• The Mathematical Education
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• v.48 no.2
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• pp.183-190
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• 2009

This is a following study of the preceding study, Flexibility of mind and divergent thinking in problem solving process that was performed by Choi & Do in 2005. In this paper, we discuss the relationship between ability to shift a viewpoint and insight into invariance, another major consideration in mathematical creativity, in the process of mathematical problem solving.

• Journal of the Korea Society of Computer and Information
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• v.10 no.6 s.38
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• pp.177-186
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• 2005

In this Paper. we propose vision-based camera localization technique using 3D information which is created by mapping of DEM and mountain image. Typically, image features for localization have drawbacks, it is variable to camera viewpoint and after time information quantify increases . In this paper, we extract invariance features of geometry which is irrelevant to camera viewpoint and estimate camera extrinsic Parameter through accurate corresponding Points matching by Proposed similarity evaluation function and Graham search method we also propose 3D information creation method by using graphic theory and visual clues, The Proposed method has the three following stages; point features invariance vector extraction, 3D information creation, camera extrinsic Parameter estimation. In the experiments, we compare and analyse the proposed method with existing methods to demonstrate the superiority of the proposed methods.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.4
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• pp.2075-2092
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• 2017

Person re-identification is to match pedestrians observed from non-overlapping camera views. It has important applications in video surveillance such as person retrieval, person tracking, and activity analysis. However, it is a very challenging problem due to illumination, pose and viewpoint variations between non-overlapping camera views. In this work, we propose a viewpoint invariant method for matching pedestrian images using orientation of pedestrian. First, the proposed method divides a pedestrian image into patches and assigns angle to a patch using the orientation of the pedestrian under the assumption that a person body has the cylindrical shape. The difference between angles are then used to compute the similarity between patches. We applied the proposed method to real-time global multi-object tracking across multiple disjoint cameras with non-overlapping field of views. Re-identification algorithm makes global trajectories by connecting local trajectories obtained by different local trackers. The effectiveness of the viewpoint invariant method for person re-identification was validated on the VIPeR dataset. In addition, we demonstrated the effectiveness of the proposed approach for the inter-camera multiple object tracking on the MCT dataset with ground truth data for local tracking.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1069-1077
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• 2013

Several authors investigated the properties which are invariant under the passage from a group to its nonabelian tensor square. In the present note we study this problem from the viewpoint of the classes of groups and the methods allow us to prove a result of invariance for some geometric properties of discrete groups.

• Journal of Information Technology Services
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• v.9 no.4
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• pp.109-121
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• 2010

Most organizations adopt their own performance measurement systems. Those organizations select performance measures to meet their goals. Organizations can give only limited description of what performance measures are. Kaplan and Norton suggest that the Balanced Scorecard (BSC) to complement the conventional performance measures. The BSC can provide management system with a comprehensive strategic vision and integrates non-financial measures with financial measures. The BSC is widely used for measuring corporate performance. This paper investigates how the BSC-based performance measures can be applied to Learning City. The Learning City's performance measures and strategy map on the basis of the BSC are suggested in this research. This paper adopt the AR(assurance region)-DEA model which could limit the range of weight on performance measures to prevent each viewpoint of BSC from having unlimited elasticity. The proposed model is based on CCR model including a property of unit invariance to use the data without normalization process.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.43 no.2 s.308
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• pp.11-19
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• 2006

In this paper, we propose a method to estimate camera extrinsic parameter based on projective and permutation invariance point features. Because feature informations in previous research is variant to c.:men viewpoint, extraction of correspondent point is difficult. Therefore, in this paper, we propose the extracting method of invariant point features, and new matching method using similarity evaluation function and Graham search method for reducing time complexity and finding correspondent points accurately. In the calculation of camera extrinsic parameter stage, we also propose two-stage motion parameter estimation method for enhancing convergent degree of LM algorithm. In the experiment, we compare and analyse the proposed method with existing method by using various indoor images to demonstrate the superiority of the proposed algorithms.

• Journal of Internet Computing and Services
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• v.6 no.6
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• pp.187-197
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• 2005

In this paper, we propose a method to estimate camera motion parameter based on invariant point features, Typically, feature information of image has drawbacks, it is variable to camera viewpoint, and therefore information quantity increases after time, The LM(Levenberg-Marquardt) method using nonlinear minimum square evaluation for camera extrinsic parameter estimation also has a weak point, which has different iteration number for approaching the minimal point according to the initial values and convergence time increases if the process run into a local minimum, In order to complement these shortfalls, we, first proposed constructing feature models using invariant vector of geometry, Secondly, we proposed a two-stage calculation method to improve accuracy and convergence by using 2D homography and LM method, In the experiment, we compared and analyzed the proposed method with existing method to demonstrate the superiority of the proposed algorithms.

• School Mathematics
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• v.5 no.4
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• pp.421-440
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• 2003

It is difficult for the learner to understand completely the ratio concept which forms a basis of proportional reasoning. And proportional reasoning is, on the one hand, the capstone of children's elementary school arithmetic and, the other hand, it is the cornerstone of all that is to follow. But school mathematics has centered on the teachings of algorithm without dealing with its essence and meaning. The purpose of this study is to analyze the essence of ratio concept from multidimensional viewpoint. In addition, this study will show the direction for improvement of ratio concept. For this purpose, I tried to analyze the historical development of ratio concept. Most mathematicians today consider ratio as fraction and, in effect, identify ratios with what mathematicians called the denominations of ratios. But Euclid did not. In line with Euclid's theory, ratio should not have been represented in the same way as fraction, and proportion should not have been represented as equation, but in line with the other's theory they might be. The two theories of ratios were running alongside each other, but the differences between them were not always clearly stated. Ratio can be interpreted as a function of an ordered pair of numbers or magnitude values. A ratio is a numerical expression of how much there is of one quantity in relation to another quantity. So ratio can be interpreted as a binary vector which differentiates between the absolute aspect of a vector -its size- and the comparative aspect-its slope. Analysis on ratio concept shows that its basic structure implies 'proportionality' and it is formalized through transmission from the understanding of the invariance of internal ratio to the understanding of constancy of external ratio. In the study, a fittingness(or comparison) and a covariation were examined as the intuitive origins of proportion and proportional reasoning. These form the basis of the protoquantitative knowledge. The development of sequences of proportional reasoning was examined. The first attempts at quantifying the relationships are usually additive reasoning. Additive reasoning appears as a precursor to proportional reasoning. Preproportions are followed by logical proportions which refer to the understanding of the logical relationships between the four terms of a proportion. Even though developmental psychologists often speak of proportional reasoning as though it were a global ability, other psychologists insist that the evolution of proportional reasoning is characterized by a gradual increase in local competence.