• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.2
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• pp.141-149
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• 2005

This paper deals with formulations of the energy equilibrium equation by an introduction of the algebraic description, quarternion, which meets conservations of system energy for the equation of motion. Then the equation is discretized to analyze the dynamits analysis of flexible multibody systems in such a way that the work done by the constrained force completely is eliminated. Meanwhile, Rodrigues parameters we used to express the finite rotation lot the proposed method. This method lot the initial essential step to a guarantee of developments of the 3D dynamical problem provides unconditionally stable conditions for the nonlinear problems through the numerical examples.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.12
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• pp.5058-5072
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• 2015

Quaternions have been commonly employed in color image processing, but when the existing pure quaternion representation for color images is used in perceptual hashing, it would degrade the robustness performance since it is sensitive to image manipulations. To improve the robustness in color image perceptual hashing, in this paper a full quaternion representation for color images is proposed by introducing the local image luminance variances. Based on this new representation, a novel Full Quaternion Discrete Cosine Transform (FQDCT)-based hashing is proposed, in which the Quaternion Discrete Cosine Transform (QDCT) is applied to the pseudo-randomly selected regions of the novel full quaternion image to construct two feature matrices. A new hash value in binary is generated from these two matrices. Our experimental results have validated the robustness improvement brought by the proposed full quaternion representation and demonstrated that better performance can be achieved in the proposed FQDCT-based hashing than that in other notable quaternion-based hashing schemes in terms of robustness and discriminability.

• Journal of Advanced Marine Engineering and Technology
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• v.39 no.10
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• pp.1023-1030
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• 2015

The purpose of this paper is to present the basic mathematical modeling of a hexacopter, which could be used to develop proper methods for stabilization and trajectory control. A hexacopter consists of six rotors with three pairs of counter-rotating fixed-pitch blades. This mechanism is an under-actuated, dynamically unstable, six-degrees-of-freedom system. The whole motion of this object consists of translational and rotational motion in three dimensions, where the translational motion is created by changing the direction and magnitude of the upward propeller thrust. The hexacopter is controlled by adjusting the angular velocities of the rotors, which are spun by electric motors. It is assumed to be a rigid body; thus, the differential equation of the hexacopter dynamics can be derived from the Newton-Euler equation. The Euler-angle parametrization of the three-dimensional rotations contains singular points in the coordinate space that can cause failure of both the dynamical model and control. In order to avoid singularities, the rotations of the hexacopter are parametrized in terms of quaternions. This choice has been made considering the linearity of the quaternion formulation and their stability and efficiency. Further, control simulation of a hexacopter applying cascaded-PID control is also presented in this paper.

• Journal of rehabilitation welfare engineering & assistive technology
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• v.7 no.2
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• pp.47-54
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• 2013

In this paper, we present an inertial sensor-based motion capturing system to measure and analyze whole body movements. This system implements a wireless AHRS(attitude heading reference system) we developed using a combination of rate gyroscope, accelerometer and magnetometer sensor signals. Several AHRS modules mounted on segments of the patient's body provide the quaternions representing the patient segments's orientation in space. We performed 3D motion capture using the quaternion data calculated. And a method is also proposed for calculating three-dimensional inter-segment joint angle which is an important bio-mechanical measure for a variety of applications related to rehabilitation. To evaluate the performance of our AHRS module, the Vicon motion capture system, which offers millimeter resolution of 3D spatial displacements and orientations, is used as a reference. The evaluation resulted in a RMSE of 2.56 degree. The results suggest that our system will provide an in-depth insight into the effectiveness, appropriate level of care, and feedback of the rehabilitation process by performing real-time limbs or gait analysis during the post-stroke recovery process.

• Journal of Educational Research in Mathematics
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• v.25 no.2
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• pp.177-188
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• 2015

In this paper, I investigated the historical development process for the product of two vectors in the plane and space, and draw implications for educational guidance to internal and external product of vectors based on it. The results of the historical analysis show that efforts to define the product of the two line segments having different direction in the plane justified the rules of complex algebraic calculations with its length of the product of their lengths and its direction of the sum of their directions. Also, the efforts to define the product of the two line segments having different direction in three dimensional space led to the introduction of quaternion. In addition, It is founded that the inner product and outer product of vectors was derived from the real part and vector part of multiplication of two quaternions. Based on these results, I claimed that we should review the current deployment method of making inner product and outer product as multiplications that are not related to each other, and suggested one approach for connecting the inner and outer product.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.36 no.2
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• pp.43-50
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• 2018

