• The Journal of Korea Robotics Society
• /
• v.18 no.3
• /
• pp.330-336
• /
• 2023

In this paper, a novel line-based simultaneous localization and mapping (SLAM) using a loss function of vanishing point measurements is proposed. In general, the Huber norm is used as a loss function for point and line features in feature-based SLAM. The proposed loss function of vanishing point measurements is based on the unit sphere model. Because the point and line feature measurements define the reprojection error in the image plane as a residual, linear loss functions such as the Huber norm is used. However, the typical loss functions are not suitable for vanishing point measurements with unbounded problems. To tackle this problem, we propose a loss function for vanishing point measurements. The proposed loss function is based on unit sphere model. Finally, we prove the validity of the loss function for vanishing point through experiments on a public dataset.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.6
• /
• pp.1377-1384
• /
• 2019

In this paper, we prove that for every surjective phase-isometry between the unit spheres of real atomic $L_p$-spaces for p > 0, its positive homogeneous extension is a phase-isometry which is phase equivalent to a linear isometry.

• Communications of the Korean Mathematical Society
• /
• v.12 no.4
• /
• pp.905-909
• /
• 1997

A characterization of Hilbert spaces is given in terms of four boundary points and two interior points of the unit sphere.

• Proceedings of the KOSOMBE Conference
• /
• v.1997 no.05
• /
• pp.123-126
• /
• 1997

We present a method for the estimation of 3D solid angle assessment of the acetabular coverage of the femoral head in 3D space. At first, femoral head and acetabulum is segmented from the original CT scan images. The slice thickness is 1.5mm and the number of slices is usually 30-40 to cover the entire acetabulum. The superior half of the femoral head is modeled as part of a sphere. Thus, the axial cross sections of the upper half of the femoral head are also modeled as circles. A set of points from each outline image of femoral head is fitted recursively into a circle by minimizing root-mean-square (RMS) error. With these fitted circles, a center point of the femoral head model is evaluated. This is a reference point for calculating the solid angle of the acetabular inner surface. Next, the tangent lines connecting from a set of points of the acetabular edge to the center of the fitted sphere are obtained. The lines pass through the unit sphere whose center is the same as that of the femoral head. With the points on the unit sphere, we calculate area and estimate the solid angle. Based on this solid angle, the deformity of the acetabulum is analyzed. In case of normal subject, the solid angle is about 4.3 (rad) and acetabular coverage is 68%.

• Honam Mathematical Journal
• /
• v.43 no.1
• /
• pp.88-99
• /
• 2021

The purpose of this paper is to assign a movable frame to an arbitrary point of a rational Bézier curve on the 2-sphere S2 in Euclidean 3-space R3 to provide a better understanding of the geometry of the curve. Especially, we obtain the formula of geodesic curvature for a quadratic rational Bézier curve that allows a curve to be characterized on the surface. Moreover, we give some important results and relations for the Darboux frame and geodesic curvature of a such curve. Then, in specific case, given characterizations for the quadratic rational Bézier curve are illustrated on a unit 2-sphere.

• Journal of the Korean Data and Information Science Society
• /
• v.10 no.1
• /
• pp.19-27
• /
• 1999

An orientation-shift model for unit random vectors in $R^3$ is defined. The Euler angles are introduced to parametrize orientation-shifts and their moment estimators are found. Through the analytic perturbation method, the asymptotic distributions of the estimators are obtained.

• Strategy21
• /
• s.44
• /
• pp.142-176
• /
• 2018

So far, the main threat to South Korea was North Korea. That is why South Korea established a strategy based on the threat of North Korea and most of the budget on defense was used to deter North Korea. Even though the neighboring countries(China, Japan, and Russia) are growing as a real threat with abilities and intentions based on their powerful naval forces, South Korea has not yet been able to establish a strategy that regards neighboring countries as a threat. But the decades-old structural mechanism of the Korean security environment is undergoing a radical change on April 27, 2018, through the South-North summit and the Panmunjom Declaration. Under the changing security environment, South Korea was placed in a complicated dilemma that had to deal with threats of two axes(China), three axes(China, Japan), and four axes(Japan, Russia). If the one axis threat(North Korea) is dominated by land threats, the second, third and fourth axis threats are threats from the sea. This paper analyzed the maritime strategy of Korea within the framework of maritime-geopolitics, in other words recognition and expansion of the sphere of maritime. I have designed that the maritime defense space that we can deny from threats is divided into three lines of defense: 1 line (radius 3,000km), 2 lines (2,000km), and 3 lines (1,000km). The three defense zones of the three lines were defined as an active defense(1 line), defensive offense(2 line), active offense(3 line). The three defense zones of the three lines were defined as the sphere of core maritime, As a power to deny the sphere of core maritime, it was analyzed as a maneuvering unit, a nuclear-powered submarine, the establishment of missile strategy, and the fortification of islands station. The marine strategy of South Korea with these concepts and means was defined as 'Offensive Maritime Denial Strategy'.

• Journal of Information Processing Systems
• /
• v.10 no.1
• /
• pp.23-35
• /
• 2014

Recently, novel application areas in digital geometry processing, such as simulation, dynamics, and medical surgery simulations, have necessitated the representation of not only the surface data but also the interior volume data of a given 3D object. In this paper, we present an efficient framework for the shape approximations of spherical solid objects based on trivariate B-splines. To do this, we first constructed a smooth correspondence between a given object and a unit solid cube by computing their harmonic mapping. We set the unit solid cube as a rectilinear parametric domain for trivariate B-splines and utilized the mapping to approximate the given object with B-splines in a coarse-to-fine manner. Specifically, our framework provides user-controllability of shape approximations, based on the control of the boundary condition of the harmonic parameterization and the level of B-spline fitting. Experimental results showed that our method is efficient enough to compute trivariate B-splines for several models, each of whose topology is identical to a solid sphere.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.15 no.1
• /
• pp.78-88
• /
• 2007

In the present study a detailed examination of various porous media models for predicting filtration efficiency and pressure drop of diesel particulate filter (DPF), such as sphere-in-cell and constricted tube models, are attempted. In order for demonstrating their validities of correct estimation on permeability, geometry of property configurations common in commercial cordierite DPFs are correlated to the porous media flow models, and validations of predicted filtration efficiencies due to the use of different unit collectors are made with experiments. The result shows that the porosity, pore size and permeability of cordierite DPF can be successfully correlated by Kuwabara flow field with correction factor of 0.6. The unit collector efficiency predicted by sphere-in-cell model agrees very well with measurements in accumulation mode, whereas that by constricted tube model with significant prediction error.

• Journal of the Korean Mathematical Society
• /
• v.44 no.2
• /
• pp.373-391
• /
• 2007

We study an (n+3)($n\;{\geq}\;7-dimensional$ real submanifold of a (4m+3)-unit sphere $S^{4m+3}$ with Sasakian 3-structure induced from the canonical quaternionic $K\"{a}hler$ structure of quaternionic (m+1)-number space $Q^{m+1}$, and especially determine contact three CR-submanifolds with (p-1) contact three CR-dimension under the equality conditions given in (4.1), where p = 4m - n denotes the codimension of the submanifold. Also we provide necessary conditions concerning sectional curvature in order that a compact contact three CR-submanifold of (p-1) contact three CR-dimension in $S^{4m+3}$ is the model space $S^{4n_1+3}(r_1){\times}S^{4n_2+3}(r_2)$ for some portion $(n_1,\;n_2)$ of (n-3)/4 and some $r_1,\;r_2$ with $r^{2}_{1}+r^{2}_{2}=1$.