• Journal of IKEEE
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• v.22 no.4
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• pp.948-952
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• 2018

Haze removal is an object of scientific desire due to its various practical applications. Existing algorithms are founded upon histogram equalization, contrast maximization, or the growing trend of applying machine learning in image processing. Since machine learning-based algorithms solve problems based on the data, they usually perform better than those based on traditional image processing/computer vision techniques. However, to achieve such a high performance, one of the requisites is a large and reliable training database, which seems to be unattainable owing to the complexity of real hazy and haze-free images acquisition. As a result, researchers are currently using the synthetic database, obtained by introducing the synthetic haze drawn from the standard uniform distribution into the clear images. In this paper, we propose the enhanced equidistribution, improving upon our previous study on equidistribution, and use it to make a new database for training machine learning-based haze removal algorithms. A large number of experiments verify the effectiveness of our proposed methodology.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.307-317
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• 2012

We say (W, {${\phi}_1,\;{\ldots}\;,{\phi}_t$}) is a polarizable dynamical system of several morphisms if ${\phi}_i$ are endomorphisms on a projective variety W such that ${\otimes}{\phi}_i^*L$ is linearly equivalent to $L^{{\otimes}q}$ for some ample line bundle L on W and for some q > t. If q is a rational number, then we have the equidistribution of small points of given dynamical system because of Yuan's work [13]. As its application, we can build a polarizable dynamical system of an automorphism and its inverse on a K3 surface and can show that its periodic points are equidistributed.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.845-871
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• 2020

We consider generalized Dedekind sums in dimension n, defined as sum of products of values of periodic Bernoulli functions. For the generalized Dedekind sums, we associate a Laurent polynomial. Using this, we associate an exponential sum of a Laurent polynomial to the generalized Dedekind sums and show that this exponential sum has a nontrivial bound that is sufficient to fulfill the equidistribution criterion of Weyl and thus the fractional part of the generalized Dedekind sums are equidistributed in ℝ/ℤ.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.736-740
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• 2007

It is not always convenient to consider isotropic meshes where the edge length depends on the orientation of the edge. It is desirable to go for anisotropic mesh strategy instead. There are many instances where the solution shows directional features such as great variations along certain directions with less significant changes along other ones. Anisotropic meshes considered to be worthy in these cases. By using anisotropic elements we can resolve the solution accurately with few elements. Many techniques have been used as a common feature that the shape, size and orientation of the triangle elements are controlled by specifying metric tensor. This paper attempts at clear understanding of the estimation and equidistribution of the error and discusses the parameters like reliability and effectivity of an anisotropic mesh in a mathematical manner. Also we study some of applications of anisotropic mesh.