• Journal of KIISE:Software and Applications
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• v.32 no.11
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• pp.1013-1020
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• 2005

This paper presents an effective and robust leaf image retrieval system based on shape feature. Specifically, we propose an improved MPP algorithm for more effective representation of leaf images and show a new dynamic matching algorithm that basically revises the Nearest Neighbor search to reduce the matching time. In particular, both leaf shape and leaf arrangement can be sketched in the query for better accuracy and efficiency. In the experiment, we compare our proposed method with other methods including Centroid Contour Distance(CCD), Fourier Descriptor, Curvature Scale Space Descriptor(CSSD), Moment Invariants, and MPP. Experimental results on one thousand leaf images show that our approach achieves a better performance than other methods.

• 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.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.333-349
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• 2019

The paper study the curvature theory of a line-trajectory of constant Disteli-axis, according to the invariants of the axodes of moving body in spatial motion. A necessary and sufficient condition for a line-trajectory to be a constant Disteli-axis is derived. From which new proofs of the Disteli's formulae and concise explicit expressions of the inflection line congruence are directly obtained. The obtained explicit equations degenerate into a quadratic form, which can easily give a clear insight into the geometric properties of a line-trajectory of constant Disteli-axis with the theory of line congruence. The degenerated cases of the Burmester lines are discussed according to dual points having specific trajectories.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1443-1482
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• 2008

In this paper we define a Myller configuration in a Finsler space and use some special configurations to obtain results about Finsler subspaces. Let $F^{n}$ = (M,F) be a Finsler space, with M a real, differentiable manifold of dimension n. Using the pull back bundle $({\pi}^{*}TM,\tilde{\pi},\widetilde{TM})$ of the tangent bundle $(TM,{\pi},M)$ by the mapping $\tilde{\pi}={\pi}/TM$ and the Cartan Finsler connection of a Finsler space, we obtain an orthonormal frame of sections of ${\pi}^{*}TM$ along a regular curve in $\widetilde{TM}$ and a system of invariants, geometrically associated to the Myller configuration. The fundamental equations are written in a very simple form and we prove a fundamental theorem. Important lines in a Finsler subspace are defined like special lines in a Myller configuration, geometrically associated to the subspace: auto parallels, lines of curvature, asymptotes. Torse forming vector fields with respect to the Cartan Finsler connection are characterized by means of the invariants of the Frenet frame of a versor field along a curve, and the new notion of torse forming vector fields in the sense of Myller is introduced. The particular cases of concurrence and parallelism in the sense of Myller are completely studied, for vector fields from the distribution $T^m$ of the Myller configuration and also from the normal distribution $T^p$.

• Proceedings of the Korean Information Science Society Conference
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• 2006.06d
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• pp.346-348
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• 2006

본 논문은 잎맥 특징을 이용한 식물의 잎 이미지 검색 방법을 제안한다. 식물의 검색을 위해 모양 기반의 검색방법을 사용하였으며, 잎의 외곽선 분만 아니라 내부의 잎맥 정보를 이용하여 정확율을 향상시켰다. 외곽선은 MPP(Minimum Perimeter Polygons) 알고리즘을 개선하여 표현하고, 내부의 잎맥의 특징은 CSS(Curvature Scale Space)를 개선하여 주맥과 교차점, 끝점을 추출하여 표현하였다. 특징 점들간의 관계와 거리값을 통해 가중치가 있는 그래프로 표현하고 이 값을 통해 유사도를 계산하였다. 실험에서는 식물도감에서 1000여개의 식물 잎 이미지를 추출하여 기존의 알고리즘인 Fourier Descriptor, CSSD, CCD, Moment Invariants, MPP와 비교하였다.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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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.

• Structural Engineering and Mechanics
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• v.82 no.1
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• pp.121-131
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• 2022

The main goal of this study is to prepare a program for analyzing High Strength Steel Fibrous Reinforced Concrete (HSSFRC) slabs and predict the response and strength of the slab instead of preparing a prototype and testing it in the laboratory. For this purpose, new equations are proposed to represent the material properties of High Strength Steel Fibrous Reinforced Concrete. The proposed equations obtained from performing regression analysis on many experimental results using statistical programs. The finite element method is adopted for non-linear analysis of the slabs. The eight-node "Serendipity element" (3 DoF) is chosen to represent the concrete. The layered approach is adopted for concrete elements and the steel reinforcement is represented by a smeared layer. The compression properties of the concrete are modeled by a work hardening plasticity approach and the yield condition is determined depending on the first two stress invariants. A tensile strength criterion is adopted in order to estimate the cracks propagation. many experimental results for testing slabs are compared with the numerical results of the present study and a good agreement is achieved regarding load-deflection curves and crack pattern. The response of the load deflection curve is slightly stiff at the beginning because the creep effect is not considered in this study and for assuming perfect bond between the steel reinforcement and the concrete, however, a great agreement is achieved between the ultimate load from the present study and experimental results. For the models of the tension stiffening and cracked shear modulus, the value of Bg and Bt (Where Bg and Bt are the curvature factor for the cracked shear modulus and tension stiffening models respectively) equal to 0.005 give good results compared with experimental result.