• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.857-869
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• 2005

Let $(X,\;B,\;{\mu},\;T)$ be a dynamical system and (Y, A, v, S) be a factor. We investigate the relative sequence entropy of a partition of X via the maximal compact extension of (Y, A, v, S). We define relative sequence entropy pairs and using them, we find the relative topological ${\mu}-Kronecker$ factor over (Y, v) which is the maximal topological factor having relative discrete spectrum over (Y, v). We also describe the topological Kronecker factor which is the maximal factor having discrete spectrum for any invariant measure.

• Construction Engineering and Management
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• v.4 no.1 s.13
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• pp.48-54
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• 2003

An automated system for scanning and characterizing unbound aggregates, called the 'Laser-based Aggregate Scanning System'(LASS), has been developed at the University of Texas at Austin. The system uses a laser profiler to acquire and analyze true three-dimensional data on aggregate particles to measure various morphological properties. Tests have demonstrated that the system can rapidly and accurately measure grain size distribution and dimensional ratios, and can objectively quantify particle shape, angularity, and texture in a size invariant manner. In its present state of development, the LASS machine is a first-generation, laboratory testing device. With additional development, this technology is expected to provide high-quality, detailed information for laboratory and on-line quality control during aggregate production.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.391-399
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• 2003

Let (X,S,$\mu$) be a measure space and M be the vector space of all real valued S-measurable functions defined on (X,S,$\mu$). For $E\;{\in}\;S$ with $\mu(E)\;<\;{\infty}$, $d_E$ is a pseudometric on M. With the notion of D = {$d_E$\mid$E\;{\in}\;S,\mu(E)\;<\;{\infty}$}, in this paper we investigate some topological structure T of M. Indeed, we shall show that it is possible to define a complete invariant metric on M which is compatible with the topology T on M.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.44 no.1
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• pp.122-129
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• 2007

As the availability of an image information has been significantly increasing, necessity of system that can manage an image information is increasing. Accordingly, we proposed the content-based image retrieval(CBIR) method based on an efficient combination of a color feature and an image's shape and position information. As a color feature, a HSI color histogram is chosen which is known to measure spatial of colors well. Shape and position information are obtained using Hu invariant moments in the luminance of HSI model. For efficient similarity computation, the extracted features(Color histogram, Hu invariant moments) are combined and then measured precision. As a experiment result using DB that was supported by http://www.freefoto.com, the proposed image search engine has 93% precision and can apply successfully image retrieval applications.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.44 no.5
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• pp.1-11
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• 2007

As the availability of an image information has been significantly increasing, necessity of system that can manage an image information is increasing. Accordingly, we proposed the region-based content retrieval(CBIR) algorithm based on an efficient combination of an image segmentation, an image texture, a color feature and an image's shape and position information. As a color feature, a HSI color histogram is chosen which is known to measure spatial of colors well. We used active contour and CWT(complex wavelet transform) to perform an image segmentation and extracting an image texture. And shape and position information are obtained using Hu invariant moments in the luminance of HSI model. For efficient similarity computation, the extracted features(color histogram, Hu invariant moments, and complex wavelet transform) are combined and then precision and recall are measured. As a experimental result using DB that was supported by www.freefoto.com. the proposed image retrieval engine have 94.8% precision, 82.7% recall and can apply successfully image retrieval system.

• Journal of the Institute of Electronics and Information Engineers
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• v.52 no.11
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• pp.147-155
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• 2015

For the image processing system to be classified the selected object in the nature, the rotation, scale and transition invariant features is to be necessary. There are many investigations to get the information for the object processing system and the log-polar transform which is to be get the invariant feature for the scale and rotation is used. In this paper, we suggested the 2 points polar coordinate transform methods to measure the selected object position out of the center in input image including the centroid method. In this proposed system, the position results of objects are very good, and we obtained the similarity ratio 99~104% for the object coordinate values.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.4
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• pp.1648-1672
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• 2020

