• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.30 no.6_2
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• pp.593-605
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• 2012

LiDAR systems provide dense and accurate topographic information. A pre-requisite to achieving the potential accuracy of LiDAR is having a proper system calibration, which aims at estimating all the systematic errors in the system measurements and the mounting parameters relating the different components. This paper presents a rigorous and two approximate methods for LiDAR system calibration. The rigorous approach makes use of the LiDAR equation and the system raw measurements. The approximate approaches utilize simplified LiDAR equations using some assumptions, which allow for less strict requirements regarding the raw measurements. The first presented approximate method, denoted as quasi-rigorous, assumes that we are dealing with a vertical platform (i.e., small pitch and roll angles). This method requires time-tagged point cloud and trajectory position data. The second approximate method, denoted as simplified, assumes that we are dealing with parallel strips, vertical platform, and minor terrain elevation variations compared to the flying height above ground. Such method can be performed using the LiDAR point cloud only. Experimental results using a real dataset, whose characteristics deviate to some extent from the utilized assumptions in the approximate methods, are presented to provide a comparative analysis of the outcome from the introduced methods.

• Structural Engineering and Mechanics
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• v.30 no.5
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• pp.619-645
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• 2008

This study presents the efficiency of simulating structural systems using a method that combines a simplified component model (SCM) and rigorous component model (RCM). To achieve a realistic simulation of structural systems, a numerical model must be adequately capturing the detailed behaviors of real systems at various scales. However, capturing all details represented within an entire structural system by very fine meshes is practically impossible due to technological limitations on computational engineering. Therefore, this research develops an approach to simulate large-scale structural systems that combines a simplified global model with multiple detailed component models adjusted to various scales. Each correlated multi-scale simulation model is linked to others using a multi-level hierarchical modeling simulation method. Simulations are performed using nonlinear finite element analysis. The proposed method is applied in an analysis of a simple reinforced concrete structure and the Reuipu Elementary School (an existing structure), with analysis results then compared to actual onsite observations. The proposed method obtained results very close to onsite observations, indicating the efficiency of the proposed model in simulating structural system behavior.

• Korean Journal of Geomatics
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• v.3 no.1
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• pp.23-32
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• 2003

Rigorous sensor and dynamic modeling techniques are required if spatial information is to be accurately extracted from video imagery. First, a mathematical model for an uncalibrated video camera and a description of a bundle adjustment with added parameters, for purposes of general block triangulation, is presented. This is followed by the application of invariance-based techniques, with constraints, to derive initial approximations for the camera parameters. Finally, dynamic modeling using the Kalman Filter is discussed. The results of various experiments with real video imagery, which apply the developed techniques, are given.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.6D
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• pp.1025-1032
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• 2006

Sensor modeling of high-resolution satellites is a prerequisite procedure for mapping and GIS applications. Sensor models, describing the geometric relationship between scene and object, are divided into two main categories, which are rigorous and approximate sensor models. A rigorous model is based on the actual geometry of the image formation process, involving internal and external characteristics of the implemented sensor. However, approximate models require neither a comprehensive understanding of imaging geometry nor the internal and external characteristics of the imaging sensor, which has gathered a great interest within photogrammetric communities. This paper described a comparison between rigorous and various approximate sensor models that have been used to determine three-dimensional positions, and proposed the appropriate sensor model in terms of the satellite imagery usage. Through the case study of using IKONOS satellite scenes, rigorous and approximate sensor models have been compared and evaluated for the positional accuracy in terms of acquirable number of ground controls. Bias compensated RFM(Rational Function Model) turned out to be the best among compared approximate sensor models, both modified parallel projection and parallel-perspective model were able to be modelled with a small number of controls. Also affine transformation, one of the approximate sensor models, can be used to determine the planimetric position of high-resolution satellites and perform image registration between scenes.

• Proceedings of the IEEK Conference
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• 2001.06c
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• pp.169-172
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• 2001

In recent years, many studies regarding the modeling of fuzzy system have been conducted. In this paper, a new computational approach to modeling of linguistic fuzzy system is proposed The fuzzy system is modeled as a combination of affine systems, The proposed method can be used in a rigorous stability analysis of fuzzy system including the linguistic fuzzy controller.

