Fast algorithm for the 3-D DCT-II

Recently, many applications for three-dimensional (3-D) image and video compression have been proposed using 3-D discrete cosine transforms (3-D DCTs). Among different types of DCTs, the type-II DCT (DCT-II) is the most used. In order to use the 3-D DCTs in practical applications, fast 3-D algorithms are essential. Therefore, in this paper, the 3-D vector-radix decimation-in-frequency (3-D VR DIF) algorithm that calculates the 3-D DCT-II directly is introduced. The mathematical analysis and the implementation of the developed algorithm are presented, showing that this algorithm possesses a regular structure, can be implemented in-place for efficient use of memory, and is faster than the conventional row-column-frame (RCF) approach. Furthermore, an application of 3-D video compression-based 3-D DCT-II is implemented using the 3-D new algorithm. This has led to a substantial speed improvement for 3-D DCT-II-based compression systems and proved the validity of the developed algorithm.

[1]  Yonghong Zeng,et al.  New polynomial transform algorithm for multidimensional DCT , 2000, IEEE Trans. Signal Process..

[2]  Gregory K. Wallace,et al.  The JPEG still picture compression standard , 1992 .

[3]  Henrique S. Malvar.  Fast computation of discrete cosine transform through fast Hartley transform , 1986 .

[4]  Hong Ren Wu,et al.  The structure of vector radix fast Fourier transforms , 1989, IEEE Trans. Acoust. Speech Signal Process..

[5]  J. Roese,et al.  Interframe Cosine Transform Image Coding , 1977, IEEE Trans. Commun..

[6]  P. Yip,et al.  Discrete Cosine Transform: Algorithms, Advantages, Applications , 1990 .

[7]  B. Lee.  A new algorithm to compute the discrete cosine Transform , 1984 .

[8]  M. Vetterli,et al.  Simple FFT and DCT algorithms with reduced number of operations , 1984 .

[9]  Yonghong Zeng,et al.  New algorithm for multidimensional type-III DCT , 2000 .

[10]  Michael W. Marcellin,et al.  Compression of hyperspectral imagery using the 3-D DCT and hybrid DPCM/DCT , 1995, IEEE Trans. Geosci. Remote. Sens..

[11]  Guoan Bi,et al.  Fast algorithms for type-III DCT of composite sequence lengths , 1999, IEEE Trans. Signal Process..

[12]  Nasir Ahmed,et al.  On Interframe Transform Coding , 1977, IEEE Trans. Commun..

[13]  Ephraim Feig,et al.  Scaled DCT's on input sizes that are composite , 1995, IEEE Trans. Signal Process..

[14]  M. Servais,et al.  Video compression using the three dimensional discrete cosine transform (3D-DCT) , 1997, Proceedings of the 1997 South African Symposium on Communications and Signal Processing. COMSIG '97.

[15]  Boon-Lock Yeo,et al.  Volume Rendering of DCT-Based Compressed 3D Scalar Data , 1995, IEEE Trans. Vis. Comput. Graph..

[16]  Jaehee You,et al.  One- and two-dimensional constant geometry fast cosine transform algorithms and architectures , 1999, IEEE Trans. Signal Process..

[17]  J. Makhoul.  A fast cosine transform in one and two dimensions , 1980 .

[18]  Chi-Wah Kok,et al.  Fast algorithm for computing discrete cosine transform , 1997, IEEE Trans. Signal Process..

[19]  Borko Furht,et al.  TheXYZAlgorithm For Real-Time Compression of Full-Motion Video , 1996, Real Time Imaging.

[20]  Borko Furht,et al.  Xyz video compression: an algorithm for real-time compression of motion video based upon the three-dimensional discrete cosine transform , 1996 .

[21]  Didier Le Gall,et al.  MPEG: a video compression standard for multimedia applications , 1991, CACM.

