Two-dimensional orthogonal DCT expansion in triangular and trapezoid regions

Soo-Chang Pei; Jian-Jiun Ding; Tzu-Heng Henry Lee

doi:10.1117/12.863477

4 August 2010 Two-dimensional orthogonal DCT expansion in triangular and trapezoid regions

Soo-Chang Pei, Jian-Jiun Ding, Tzu-Heng Henry Lee

Proceedings Volume 7744, Visual Communications and Image Processing 2010; 77442D (2010) https://doi.org/10.1117/12.863477
Event: Visual Communications and Image Processing 2010, 2010, Huangshan, China

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.

Citation Download Citation

Soo-Chang Pei, Jian-Jiun Ding, and Tzu-Heng Henry Lee "Two-dimensional orthogonal DCT expansion in triangular and trapezoid regions", Proc. SPIE 7744, Visual Communications and Image Processing 2010, 77442D (4 August 2010); https://doi.org/10.1117/12.863477

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