• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.399-406
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• 2019

Let n be the spatial dimension. For d, $0<d{\leq}n$, let $H^d$ be the d-dimensional Hausdorff content. The purpose of this paper is to prove the boundedness of the dyadic strong maximal operator on the Choquet space $L^p(H^d,{\mathbb{R}}^n)$ for min(1, d) < p. We also show that our result is sharp.

• International Journal of Contents
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• v.6 no.3
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• pp.5-9
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• 2010

To manage large database system with video, effective video indexing and retrieval are required. A large number of video retrieval algorithms have been presented for frame-wise user query or video content query, whereas a few video identification algorithms have been proposed for video sequence query. In this paper, we propose an effective video identification algorithm for video sequence query that employs the Cauchy function of histograms between successive frames and the modified Hausdorff distance. To effectively match the video sequences with a low computational load, we make use of the key frames extracted by the cumulative Cauchy function and compare the set of key frames using the modified Hausdorff distance. Experimental results with several color video sequences show that the proposed algorithm for video identification yields remarkably higher performance than conventional algorithms such as Euclidean metric, and directed divergence methods.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.959-971
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• 1997

In the paper we introduce Hausdorff measures which are suitable or the study of Lipschitz regularity of M-harmonic function in the unit ball B in $C^n$. For an M-harmonic function h which satisfies certain integrability conditions, we show that there is an open set $\Omega$, whose Hausdorff content is arbitrarily small, such that h is Lipschitz smooth on $B \backslash \Omega$.

• International Journal of Contents
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• v.12 no.1
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• pp.1-5
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• 2016

To manipulate large video contents, effective video indexing and retrieval are required. A large number of video indexing and retrieval algorithms have been presented for frame-wise user query or video content query whereas a relatively few video sequence matching algorithms have been proposed for video sequence query. In this paper, we propose an efficient algorithm that extracts key frames using color histograms and matches the video sequences using edge features. To effectively match video sequences with a low computational load, we make use of the key frames extracted by the cumulative measure and the distance between key frames, and compare two sets of key frames using the modified Hausdorff distance. Experimental results with real sequence show that the proposed video sequence matching algorithm using edge features yields the higher accuracy and performance than conventional methods such as histogram difference, Euclidean metric, Battachaya distance, and directed divergence methods.

• Journal of the Institute of Convergence Signal Processing
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• v.7 no.1
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• pp.11-16
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• 2006

To manipulate large video databases, effective video indexing and retrieval are required. A large number of video indexing and retrieval algorithms have been presented for frame-w]so user query or video content query whereas a relatively few video sequence matching algorithms have been proposed for video sequence query. In this paper, we propose an efficient algorithm to extract key frames using color histograms and to match the video sequences using edge features. To effectively match video sequences with low computational load, we make use of the key frames extracted by the cumulative measure and the distance between key frames, and compare two sets of key frames using the modified Hausdorff distance. Experimental results with several real sequences show that the proposed video retrieval algorithm using color and edge features yields the higher accuracy and performance than conventional methods such as histogram difference, Euclidean metric, Battachaya distance, and directed divergence methods.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.46 no.2
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• pp.92-99
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• 2009

This paper established the range of the wavelength of traffic lights to detection the color of traffic lights and the color component segmentation with the range of the wavelength. Development of traffic light automatic discrimination system is consists of the color detection and the traffic lights recognition. In this thesis, it established the range of the wavelength of traffic lights to detection the color of traffic lights and the color segmentation with the range of the wavelength. By the segmentation, the traffic light colors(red, orange and green) can be detected and the background is changed into gray image. Next, we proposed the algorithm which can detect the area of traffic lights in the various surroundings with the wavelet transformation algorithm. Also, we proposed traffic lights recognition algorithm using between the edge operator and the Hausdorff distance algorithm based on CBIR(Content-based Image retrieval). Therefore, the proposed algorithm is more superior to the conventional algorithm by experimenting with the illumination including the traffic lights and the backgrounds with various images.

• Proceedings of the KIEE Conference
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• 2005.10b
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• pp.539-541
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• 2005

We propose efficient video retrieval scheme which use fast key frame extraction in DCT domain. Our scheme extract key frame using the edge histogram difference which is extracted in compressed domain for I-frames. And the video retrieval is implemented using Hausdorff distance function about edge histogram of key frame. This approach enables fast content-based video retrieval of the compressed video content without decompression process. Experimental results show our scheme is very fast and efficient.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.12
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• pp.8649-8653
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• 2015

A number of video indexing and retrieval algorithms have been proposed to manage large video databases efficiently. The video similarity measure is one of most important technical factor for video content management system. In this paper, we propose the luminance characteristics model to measure the video similarity efficiently. Most algorithms for video indexing have been commonly used histograms, edges, or motion features, whereas in this paper, the proposed algorithm is employed an efficient similarity measure using the luminance projection. To index the video sequences effectively and to reduce the computational complexity, we calculate video similarity using the key frames extracted by the cumulative measure, and compare the set of key frames using the modified Hausdorff distance. Experimental results show that the proposed luminance projection model yields the remarkable improved accuracy and performance than the conventional algorithm such as the histogram comparison method, with the low computational complexity.