• Research in Mathematical Education
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• v.25 no.3
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• pp.201-225
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• 2022

This paper details case study vignettes that focus on enhancing the teaching and learning of geometry and measurement in the elementary grades with attention to pedagogical practices for teaching through problem solving with rigor and centering equitable teaching practices. Rigor is a matter of equity and opportunity (Dana Center, 2019). Rigor matters for each and every student and yet research indicates historically disadvantaged and underserved groups have more of an opportunity gap when it comes to rigorous mathematics instruction (NCTM, 2020). Along with providing a conceptual framework that focuses on the importance of equitable instruction, our study unpacks ways teachers can leverage their deep understanding of geometry and measurement learning trajectories to amplify the mathematics through rigorous problems using multiple approaches including learning by doing, challenged-based and mathematical modeling instruction. Through these vignettes, we provide examples of tasks taught through rigorous problem solving approaches that support conceptual teaching and learning of geometry and measurement. Specifically, each of the three vignettes presented includes a task that was implemented in an elementary classroom and a vertically articulated task that engaged teachers in a professional learning workshop. By beginning with elementary tasks to more sophisticated concepts in higher grades, we demonstrate how vertically articulating a deeper understanding of the learning trajectory in geometric thinking can add to the rigor of the mathematics.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.37 no.2
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• pp.55-62
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• 2019

The stereo geometry establishment based on the precise sensor modeling is prerequisite for accurate stereo data processing. Ground control points are generally required for the accurate sensor modeling though it is not possible over the area where the accessibility is limited or reference data is not available. For the areas, the relative orientation should be carried out to improve the geometric consistency between the stereo data though it does not improve the absolute positional accuracy. The relative orientation requires conjugate points that are well distributed over the entire image region. Therefore the automatic conjugate point extraction is required because the manual operation is labor-intensive. In this study, we applied the method consisting of the key point extraction, the search space minimization based on the epipolar line, and the rigorous outlier detection based on the RPCs (Rational Polynomial Coefficients) bias compensation modeling. We tested different parameters of window sizes for Kompsat-2 across track stereo data and analyzed the RPCs precision after the bias compensation for the cases whether the epipolar line information is used or not. The experimental results showed that matching outliers were inevitable for the different matching parameterization but they were successfully detected and removed with the rigorous method for sub-pixel level of stereo RPCs precision.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.8
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• pp.1165-1173
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• 2003

The effects of (1) phonon dispersion on thermal conductivity model and (2) differentiation of group velocity and phase velocity are examined for germanium. The results show drastic change of thermal conductivity regardless of the same relaxation time model. Also the contribution of transverse acoustic (TA) phonon and longitudinal acoustic (LA) phonon on the thermal conductivity at high temperatures is reassessed by considering more rigorous dispersion model. Holland model, which is commonly used for modeling thermal conductivity, underestimates the scattering rate for TA phonon at high frequency. This leads the conclusion that TA is dominant heat transfer mode at high temperatures. But according to the rigorous consideration of phonon dispersion, the reduction of thermal conductivity is much larger than the estimation of Holland model, thus the TA at high frequency is expected to be no more dominant heat transfer mode. Another heat transfer mechanism may exist at high temperatures. Two possible explanations we the roles of (1) Umklapp scattering of LA phonon at high frequency and (2) optical phonon.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.11 no.6
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• pp.859-867
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• 2000

In order to analyze the effect of a cover layer or radome for an antenna, the moment method is applied to the analysis of the circular microstrip patch antenna with dielectric superstrate fed by coaxial probe. The probe feed is modeled as a attachment mode method which can solve more exact analysis. In case of a ideal probe feed modeling, the probe self-impedance as well as the rapidly-varying patch current at the vicinity of the feed point was neglected. But a rigorous probe feed model which overcomes these deficiencies are developed, and used in the analysis of isolated circular patches. Measurements were performed to validate the numerical results. These are good agreement with each other.

• 한국연소학회:학술대회논문집
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• 2000.12a
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• pp.24-32
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• 2000

A brief introduction is given on the conditional moment closure model for turbulent nonpremixed combustion. It is based on the transport equations derived through a rigorous mathematical procedure for the conditionally averaged quantities and appropriate modeling forms for conditional scalar dissipation rate, conditional mean velocity and reaction rate. Examples are given for prediction of NO and OH in bluffbody flames, soot distribution in jet flames and autoignition of a methane/ethane jet to predict the ignition delay with respect to initial temperature, pressure and fuel composition. Conditional averaging may also be a powerful modeling concept in other approaches involved in turbulent combustion problems in various different regimes.