt{(n-2)(n-1)}}}$ is appropriate real constant, depending on the dimension.

• 대한수학회지
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• 제57권5호
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• pp.1299-1322
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• 2020

We consider closed, star-shaped, admissible hypersurfaces in ℝⁿ⁺¹ expanding along the flow Ẋ = |X|^α-1 F^-β, α ≤ 1, β > 0, and prove that for the case α ≤ 1, β > 0, α + β ≤ 2, this evolution exists for all the time and the evolving hypersurfaces converge smoothly to a round sphere after rescaling. Besides, for the case α ≤ 1, α + β > 2, if furthermore the initial closed hypersurface is strictly convex, then the strict convexity is preserved during the evolution process and the flow blows up at finite time.