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Updated: May 10, 2026
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High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
Published on: December 3, 2013
Two-dimensional orthogonal DCT expansion in trapezoid and triangular blocks and modified JPEG image compression
Jian-Jiun Ding1, Ying-Wun Huang, Pao-Yen Lin
1Graduate Institute of Communication Engineering, National Taiwan University, Taipei 106, Taiwan. djj@cc.ee.ntu.edu.tw
Summary
This study generalizes the JPEG algorithm using trapezoid and triangular blocks for image compression. This novel approach enhances compression ratios and image quality (PSNR) compared to standard methods.
Area of Science:
- Digital image processing
- Signal processing
- Data compression
Background:
- Conventional JPEG uses 8x8 blocks and 2-D DCT for image encoding.
- Existing shape-adaptive algorithms can be complex and introduce boundary errors.
Purpose of the Study:
- To generalize the JPEG algorithm for improved image compression.
- To explore the orthogonality of 2-D DCT on non-rectangular blocks.
- To achieve higher compression ratios and better image quality.
Main Methods:
- Investigated the orthogonality of 2-D DCT on trapezoid and triangular blocks.
- Developed a generalized JPEG algorithm using these non-rectangular blocks.
- Compared performance against standard JPEG and other shape-adaptive algorithms.
Main Results:
- The 2-D DCT is orthogonal in trapezoid and triangular blocks.
- The proposed algorithm achieves higher Peak Signal-to-Noise Ratio (PSNR) at fixed bit rates.
- Reduced overhead for encoding object edges compared to exact shape matching.
Conclusions:
- Generalizing JPEG with trapezoid and triangular blocks offers superior compression and quality.
- The method avoids high-frequency errors at block boundaries.
- Applicable to various orthogonal bases beyond 2-D DCT.
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