There are several types of image registration in the sense of stitching separated images that overlap each other. One of these is feature-based registration by a common feature descriptor. In this study, we generate a mosaic of images using feature-based registration for drone aerial images. As a feature descriptor, we apply the scale-invariant feature transform descriptor. In order to investigate the authenticity of the feature points and to have the mapping function, we employ the sample consensus method; we consider the sensed image's inherent characteristic such as the geometric congruence between the feature points of the images to propose a novel hypothesis estimation of the mapping function of the stitching via some optimally chosen initial candidate inliers in the sample consensus method. Based on the experimental results, we show the efficiency of the proposed method compared with benchmark methodologies of random sampling consensus method (RANSAC); the well-ordering property defined in the context and the extensive stitching examples have supported the utility. Moreover, the sample consensus scheme proposed in this study is uncomplicated and robust, and some fatal miss stitching by RANSAC is remarkably reduced in the measure of the pixel difference.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.417-426
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• 2011

Let ${\mu}$ be a finite positive Borel measure on the unit ball $B{\subset}{\mathbb{C}}^n$ and ${\nu}$ be the Euclidean volume measure such that ${\nu}(B)=1$. For the unit sphere $S=\{z:{\mid}z{\mid}=1\}$, ${\sigma}$ is the rotation-invariant measure on S such that ${\sigma}(S) =1$. Let ${\mathcal{P}}[f]$ be the Poisson-$Szeg{\ddot{o}}$ integral of f and $\tilde{\mu}$ be the Berezin transform of ${\mu}$. In this paper, we show that if there is a constant M > 0 such that ${\int_B}{\mid}{\mathcal{P}}[f](z){\mid}^pd{\mu}(z){\leq}M{\int_B}{\mid}{\mathcal{P}}[f](z){\mid}^pd{\nu}(z)$ for all $f{\in}L^p(\sigma)$, then ${\parallel}{\tilde{\mu}}{\parallel}_{\infty}{\equiv}{\sup}_{z{\in}B}{\mid}{\tilde{\mu}}(z){\mid}<{\infty}$, and we show that if ${\parallel}{\tilde{\mu}{\parallel}_{\infty}<{\infty}$, then ${\int_B}{\mid}{\mathcal{P}}[f](z){\mid}^pd{\mu}(z){\leq}C{\mid}{\mid}{\tilde{\mu}}{\mid}{\mid}_{\infty}{\int_S}{\mid}f(\zeta){\mid}^pd{\sigma}(\zeta)$ for some constant C.

• Communications for Statistical Applications and Methods
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• v.30 no.1
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• pp.37-48
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• 2023

Shape analysis is a method for measuring, describing and comparing the shape of objects in geometric space. An important aspect is to obtain Procrustes distance based on least square method. We note that the shape is all the geometrical information that remains when location, scale and rotational effects are filtered out from an object. However, and unfortunately, when we cannot measure some landmarks which are some biologically or geometrically meaningful points of any object, it is not possible to measure the variation of all shapes of an object, including that of the incomplete object. Hence, we need to replace the missing landmarks. In particular, Albers and Gower (2010) studied the missing rows of configurations in Procrustes analysis. They noted that the convergence of their approach can be quite slow. In this study, alternatively, we derive an algorithm for estimating the missing landmarks based on the pre-shapes. The pre-shape is invariant under the location and scaling of the original configuration with the centroid size of the pre-shape being one. Therefore we expect that we can reduce the amount of total computing time for obtaining the estimate of the missing landmarks.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.2
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• pp.91-97
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• 2005

If ${\beta}\;>\;1$, then every non-negative number x has a ${\beta}-expansion$, i.e., $$x\;=\;{\epsilon}_0(x)\;+\;{\frac{\epsilon_1(x)}{\beta}}\;+\;{\frac{\epsilon_2(x)}{\beta}}\;+\;{\cdots}$$ where ${\epsilon}_0(x)\;=\;[x],\;{\epsilon}_1(x)\;=\;[\beta(x)],\;{\epsilon}_2(x)\;=\;[\beta(({\beta}x))]$, and so on ([x] denotes the integral part and (x) the fractional part of the real number x). Let T be a transformation on [0,1) defined by $x\;{\rightarrow}\;({\beta}x)$. It is well known that the relative frequency of $k\;{\in}\;\{0,\;1,\;{\cdots},\;[\beta]\}$ in ${\beta}-expansion$ of x is described by the T-invariant absolutely continuous measure ${\mu}_{\beta}$. In this paper, we show the mod M normality of the sequence $\{{\in}_n(x)\}$.