The camera is a key element in image-based three-dimensional positioning, and camera calibration, which properly determines the internal characteristics of such a camera, is a necessary process that must be preceded in order to determine the three-dimensional coordinates of the object. In this study, a new methodology was proposed to determine interior orientation parameters of a camera semi-automatically without being influenced by size and shape of checkerboard for camera calibration. The proposed method consists of exterior orientation parameters estimation using quaternion, recognition of calibration target, and interior orientation parameter determination through bundle block adjustment. After determining the interior orientation parameters using the chessboard calibration target, the three-dimensional position of the small 3D model was determined. In addition, the horizontal and vertical position errors were about ${\pm}0.006m$ and ${\pm}0.007m$, respectively, through the accuracy evaluation using the checkpoints.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.27 no.5
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• pp.555-563
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• 2009

When a mobile mapping system or a robot is equipped with only a GPS (Global Positioning System) and multiple stereo camera system, a transformation from a local camera coordinate system to GPS coordinate system is required to link camera poses and 3D data by V-SLAM (Vision based Simultaneous Localization And Mapping) to GIS data or remove the accumulation error of those camera poses. In order to satisfy the requirements, this paper proposed a novel method that calculates a camera rotation in the GPS coordinate system using the three pairs of camera positions by GPS and V-SLAM, respectively. The propose method is composed of four simple steps; 1) calculate a quaternion for two plane's normal vectors based on each three camera positions to be parallel, 2) transfer the three camera positions by V-SLAM with the calculated quaternion 3) calculate an additional quaternion for mapping the second or third point among the transferred positions to a camera position by GPS, and 4) determine a final quaternion by multiplying the two quaternions. The final quaternion can directly transfer from a local camera coordinate system to the GPS coordinate system. Additionally, an update of the 3D data of captured objects based on view angles from the object to cameras is proposed. This paper demonstrated the proposed method through a simulation and an experiment.

• Journal of rehabilitation welfare engineering & assistive technology
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• v.9 no.2
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• pp.137-144
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• 2015

In this paper, we present an inertial sensor-based gait analysis system to measure and analyze lower-limb movements. We developed an integral AHRS(Attitude Heading Reference System) using a combination of rate gyroscope, accelerometer and magnetometer sensor signals. Several AHRS modules mounted on segments of the patient's body provide the quaternions representing the patient segments's orientation in space. And a method is also proposed for calculating three-dimensional inter-segment joint angle which is an important bio-mechanical measure for a variety of applications related to rehabilitation. To evaluate the performance of our AHRS module, the Vicon motion capture system, which offers millimeter resolution of 3D spatial displacements and orientations, is used as a reference. The evaluation resulted in a RMSE(Root Mean Square Error) of 1.08 and 1.72 degree in yaw and pitch angle. In order to evaluate the performance of our the gait analysis system, we compared the joint angle for the hip, knee and ankle with those provided by Vicon system. The result shows that our system will provide an in-depth insight into the effectiveness, appropriate level of care, and feedback of the rehabilitation process by performing real-time limb or gait analysis during the post-stroke recovery.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.38 no.3
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• pp.175-185
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• 2020

Three-dimensional registration is a process of matching data with or without a coordinate system to a reference coordinate system, which is used in various fields such as the absolute orientation of photogrammetry and data combining for producing precise road maps. Three-dimensional registration is divided into a method using points and a method using linear features. In the case of using points, it is difficult to find the same conjugate point when having different spatial resolutions. On the other hand, the use of linear feature has the advantage that the three-dimensional registration is possible by using not only the case where the spatial resolution is different but also the conjugate linear feature that is not the same starting point and ending point in point cloud type data. In this study, we proposed a method to determine the scale and the three-dimensional translation after determining the three-dimensional rotation angle between two data using quaternion to perform three-dimensional registration using linear features. For the verification of the proposed method, three-dimensional registration was performed using the linear features constructed an indoor and the linear features acquired through the terrestrial mobile mapping system in an outdoor environment. The experimental results showed that the mean square root error was 0.001054m and 0.000936m, respectively, when the scale was fixed and if not fixed, using indoor data. The results of the three-dimensional transformation in the 500m section using outdoor data showed that the mean square root error was 0.09412m when the six linear features were used, and the accuracy for producing precision maps was satisfied. In addition, in the experiment where the number of linear features was changed, it was found that nine linear features were sufficient for high-precision 3D transformation through almost no change in the root mean square error even when nine linear features or more linear features were used.