• Journal of Digital Contents Society
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• v.5 no.4
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• pp.289-294
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• 2004

For the purpose of image analysis, we usually take the application method relying on the various mathematical theories. On the respect of image as two variable function one may uses the gradient vector or several type of energy functions induced by the conventional (partial) derivative. We also have used the tangent plane or curvature vector from the concept of differential geometry {**]. However, these mathematical tools my assume that the given function should be sufficiently smoothing enough to depict every local variation continuously. But the real application of these mathematical methods to the natural images or phenomena may occur the ill-posed problem. In this paper, we have defined the weak derivative as a loose form of the derivative so that it my applied to the irregular case with less ill-posed problem.

• Bulletin of the Korean Mathematical Society
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• v.33 no.2
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• pp.229-232
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• 1996

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.331-335
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• 1995

We prover Fredholm alternatives for AF algebras: If an element have the finite null projection and the confinite range projection then its image in the relative Calkin algebra is invertible.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.321-332
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• 2010

In this paper, we experiment image warping and morphing. In image warping, we use radial basis functions : Thin Plate Spline, Multi-quadratic and Gaussian. Then we obtain the fact that Thin Plate Spline interpolation of the displacement with reverse mapping is the efficient means of image warping. Reflecting the result of image warping, we generate two examples of image morphing.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.11
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• pp.4290-4309
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• 2020

In recent years, advancements in machine learning capabilities have allowed it to see widespread adoption for tasks such as object detection, image classification, and anomaly detection. However, despite their promise, a limitation lies in the fact that a network's performance quality is based on the data which it receives. A well-trained network will still have poor performance if the subsequent data supplied to it contains artifacts, out of focus regions, or other visual distortions. Under normal circumstances, images of the same scene captured from differing points of focus, angles, or modalities must be separately analysed by the network, despite possibly containing overlapping information such as in the case of images of the same scene captured from different angles, or irrelevant information such as images captured from infrared sensors which can capture thermal information well but not topographical details. This factor can potentially add significantly to the computational time and resources required to utilize the network without providing any additional benefit. In this study, we plan to explore using image fusion techniques to assemble multiple images of the same scene into a single image that retains the most salient key features of the individual source images while discarding overlapping or irrelevant data that does not provide any benefit to the network. Utilizing this image fusion step before inputting a dataset into the network, the number of images would be significantly reduced with the potential to improve the classification performance accuracy by enhancing images while discarding irrelevant and overlapping regions.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.447-452
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• 2008

We provide some examples around AP and WAP spaces which are connected with higher convergence properties-radiality, semiradiality and pseudoradiality. We also prove a theorem (Theorem 3.2) that (a) any pseudo-open continuous image of an AP-space is an AP-space and (b) any pseudo-open continuous image of an WAP-space is an WAP-space. This answers the question posed by V. V. Tkachuk and I. V. Yaschenko [10].

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1591-1600
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• 2008

In this paper, we introduce an iterative scheme given by infinite nonexpansive mappings in Banach spaces. We prove strong convergence theorems which are connected with the problem of image recovery. Our results enrich and complement the recent many results.

• Journal of the Korean Mathematical Society
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• v.51 no.5
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• pp.941-953
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• 2014

In this paper, a 2-circular matrix theory is developed, and a concept of spectral radius for biorthogonal wavelet is introduced. We propose a novel design method by minimizing the spectral radius and obtain a wavelet which has better performance than the famous 9-7 wavelet in terms of image compression coding.

• Proceedings of the IEEK Conference
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• 2003.11a
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• pp.485-488
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• 2003

A conventional correlation target tracker is analysed with a simple mathematical approach. And, we will propose a correlation measure with selective attentional property in order to overcome the false-peak problem of the conventional methods. Various experimental results show that the proposed correlation measure is able to reduce considerably the probability of false-peaks degraded by the correlation between background images of a reference block and a distorted and noisy sensor input image.

• The Mathematical Education
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• v.13 no.2
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• pp.29-31
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• 1974

P.Zenor에 의해서 Monotonically Normal space가 정의되었으며 그후 R. Health와 D. Lutzer에 의해서 Linearly ordered topological space가 Monotonically Normal 임을 증명했다. 한편 Zenor는 Monotonically Normal Space의 hereditary에 관한 것을 question으로 남겼는데 Health와 Lutzer가 증명했고 또 그 증명보다 더 간단한 증명을 Calos R. Boyers가 증명했다[3]. 뿐만 아니라 그 결과로서 Linearly ordered topological space와 Elastic space 가 Monotonically Normal space임을 밝혔다. 또 [4]에서 Gary Gruenhage가 Monotonically Normal space가 Elastic space가 안됨을 counterexample을 들어서 증명했다. 결론적으로 Monotonically Normal spare와 Elastic space는 완전히 분리되었다. 또 Elastic space의 closed continuous image는 paracompact이고 Monotonically Normal 임을 증명했다. 이 논문에서는 본인이 밝힌 것은 Monotonically Normal space의 closed continuous image가 Mono tonically Normal임을 밝혔다.