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Proceedings Paper

Two-dimensional orthogonal DCT expansion in triangular and trapezoid regions
Author(s): Soo-Chang Pei; Jian-Jiun Ding; Tzu-Heng Henry Lee
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Paper Abstract

It is known that the 2-D DCT basis is complete and orthogonal in a rectangular region. In this paper, we introduce the way to generate the complete and orthogonal 2-D DCT basis in a trapezoid region or a triangular region without using the complicated Gram-Schmidt method. Moreover, since a polygon can be decomposed several triangular regions, the proposed method is also suitable for the polygonal region. Our algorithm can much generalize the JPEG algorithm. Instead of dividing an image into 8 by 8 blocks, we can divide an image into trapezoid or triangular regions and then transform and code each of them. In addition to the DCT basis, our method can also be used for generating the 2-D complete and orthogonal DFT basis, KLT basis, Legendre basis, Hadamard (Walsh) basis, and polynomial basis in the trapezoid and triangular regions.

Paper Details

Date Published: 4 August 2010
PDF: 10 pages
Proc. SPIE 7744, Visual Communications and Image Processing 2010, 77442D (4 August 2010); doi: 10.1117/12.863477
Show Author Affiliations
Soo-Chang Pei, National Taiwan Univ. (Taiwan)
Jian-Jiun Ding, National Taiwan Univ. (Taiwan)
Tzu-Heng Henry Lee, National Taiwan Univ. (Taiwan)

Published in SPIE Proceedings Vol. 7744:
Visual Communications and Image Processing 2010
Pascal Frossard; Houqiang Li; Feng Wu; Bernd Girod; Shipeng Li; Guo Wei, Editor(s)

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