• Proceedings of the IEEK Conference
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• 1999.06a
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• pp.639-642
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• 1999

There exist geometrically invariant relations in single-view images under a specific geometrical structure. This invariance may be utilized for 3D object recognition. Two types of invariants are compared in terms of the robustness to the variation of the feature points. Deviation of the invariant relations are measured by adding random noise to the feature point location. Zhu’s invariant requires six points on adjacent planes having two sets of four coplanar points, whereas the Kaist method requires four coplanar points and two non-coplanar points. Experimental results show that the latter method has the advantage in choosing feature points while suffering from weak robustness to the noise.

• East Asian mathematical journal
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• v.37 no.4
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• pp.355-379
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• 2021

In this article, we investigated plane figures introduced in elementary school mathematics in the perspective of traditional classification, and also analyzed plane figures focused on the invariance of plane figures out of traditional classification. In the view of traditional classification, how to treat trapezoids was a key argument. In the current mathematics curriculum of the elementary school mathematics, the concept of sliding, flipping, and turning are introduced as part of development activities of spatial sense, but it is rare to apply them directly to figures. For example, how are squares and rectangles different in terms of symmetry? One of the main purposes of geometry learning is the classification of figures. Thus, the activity of classifying plane figures from a symmetrical point of view has sufficiently educational significance from Klein's point of view.

• Proceedings of the Korean Information Science Society Conference
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• 2011.06c
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• pp.429-432
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• 2011

Recognizing human activities from image sequences is an active area of research in computer vision. Most of the previous work on activity recognition focuses on recognition from a single view and ignores the issue of view invariance. In this paper, we present an independent Gabor features (IGFs) method comes from the derivation of independent Gabor features in the feature extraction stage. The Gabor transformed human image exhibit strong characteristics of spatial locality, scale and orientation selectivity.

• The Korean Journal of Applied Statistics
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• v.1 no.1
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• pp.39-44
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• 1987

For obtaining the m.l.e. of $\Sigma$ from p-variate Non-singular Normal parent, $N_p(\mu, \Sigma)$, Andersous' Procedure based on the invariance property of the m.l.e. seems to be generally Preferred in the view of its simplicity. This paper shows that his approach with respect to $\Sigma^{-1}$ rather than $\Sigma$ itself, he burther applicable to deriving the m.l.e. of parametersinvolved in the common factor model an dsimplex model as well.

• Research in Mathematical Education
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• v.12 no.3
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• pp.215-233
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• 2008

Deep comprehension of basic mathematical notions and concepts is a basic condition of a successful teaching. Some elements of algebraic thinking belong to the elementary school mathematics. The question "What stays the same and what changes?" link arithmetic problems with algebraic conception of variable. We have studied beliefs and comprehensions of future elementary school mathematics teachers on early algebra. Pre-service teachers from three academic pedagogical colleges deal with mathematical problems from the pre-algebra point of view, with the emphasis on changes and invariants. The idea is that the intensive use of non-formal algebra may help learners to construct a better understanding of fundamental ideas of arithmetic on the strong basis of algebraic thinking. In this article the study concerning arithmetic series is described. Considerable number of pre-service teachers moved from formulas to deep comprehension of the subject. Additionally, there are indications of ability to apply the conception of change and invariance in other mathematical and didactical contexts.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.2
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• pp.69-79
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• 1994

The conventional machine vision system which has uniform rectangular grid requires tremendous amount of computation for processing and analysing an image especially in 2-D image transfermations such as scaling, rotation and 3-D reconvery problem typical in robot application environment. In this study, the imaging system with nonuiformly distributed image sensors simulating human visual system, referred to as Ploar Exponential Grid(PEG), is compared with the existing conventional uniform rectangular grid system in terms of image resolution and computational complexity. By mimicking the geometric structure of the PEG sensor cell, we obtained PEG-like images using computer simulation. With the images obtained from the simulation, image resolution of the two systems are compared and some basic image processing tasks such as image scaling and rotation are implemented based on the PEG sensor system to examine its performance. Furthermore Fourier transform of PEG image is described and implemented in image analysis point of view. Also, the range and heading-angle measurement errors usually encountered in 3-D coordinates recovery with stereo camera system are claculated based on the PEG sensor system and compared with those obtained from the uniform rectangular grid system. In fact, the PEC imaging system not only reduces the computational requirements but also has scale and rotational invariance property in Fourier spectrum. Hence the PEG system has more suitable image coordinate system for image scaling, rotation, and image recognition problem. The range and heading-angle measurement errors with PEG system are less than those of uniform rectangular rectangular grid system in practical measurement range.

• The Mathematical Education
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• v.50 no.4
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• pp.489-505
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• 2011

This study is an analysis on the focus of textbooks regarding the statistical chapters of "measures of representative(central tendency) and of the spread". Applying the summary-concept criteria of Juhyeon Nam(2007), 4 kinds of aspect of the chapter; (1) definition and its teleological validity of the measures of representative, (2) definition and practical value of the measures of spread (3) distributional form on the measures of representative and of spread (4) location and scale preservation or invariance of the measures of representative and of spread were observed. On the measures of representative, some definitions were insufficient to check the teleological validity of the measure. Most definitions of the measure of spread were based on the practical view points but no preparation for the future statistical inferences were found even by implication. Some books mention about the measures of representative and of spread for distributions, but we could not find any comments on the correspondence between the sample mean and the expectation of a distribution or population mean. However it is stimulant that some books check the validity of corresponding measures with the location and scale preservation or invariant property, that were not found in the previous curriculum.

• The Korean Journal of Applied Statistics
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• v.4 no.1
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• pp.1-11
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• 1991

It is of great interest to consider the homogeniety of covariance matrices in MANOVA of discriminant analysis. If we lock at the problem of testing hypothesis, H : $\Sigma_1 = \Sigma_2$ from an invariance point of view where $\Sigma_i$ are the covariance matrix of two independent p-variate distribution, the testing problem is invariant under the group of nonsingular transformations and the hypothesis becomes H : $\delta_1 = \delta_2 = \cdots = \delta_p = 1$ where $\delta = (\delta_1, \delta_2, \cdots, \delta_p)$ is a vector of latent roots of $\Sigma$. Bias-corrected estimators of eigenvalues and sampling distribution of the test statistics proposed are obtained. Pooled-bootstrap method also considered for Bartlett's modified likelihood ratio statistics.

• Journal of Broadcast Engineering
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• v.24 no.1
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• pp.142-152
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• 2019

There is growing interest in ultra-high-resolution content that gives a more realistic sense of presence than existing broadcast content. However, in order to provide ultra-high-resolution contents in existing broadcast services, there are limitations in view angle and resolution of the image acquisition device. In order to solve this problem, many researches on stitching, which is an image synthesis method using a plurality of input devices, have been conducted. In this paper, we propose method of dynamic object based video stitching using minimal error seam in order to overcome the temporal invariance degradation of moving objects in the stitching process of horizontally oriented videos.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.3
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• pp.271-274
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• 2006

This paper deals with a similarity decision method between the shape of hand-postures and their structures to improve performance of the vision-based hand-posture recognition system. Hand-posture recognition by vision sensors has difficulties since the human hand is an object with high degrees of freedom, and hence grabbed images present complex self-occlusion effects and, even for one hand-posture, various appearances according to viewing directions. Therefore many approaches limit the relative angle between cameras and hands or use multiple cameras. The former approach, however, restricts user's operation area. The latter requires additional considerations on the way of merging the results from each camera image to get the final recognition result. To recognize hand-postures, we use both of appearance and structural features and decide the similarity between the two types of features by learning.