• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.5C
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• pp.461-467
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• 2003

We propose an efficient method for separable symmetric linear filtering in the DCT domain. First, separable 2-D linear filtering is decomposed into the cascade of 1-D filtering in the DCT domain. We investigate special characteristics of DCT domain filtering matrices when the filter coefficients are symmetric. Then we present the DCT domain 2-D filtering method using these characteristics. The proposed method requires smaller number of multiplications including typical sparseness of DCT coefficients compared to previous DCT domain linear filtering methods. Also, the proposed method is composed of simple and regular operations, which would be appropriate for efficient VLSI implementation.

• 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 Journal of Korean Institute of Communications and Information Sciences
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• v.15 no.3
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• pp.221-231
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• 1990

In this paper, A new 2-D DCT algorithm is proposed to reduce the computational amount of transform operation using the distribution of the motion compensated error signal and the bit allocation table. In the this algorithm, 2-D Walsh-Hadamard transform is directly computed and then multiplied by a constant matrix. Multiplications are concentrated on the final stage in thie algorithm, thus the computational amount is reduced in proportion to the number of transform coefficients that are excluded from quatization. The computational amount in computing only the DCT coefficients allocated to the bit allocation table is calculated. As the result, the number of multiplications is less thn the algorithm known to have the fewest number of computations when less than 0.6 bits per pixel are allocated to tranform coding for the motion compensated error image in the case of the proposed algorithm. Thus, it shows that the proposed algorithm is valid in reducing the computational loads of transform coding.

• The Transactions of the Korea Information Processing Society
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• v.1 no.1
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• pp.81-91
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• 1994

A DCT map and new cldebook design algorithm based on a two-dimension discrete cosine transform (2D-DCT) is presented for coder of image vector quantizer. We divide the image into smaller subblocks, then, using 2D DCT, separate it into blocks which are hard to code but it bears most of the visual information and easy to code but little visual information, and DCT map is made. According to this map, the significant features of training image are extracted by using the 2D DCT. A codebook is generated by partitioning the training set into a binary tree based on tree-structure. Each training vector at a nonterminal node of the binary tree is directed to one of the two descendants by comparing a single feature associated with that node to a threshold. Compared with the pairwise neighbor (PPN) and classified VQ(CVQ) algorithm, about 'Lenna' and 'Boat' image, the new algorithm results in a reduction in computation time and shows better picture quality with 0.45 dB and 0.33dB differences as to PNN, 0.05dB and 0.1dB differences as to CVQ respectively.

• Journal of Korea Multimedia Society
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• v.1 no.2
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• pp.194-203
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• 1998

In this paper, a new DCT-VQ method is proposed which can solve the problems of VQ such as the degradation of edge and enormous calculations. VQ is carried in DCT domain but spatial domain in order to protect the degradation of edge. DCT makes high correlated image data decorrelated and the energy concentrated on a few coefficients. In DCT domain, the DC coefficient is quantized with 8 bits uniform scalar quantizer and the AC coefficients are divided to three regions and coded with vector qiantizer for considering edge components. For the decrease of the calculation and memory, the vectors for three region have small dimension of $1{\times}7$ and use the same codebook. Thus, the proposed method can fully express the edge components by considering AC coefficients in DCT domain and decrease the calculation and memory be reducing the dimension of vectors.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.39 no.4
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• pp.442-454
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• 2002

It's noticed that the SA-DCT (Shape-Adaptive Discrete Cosine Transform) produces different 2-dimensional transform coefficients according as the first 1-dimensional transform is applied in horizontal or vertical direction for an arbitrarily shaped boundary block. Performing the first 1-dimensional transform in the direction, which has higher spatial correlation or smaller shifting distance, can compact the energy on the smaller number of AC coefficients around DC. This paper shows, experimentally, the compaction capability improvement by choosing the first 1-dimensional transform direction with higher spatial correlation or smaller shifting distance. Two adaptive selection methods are proposed to decide efficiently the spatial direction with higher correlation in a boundary block. One is based on the gradients between DC coefficients of neighboring and current blocks, and the other is based on the final coding efficiency that means the number of bits required for coding the block. Using the MPEG-4 video coder, the proposed method shows coding efficiency gain up to 10.87% compared to the conventional SA-DCT method.

• Journal of Internet Computing and Services
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• v.6 no.2
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• pp.59-68
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• 2005

In this paper, for compression and transmission of 3D image, we propose an algorithm which executes 3D discrete cosine transform(DCT) for 3D images, hierarchically segments 3D blocks of an image in comparison with the original image and executes finite-state vector quantization(FSVQ) for each 3D block. Using 3D DCT coefficient feature, a 3D image is segmented hierarchically into large smooth blocks and small edge blocks, then the block hierarchy informations are transmitted. The codebooks are constructed for each hierarchical blocks respectively, the encoder transmits codeword index using FSVQ for reducing encoded bit with hierarchical segmentation information. The new algorithm suggested in this paper shows that the quality of Small Lobster and Head image increased by 1,91 dB and 1.47 dB respectively compared with those of HFSVQ.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.40 no.3
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• pp.156-163
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• 2003

Most watermarking techniques insert watermarks into transform coefficients in the frequency domain because we can consider robust or imperceptible frequency bands against malicious attacks to remove them. However, parameterization of 3-D data is not easy because of irregular attribution of connectivity information, while 1-I) or 2-D data is regular. In this paper we propose a new watermarking scheme for 3-D polygonal mesh models in the DCT domain. After we generate triangle strips by traversing the 3-D model and transform its vertex coordinates into the DCT domain, watermark signals are inserted into mid-frequency bands of AC coefficients for robustness and imperceptibility. We demonstrate that our scheme is robust against additive random noise, the affine transformation, and geometry compression by the MPEG-4 SNHC standard.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.12
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• pp.1970-1982
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• 1993

This paper describes an efficient array algorithm for parallel computation of vector-radix two-dimensional (2-D) fast discrete cosine transform (VR-FCT), and its VLSI implementation. By mapping the 2-D VR-FCT onto a 2-D array of processing elements (PEs), the butterfly structure of the VR-FCT can be efficiently importanted with high concurrency and local communication geometry. The proposed array algorithm features architectural modularity, regularity and locality, so that it is very suitable for VLSI realization. Also, no transposition memory is required, which is invitable in the conventional row-column decomposition approach. It has the time complexity of O(N+Nnzp-log2N) for (N*N) 2-D DCT, where Nnzd is the number of non-zero digits in canonic-signed digit(CSD) code, By adopting the CSD arithmetic in circuit desine, the number of addition is reduced by about 30%, as compared to the 2`s complement arithmetic. The computational accuracy analysis for finite wordlength processing is presented. From simulation result, it is estimated that (8*8) 2-D DCT (with Nnzp=4) can be computed in about 0.88 sec at 50 MHz clock frequency, resulting in the throughput rate of about 72 Mega pixels per second.