• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.2C
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• pp.113-123
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• 2007

In Ubiquitous communication environment, various conversions of images are essential, and most digital images are compressed by standard methods such as the Joint Photographic Expert Group (JPEG) and Motion Picture Expert Group (MPEG) which are based on the discrete cosine transform (DCT). In this paper, various image resizing algorithms in the DCT domain are analyzed, and a new image resizing algorithm, which shows superior performance compared with the conventional methods, is proposed. For arbitrary-ratio image resizing in the DCT domain, several blocks of $8{\times}8$ DCT coefficients are converted into one block using the conversion formula in the proposed algorithm, and the size of the inverse discrete cosine transform (IDCT) is decided optimally. The performance is analyzed by comparing the peak signal to noise ratio (PSNR) between original images and converted images. The performance of the proposed algorithm is better than that of the conventional algorithm, since the correlation of pixels in images is utilized more efficiently.

• Proceedings of the IEEK Conference
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• 2003.07e
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• pp.1940-1943
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• 2003

본 논문은 Polynomial 변환을 이용하여 2차원 Discrete Cosine Transform (2D-DCT)의 계산을 1차원 DCT로 변환하여 계산하는 알고리즘을 개발한다. 기존의 일반적인 알고리즘인 row-column이 N×M의 2D-DCT에서 3/2NMlog₂(NM)-2NM＋N＋M의 합과 1/2NMlog₂(NM)의 곱셈이 필요한데 비하여 본 논문에서 제시한 알고리즘은 3/2NMlog₂M ＋NMlog₂N-M-N/2＋2의 합과 1/2NMlog₂M의 곱셈 수를 필요로 한다. 기존의 polynomial 변환에 의한 2D DCT는 Euler 공식을 적용하였기 때문에 복소 연산이 필요하지만 본 논문에서 제시한 polynomial 변환은 DCT의 modular 규칙을 이용하여 2D DCT를 ID DCT의 합으로 직접 변환하므로 복소 연산이 필요하지 않다. 또한 본 논문에서 제시한 알고리즘은 각 차원에서 데이터 크기가 다른 임의 크기의 2차원 데이터 변환에도 적용할 수 있다.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1998.06a
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• pp.121-126
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• 1998

DV(Digital Video) 영상 압축 방식에서 MPEG-2로 변환할 때 처리단계를 줄이기 위하여 DCT 영역에서 변환하였다. DV 방식의 색차신호 포맷인 4:1:1에서 4:2:2로 변환하고, 2-4-8 DCT 모드를 변환할 때 행렬을 이용하여 변환함으로써 중간과정을 줄였으며, DCT 영역에서 MPEG-2의 율 제어를 구현하였다. DV에서 만든 DCT 계수를 이용하여, 단계적으로 움직임 추정을 함으로써 전역탐색 블록 매칭 방식보다 처리 속도를 개선하였다.

• Journal of KIISE:Databases
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• v.33 no.7
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• pp.693-707
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• 2006

To improve performance using a multidimensional index in similar sequence matching, we transform a high-dimensional sequence to a low-dimensional sequence, and then construct a low-dimensional MBR that contains multiple transformed sequences. In this paper we propose a formal method that transforms a high-dimensional MBR itself to a low-dimensional MBR, and show that this method significantly reduces the number of lower-dimensional transformations. To achieve this goal, we first formally define the new notion of MBR-safe. We say that a transform is MBR-safe if a low-dimensional MBR to which a high-dimensional MBR is transformed by the transform contains every individual low-dimensional sequence to which a high-dimensional sequence is transformed. We then propose two MBR-safe transforms based on DFT and DCT, the most representative lower-dimensional transformations. For this, we prove the traditional DFT and DCT are not MBR-safe, and define new transforms, called mbrDFT and mbrDCT, by extending DFT and DCT, respectively. We also formally prove these mbrDFT and mbrDCT are MBR-safe. Moreover, we show that mbrDFT(or mbrDCT) is optimal among the DFT-based(or DCT-based) MBR-safe transforms that directly convert a high-dimensional MBR itself into a low-dimensional MBR. Analytical and experimental results show that the proposed mbrDFT and mbrDCT reduce the number of lower-dimensional transformations drastically, and improve performance significantly compared with the $na\"{\i}ve$ transforms. These results indicate that our MBR- safe transforms provides a useful framework for a variety of applications that require the lower-dimensional transformation of high-dimensional MBRs.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.19 no.10
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• pp.2403-2408
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• 2015

For image data the discrete cosine transform (DCT) has comparable energy compaction capability to Karhunen-Loeve transform (KLT) which is optimal. Hence DCT has been widely accepted in various image and video compression standard such as JPEG, MPEG-2, and MPEG-4. Recently some approximate DCT's have been reported, which can be computed much faster than the original DCT because their coefficients are either zero or the power of 2. Although the level of energy compaction is slightly degraded, the approximate DCT's can be utilized in real time implementation of image or visual compression applications. In this paper, an approximate 8-point DCT which contains 17 non-zero power-of-2 coefficients and high energy compaction capability comparable to DCT is proposed. Transform coding experiments with several images show that the proposed transform outperforms the published works.