[22]  Martin Vetterli,et al.  Trade-off's in the computation of mono- and multi-dimensional DCT's , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[23]  Said Boussakta,et al.  Radix-2 × 2 × 2 algorithm for the 3-D discrete Hartley transform , 2001, IEEE Trans. Signal Process..

[24]  S. C. Chan,et al.  Direct methods for computing discrete sinusoidal transforms , 1990 .

[25]  Cairong Zou,et al.  A generalized fast algorithm for n-D discrete cosine transform and its application to motion picture coding , 1999 .

[26]  K. L. Ho,et al.  A new two-dimensional fast cosine transform algorithm , 1991, IEEE Trans. Signal Process..

[27]  Hsieh S. Hou.  A fast recursive algorithm for computing the discrete cosine transform , 1987, IEEE Trans. Acoust. Speech Signal Process..

[28]  Wan-Chi Siu,et al.  Mixed-radix discrete cosine transform , 1993, IEEE Trans. Signal Process..

[29]  Yonghong Zeng,et al.  Combined Polynomial Transform and Radix-q Algorithm for Multi-dimensional DCT-III , 2002, Multidimens. Syst. Signal Process..

[30]  E. Feig,et al.  On the multiplicative complexity of discrete cosine transforms , 1992, IEEE Trans. Inf. Theory.

[31]  David Akopian,et al.  Constant geometry algorithm for discrete cosine transform , 2000, IEEE Trans. Signal Process..

[32]  Athanassios N. Skodras,et al.  COMPARATIVE PERFORMANCE EVALUATION OF ALGORITHMS FOR FAST COMPUTATION OF THE TWO-DIMENSIONAL DCT , 1994 .

[33]  Pierre Duhamel,et al.  Polynomial transform computation of the 2-D DCT , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[34]  Hussein M. Alnuweiri,et al.  A new multidimensional recursive architecture for computing the discrete cosine transform , 2000, IEEE Trans. Circuits Syst. Video Technol..

[35]  Yun Liu,et al.  PVH-3DDCT: an algorithm for layered video coding and transmission , 2000, Proceedings Fourth International Conference/Exhibition on High Performance Computing in the Asia-Pacific Region.

[36]  Moon Gi Kang,et al.  DCT-based regularized algorithm for high-resolution image reconstruction , 1999, Proceedings 1999 International Conference on Image Processing (Cat. 99CH36348).

[37]  Ephraim Feig,et al.  Fast algorithms for the discrete cosine transform , 1992, IEEE Trans. Signal Process..

[38]  Kai-Kuang Ma,et al.  On the computation of two-dimensional DCT , 2000, IEEE Trans. Signal Process..

[39]  Khalid Sayood,et al.  Introduction to Data Compression , 1996 .

[40]  Shen-Chuan Tai,et al.  An adaptive 3-D discrete cosine transform coder for medical image compression , 2000, IEEE Transactions on Information Technology in Biomedicine.

[41]  R. Clarke,et al.  Relation between the Karhunen Loève and cosine transforms , 1981 .

[42]  Jianming Yang,et al.  Recognition of traffic marks in the images of WAHD lens by using color information and neural networks , 1998, IECON '98. Proceedings of the 24th Annual Conference of the IEEE Industrial Electronics Society (Cat. No.98CH36200).

[43]  Said Boussakta,et al.  Fast algorithm for the 3-D discrete Hartley transform , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[44]  D. Legall,et al.  MPEG : A video compression standard for multimedia applications , 1991 .

[45]  Ming Lei Liou,et al.  Overview of the p×64 kbit/s video coding standard , 1991, CACM.

[46]  N. Ahmed,et al.  Discrete Cosine Transform , 1996 .

[47]  Yui-Lam Chan,et al.  Variable temporal-length 3-D discrete cosine transform coding , 1997, IEEE Trans. Image Process..

[48]  Young-Min Kim,et al.  Fast Scene Change Detection using Direct Feature Extraction from MPEG Compressed Videos , 2000, IEEE Trans. Multim..