分離法( Split method )為一種以分離影像像素為基礎的影像放大方法，本研究主要目的為改善分離法。分離法最初是針對黑白影像所設計的，如車牌影像，因此分離法較不適用於其他影像。而原始的分離法為零階( Zero-order )分離法，在此我們提出ㄧ階( 1st order )以及二階( 2nd order )的分離法，希望分離法能夠應用於灰階度變化較複雜的影像。為了探討何種方法為較佳的影像放大方法，本研究將測試上述方法與各種常見的影像放大方法以進行比較。
　　本研究所使用的測試影像共有三種類型，第一種測試影像是經由退化模型所模擬的低解析度影像；第二種測試影像是實際拍攝之低解析度影像；第三種測試影像是影像處理領域常見之影像。最後本研究再進一步討論雙立方內插法與二階分離法的優劣。由實驗結果可知本研究所提出的影像放大方法除了快速、簡單，還能夠有效的提高影像對比度，且使影像輪廓較為清晰。

The objective of this study is to improve split method which was previously proposed for image enlargement. The split method was originally designed for image with two levels such as vehicle license image enlargement. Therefore, it might not fit for other purpose. And we noted the original split method as zero-order split method. In this study, a 1st order and 2nd order split method are proposed. For comparison, the proposed methods and several image enlarging methods are tested.
There are three sets of test images were used in this study. The first set of images is images degraded from a referential image. The second set of images is low resolution images taken directly from camera. The third set of images is some images frequently used in literature. Further comparison is made between the proposed 2nd order split method and the bi-cubic interpolation method. Results show that the proposed methods are not only simple but also increasing image contrast and clearing image outline.

[1] Y. C. Chien, “Reconstruct Low-resolution License plate Images Base on Static Image Enlargement, “ 國立清華大學動力機械工程學系碩士班, 碩士論文, 2007.

[2] R. R. Schultz, R. L. Stevenson, “A Bayesian approach to image expansion for improved definition,” IEEE Trans. on Image Processing, vol. 3, pp. 233-242, 1994

[3] R. Y. Tsai, T. S. Huang, “Multiframe image restoration and registration,” Advances in Computer Vision and Image Processing, vol. 1, pp. 317-339, 1984.

[4] S. C. Park, M. K. Park, M. G. Kang, “Super-resolution image reconstruction: a technical overview,” Signal Processing Magazine, IEEE, vol. 20, pp. 21-36, 2003.

[5] W. K. Pratt, Digital Image Processing, Toronto, Ont. Canada: Wiley, 1978.

[6] R. G. Keys, ”Cubic Convolution Interpolation for Digital Image Processing,” IEEE Trans. vol. ASSP-29, pp. 1153-1160, 1981.

[7] X. Li and M. T. Orchard, “New Edge-Directed Interpolation,” IEEE Trans. on Image Processing, vol. 10, pp. 1521-1527, 2001.

[8] G. Ramponi, ”Warped Distance for Space-Variant Linear Image Interpolation,” IEEE Trans. on Image Processing, vol. 8, pp. 629-639, 1999.

[9] J. G. Leu, “Edge sharpening through ramp width reduction,” Image and Vision Computing, vol. 18, pp. 501-514, 2000.

[10] M. J. Chen, C. H. Huang, W. L. Lee, “A fast edge-oriented algorithm for image interpolation,” Image and Vision Computing, vol. 23, pp. 791-798, 2005.

[11] W. T. Freeman, E. C. Pasztor, and O. T. Carmichael, “Learning Low-Level Vision,” International Journal of Computer Vision, vol. 40, pp. 25-47, 2000.

[12] W. T. Freeman, T. R. Jones, and E. C. Pasztor, “Example-Based Super-Resolution,” IEEE Trans. Computer Graphics and Applications, vol. 22, pp. 55-65, 2002.

[13] S. A. Nene, S. K. Nayar, “A Simple Algorithm for Nearest Neighbor Search in High Dimensions,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, pp. 989-1003, 1997.

[14] S. Baker and T. Kanade, “Limits on Super-Resolution and How to Break Them,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, pp. 1167-1183, 2002.

[15] J. Sun, N. N. Zheng, H. Tao, and H. Y. Shum, “Image Hallucination with Primal Sketch Priors,” Proceedings of CVPR ’03, Madison, Wisconsin, pp. 729-736, 2003.

[16] C. Su, Y. Zhuang, L. Huang, and F. Wu, “Steerable Pyramid-based Face Hallucination,” Pattern Recognition, vol. 38, pp. 813-824, 2005.

[17] Z. Wang, F. Qi, “On Ambiguities in Super-Resolution Modeling,” Signal Processing Letters, IEEE, vol. 11, pp. 678-681, 2004.

[18] M. V. Joshi, S. Chaudhuri, and R. Panuganti, “A Learning-Based Method for Image Super-Resolution From Zoomed Observations,” IEEE Trans. on System Man and Cybernetics, vol. 35, pp. 527-537, 2005.

[19] R. C. Gonzalez, R. E. Woods, “Digital Image Processing 2/E,” Prentice Hall Publication, pp. 57-58, pp. 220-262, 2002.

[20] E. D. Castro, C. Morandi, “Registration of translated and rotated images using finite Fourier transform,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.9, pp. 700-703, 1987.