• Proceedings of the Korean Information Science Society Conference
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• 2004.10c
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• pp.460-462
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• 2004

최신의 동영상 압축 표준인 H.264[1]는 기존의 동영상 압축 표준에 비해 압축 성능이 매우 높으며 4$\times$4 DCT(Discrete Cosine Transform)를 수행하는 특징이 있다. H.264 표준에서는 압축 효율을 높이기 위해 Intra 프레임 내의 이웃한 픽셀칸의 연관성을 이용한 프레임 내 창조(Intra Prediction)를 수행한다. 그러므로 기존의 동영상 압축 데이터를 H.264로 변환하기 위해서는 intra 프레임의 프레임 내 창조와 8$\times$8 DCT 블록의 4$\times$4 정수형 DCT 블록으로의 변환을 필수적으로 수행해야 한다. 또한, Intra 프레임은 GOP 내의 다른 프레임의 창조 대상이 되므로 변환 시 화질의 최적화가 필수적이다[2]. 본 논문에서는 Intra 프레임의 변환 시 화질의 최적화를 위해 DCT 도메인 상에서 프레임 내 창조를 수행하는 기법을 제안한다. 제안된 기법은 추가적인 계산없이 DCT 변환으로 인한 오류를 줄여 변환된 intra 프레임의 화질을 개선할 수 있다.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.40 no.6
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• pp.127-140
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• 2003

This paper develops a novel algorithm of computing 2 Dimensional Discrete Cosine Transform (2D-DCT) via Polynomial Transform (PT) converting 2D-DCT to the sum of 1D-DCTs. In computing N${\times}$M size 2D-DCT, the conventional row-column algorithm needs 3/2NMlog$_2$(NM)-2NM＋N＋M additions and 1/2NMlog$_2$(NM) additions and 1/2NMlog$_2$(NM) multiplications, while the proposed algorithm needs 3/2NMlog$_2$M＋NMlog$_2$N-M-N/2＋2 additions and 1/2NMlog$_2$M multiplications The previous polynomial transform needs complex operations because it applies the Euler equation to DCT. Since the suggested algorithm exploits the modular regularity embedded in DCT and directly decomposes 2D DCT into the sum of ID DCTs, the suggested algorithm does not require any complex operations.

• The KIPS Transactions:PartA
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• v.18A no.2
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• pp.39-44
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• 2011

This paper proposes the new high-performance circuit architecture of the transform and quantization for unified video CODEC. The proposed architecture can be applied to all kinds of transforms and quantizations for the video compression standards such as JPEG, MPEG-1/2/4, H.264 and VC-1. We defined the permutation matrices to reorder the transform matrix of the $8{\times}8$ DCT and partitioned the reordered $8{\times}8$ transform matrix into four $4{\times}4$ sub-matrices. The $8{\times}8$ DCT is performed by repeating the $4{\times}4$ DCT's based on the reordered and partitioned transform matrices. Since our circuit accepts the transform coefficients from the users, it can be extended very easily to cover any kind of DCT-based transforms for future standards. The multipliers in the DCT circuit are shared by the quantization circuit in order to minimize the circuit size. The quantization circuit is merged into the DCT circuit without any significant increase of circuit resources and processing time. We described the proposed DCT and quantization circuit at RTL, and verified its operation on FPGA board.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2014.11a
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• pp.12-14
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• 2014

본 논문에서는 AZB (All-Zero Block) 검출을 이용한 조기 부호화 단위(Coding Unit, CU) 결정 방법을 제안한다. HEVC 영상 코덱의 하드웨어 구현에서 이산여현변환(DCT)는 많은 부호화 자원을 필요로 하는 과정으로 DCT 수행 이전에 블록 내의 모든 양자화 계수가 0 이 되는 영블록(All-zero Block)을 미리 검출하여 DCT 및 양자화 과정을 생략하고 CU 의 부호화 과정을 조기에 종료함으로써 부호화 복잡도를 크게 감소시키는 방법을 제안한다. 기존의 SAD (Sum of Absolute Difference) 또는 SATD (Sum of Absolute Transform Difference)에 기반하는 AZB 검출 방법은 HEVC 에서 새롭게 추가된 큰 크기의 $16{\times}16$와 $32{\times}32$ DCT 에서 AZB 을 효율적으로 검출할 수 없는 한계가 존재한다. 본 논문에서는 DCT 변환 커널이 하다마드 변환 커널과 또 다른 정규 직교 변환 커널로 분할하여 표현할 수 있는 성질을 이용하여, 부화소 움직임벡터 추정 과정을 통해 생성된 하드마드 변환 계수에 DCT 를 생성하는 변환 커널을 곱하여 DCT 변환 커널을 생성한 후 양자화 계수를 이용하여 CU 단위의 AZB 을 검출하는 방법을 제안한다. 또한 AZB 검출과 움직임 벡터의 크기를 이용하여 현재 CU 의 부호화 과정을 조기에 종료하는 방법을 제안한다. 제안하는 AZB 검출과 CU 조기 종료 부호화 방법을 사용하면 평균적으로 34.7%의 부호화 시간을 감소시켜 부호화 복잡도를 크게 줄일 수 있다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.16 no.12
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• pp.1236-1248
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• 1991

A new fast algorithm for computing the discrete cosine transform(DCT) Is developed decomposing N-point DCT into an N /2-point DCT and two N /4 point transforms(transpose of an N /4-point DCT. TN/t'and)It has an important characteristic that in this method, the roundoff noise power for a fixed point arithmetic can be reduced significantly with respect to the wellknown fast algorithms of Lee and Chen. since most coefficients for multiplication are distributed at the nodes close to the output and far from the input in the signal flow graph In addition, it also shows three other versions of factorization of DCT matrix with the same number of operations but with the different distributions of multiplication coefficients.