• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.12.2-12
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• 2003

미분 가능한 함수가 독립변수의 각 점에서 미분계수를 가지듯이 가장 일반화된 Cantor집합의 각 점에서 weak local dimension 을 갖는다. 이러한 weak local dimension 은 두 가지가 있는데 weak lower local dimension 과 weak upper local dimension 이 있다 weak lower local dimension 은 국소적인 의미로 perturbed Cantor 집합의 lower Cantor dimension 이고 Hausdorff dimension 과 관련이 있다. weak upper local dimension 은 국소적인 의미로 perturbed Cantor 집합의 upper Cantor dimension 이고 packing dimension 과 관련이 있다. 이때 각 점에 대응하는 유관한 측도는 quasi-self-similar measure 이며 그 점의 weak lower local dimension 이 s 이면 그 점의 s-차원 quasi-self-similar measure 의 lower local dimension 이 s 가 된다. 마찬가지로 그 점의 weak upper local dimension 이 s 이면 그 점의 s-차원 quasi-self-similar measure 의 upper local dimension 이 s 가 된다. 따라서 이와 같은 사실을 이용하면 가장 일반화된 Cantor집합의 각 점에서의 weak local dimension 을 이용하여 그 집합의 Hausdorff 또는 packing 차원의 정보를 얻을 수 있을 뿐 더러 weak local dimension 을 이용한 spectrum 을 또한 구할 수 있다. 한편 weak local dimension 과 유관한 quasi-self-similar measure 는 집합의 spectrum을 생성하며 이 spectrum 을 이루는 각 부분집합의 차원에 대하여 보다 좋은 정보를 주는 transformed dimension 과 또 다른 관련을 갖게 된다.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.695-702
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• 2005

We study the transformed measures with respect to the real parameters of a self-similar measure on a self-similar Can­tor set to give a simple proof for some result of its multifractal spectrum. A transformed measure with respect to a real parameter of a self-similar measure on a self-similar Cantor set is also a self­similar measure on the self-similar Cantor set and it gives a better information for multifractals than the original self-similar measure. A transformed measure with respect to an optimal parameter deter­mines Hausdorff and packing dimensions of a set of the points which has same local dimension for a self-similar measure. We compute the values of the transformed measures with respect to the real parameters for a set of the points which has same local dimension for a self-similar measure. Finally we investigate the magnitude of the local dimensions of a self-similar measure and give some correlation between the local dimensions.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.497-503
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• 2007

We consider a non-empty subset having same local dimension of a self-similar measure on a most generalized Cantor set. We study trans-formed lower(upper) local dimensions of an element of the subset which are local dimensions of all the self-similar measures on the most generalized Cantor set. They give better information of Hausdorff(packing) dimension of the afore-mentioned subset than those only from local dimension of a given self-similar measure.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.403-406
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• 2003

This paper presents a robust algorithm for edge detection based on fuzzy fusion, using a novel local edge information measure based on Renyi's a-order entropy. The calculation of the proposed measure is carried out using a parametric classification scheme based on local statistics. By suitably tuning its parameters, the local edge information measure is capable of extracting different types of edges, while exhibiting high immunity to noise. The notions of fuzzy measures and the Choquet fuzzy integral are applied to combine the different sources of information obtained using the local edge information measure with different sets of parameters. The effectiveness and the robustness of the new method are demonstrated by applying our algorithm to various synthetic computer-generated and real-world images.

• Journal of the Korean Statistical Society
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• v.31 no.4
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• pp.447-458
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• 2002

The influence of observations in the equicorrelation model is investigated using the local influence approach when all parameters or subsets of parameters are of interest. When a parameter of interest is scalar, an analytical form of the local influence measure can be found. We will derive a measure for identifying observations that have a large influence on the test of fitting the equicorrelation model. An example is given for illustration.

• Safety and Health at Work
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• v.4 no.1
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• pp.46-51
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• 2013

Objectives: Load carrying tasks are recognized as one of the primary occupational factors leading to slip and fall injuries. Nevertheless, the mechanisms associated with load carrying and walking stability remain illusive. The objective of the current study was to apply local dynamic stability measure in walking while carrying a load, and to investigate the possible adaptive gait stability changes. Methods: Current study involved 25 young adults in a biomechanics research laboratory. One tri-axial accelerometer was used to measure three-dimensional low back acceleration during continuous treadmill walking. Local dynamic stability was quantified by the maximum Lyapunov exponent (maxLE) from a nonlinear dynamics approach. Results: Long term maxLE was found to be significant higher under load condition than no-load condition in all three reference axes, indicating the declined local dynamic stability associated with load carrying. Conclusion: Current study confirmed the sensitivity of local dynamic stability measure in load carrying situation. It was concluded that load carrying tasks were associated with declined local dynamic stability, which may result in increased risk of fall accident. This finding has implications in preventing fall accidents associated with occupational load carrying.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.2
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• pp.81-85
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• 2024

In this paper, we prove that if a transitive set Λ is robustly weak measure-expansive then Λ is hyperbolic.

• ETRI Journal
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• v.44 no.5
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• pp.769-779
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• 2022

Spectral clustering has become a typical and efficient clustering method used in a variety of applications. The critical step of spectral clustering is the similarity measurement, which largely determines the performance of the spectral clustering method. In this paper, we propose a novel spectral clustering algorithm based on the local similarity measure of shared neighbors. This similarity measurement exploits the local density information between data points based on the weight of the shared neighbors in a directed k-nearest neighbor graph with only one parameter k, that is, the number of nearest neighbors. Numerical experiments on synthetic and real-world datasets demonstrate that our proposed algorithm outperforms other existing spectral clustering algorithms in terms of the clustering performance measured via the normalized mutual information, clustering accuracy, and F-measure. As an example, the proposed method can provide an improvement of 15.82% in the clustering performance for the Soybean dataset.

• ETRI Journal
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• v.24 no.1
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• pp.23-30
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• 2002

MPEG-7 Visual Standard specifies a set of descriptors that can be used to measure similarity in images or video. Among them, the Edge Histogram Descriptor describes edge distribution with a histogram based on local edge distribution in an image. Since the Edge Histogram Descriptor recommended for the MPEG-7 standard represents only local edge distribution in the image, the matching performance for image retrieval may not be satisfactory. This paper proposes the use of global and semi-local edge histograms generated directly from the local histogram bins to increase the matching performance. Then, the global, semi-global, and local histograms of images are combined to measure the image similarity and are compared with the MPEG-7 descriptor of the local-only histogram. Since we exploit the absolute location of the edge in the image as well as its global composition, the proposed matching method can retrieve semantically similar images. Experiments on MPEG-7 test images show that the proposed method yields better retrieval performance by an amount of 0.04 in ANMRR, which shows a significant difference in visual inspection.

• Journal of Advanced Marine Engineering and Technology
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• v.38 no.9
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• pp.1112-1118
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• 2014

In this paper, we propose a local descriptor and a similarity measure that is robust to radiometic variations. The proposed local descriptor is made up Haar wavelet filter and it can contain frequency informations about the feature point and its surrounding pixels in fixed region, and it is able to describe feature point clearly under ununiform illumination condition. And a proposed similarity measure is combined with conventional entropy-based similarity and another similarities that is generated by local descriptor. It can reflect similarities between image regions accurately under radiometic illumination variations. We validate with experimental results on some images and we confirm that the proposed algorithm is more superior than conventional algorithms.