• Journal of Biomedical Engineering Research
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• v.20 no.3
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• pp.265-274
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• 1999

In this paper, we propose a novel interframe coding algorithm especially appropriate for 3-D medical images. The proposed algorithm is based on a video coding algorithm using motion estimation/ compensation and transform coding. In the algorithm, warping is adopted lor motion compensation (MC). Then, by using adaptive mode selection, a motion compensated residual image and original image are mixed up in the wavelet transform domain for improvement in coding performance. The mixed image is then compressed by the zerotree coding method. We prove that the adaptive mode selection technique in the wavelet transform domain is very useful lor 3-D medical image coding. Simulation results show that the proposed scheme provides good performance regardless of inter-slice distance and is prospective for 3-D medical image compression.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.93-111
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• 2004

In this paper, we use a generalized Brownian motion process to define a generalized Feynman integral and a generalized Fourier-Feynman transform. We also define the concepts of the multiple Lp analytic generalized Fourier-Feynman transform and the generalized convolution product of functional on function space $C_{a,\;b}[0,\;T]$. We then verify the existence of the multiple $L_{p}$ analytic generalized Fourier-Feynman transform for functional on function space that belong to a Banach algebra $S({L_{a,\;b}}^{2}[0, T])$. Finally we establish some relationships between the multiple $L_{p}$ analytic generalized Fourier-Feynman transform and the generalized convolution product for functionals in $S({L_{a,\;b}}^{2}[0, T])$.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.281-296
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• 2021

In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space C_a,b[0, T]. The function space C_a,b[0, T] is induced by the generalized Brownian motion process with mean function a(t) and variance function b(t). To do this, we study the generalized Fourier-Feynman transform associated with the Gaussian process Ƶ_k of exponential-type functionals. We then establish that a composition of the Ƶ_k-generalized Fourier-Feynman transforms acts like an inverse generalized Fourier-Feynman transform.

• ETRI Journal
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• v.34 no.5
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• pp.795-798
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• 2012

This letter proposes a new low-complexity motion estimation method. The proposed method classifies various nonmatching pixel pairs into several categories and assigns an appropriate weight for each category in the matching stage. As a result, it can significantly improve performance compared to that of the conventional methods by adding only one 1-bit addition and two Boolean operations per pixel.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.1
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• pp.1-16
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• 1996

In this paper, by combining the motion compensated transform coding with the sub-band decomposition technique, we present a motion compensated sub-band coding technique(MCSBC) for image sequence coding. Several problems related to the MCSBC, such as a scheme for motion compensation in each sub-band and the efficient VWL coding of the DCT coefficients in each sub-band are discussed. For an efficient coding, the motion estimation and compensation is performed only on the LL sub-band, but the discrete cosine transform(DCT) is employed to encode all sub-bands in our approach. Then, the transform coefficients in each sub-band are scanned in a different manner depending on the energy distributions in the DCT domain, and coded by using separate 2-D Huffman code tables, which are optimized to the probability distributions in the DCT domain, and coded by using separate 2-D Huffman code tables, which are optimized to the probability distribution of each sub-band. The performance of the proposed MCSBC technique is intensively examined by computer simulations on the HDTV image sequences. The simulation results reveal that the proposed MCSBC technique outperforms other coding techniques, especially the well-known motion compensated transform coding technique by about 1.5dB, in terms of the average peak signal to noise ratio.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.73-90
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• 2007

In this paper, we define a generalized Feynman integral and a generalized Fourier-Feynman transform on function space induced by generalized Brownian motion process. We then give existence theorems and several properties for these concepts. Finally we investigate relationships of the Fourier transform and the generalized Fourier-Feynman transform.

• Proceedings of the IEEK Conference
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• 2000.06d
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• pp.35-38
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• 2000

The method of Content-based Triangular Mesh Image representation in moving pictures makes better performance in prediction error ratio and visual efficiency than that of classical block matching. Specially if background and objects can be separated from image, the objects are designed by Irregular mesh. In this case this irregular mesh design has an advantage of increasing video coding efficiency. This paper presents the techniques of mesh generation, motion estimation using these mesh, uses image warping transform such as Affine transform for image reconstruction, and evaluates the content based mesh design through computer simulation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.2
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• pp.181-192
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• 2014

In this paper, we propose a robust real-time myocardial border tracking algorithm for echocardiography. Commonly, after an initial contour of LV border is traced at one or two frame from the entire cardiac cycle, LV contour tracking is performed over the remaining frames. Among a variety of tracking techniques, optical flow method is the most widely used for motion estimation of moving objects. However, when echocardiography data is heavily corrupted in some local regions, the errors bring the tracking point out of the endocardial border, resulting in distorted LV contours. This shape distortion often occurs in practice since the data acquisition is affected by ultrasound artifacts, dropout or shadowing phenomena of cardiac walls. The proposed method deals with this shape distortion problem and reflects the motion realistic LV shape by applying global deformation modeled as affine transform partitively to the contour. We partition the tracking points on the contour into a few groups and determine each affine transform governing the motion of the partitioned contour points. To compute the coefficients of each affine transform, we use the least squares method with equality constraints that are given by the relationship between the coefficients and a few contour points showing good tracking results. Many real experiments show that the proposed method supports better performance than existing methods.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1999.11b
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• pp.21-25
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• 1999

Wavelet transform decomposes a video frame into a set of subframes with different resolutions corresponding to different frequency bands. The block size of highest layer subframe is too small to estimate correct motion. To decrease this aperture problem in the approximation frame, multiresolution motion estimation (MRME) using hierarchical block matching is presented in this paper. In the multiresolution motion estimation approach, motion vectors in the subframes are estimated by the motion vectors in the approximation frame and are refined at each subframe. It reduces computational time in motion estimation. It is shown that our MRME approach has a superior performance than traditional MRME approaches.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.9C
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• pp.564-572
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• 2011

Distributed video coding (DVC) system has been proposed to reduce encoder complexity by using the correlation of frames in decoders. Since the block based motion estimation operation is not performed in the encoder of DVC system, lapped transforms, in which adjacent two blocks are transformed into one block, can be efficiently used in the DVC system. In this paper, an efficient DVC system using lapped transforms is proposed. The overlapped block motion compensated interpolation is used to produce side information, and the corresponding correlation noise between original Wyner-Ziv frame and side information is modeled. Extensive computer simulations show that the proposed DVC system outperforms conventional DVC systems.