Convolution-based interpolation for fast, high-quality rotation of images Export

@article{citeulike:5761023, abstract = {This paper focuses on the design of fast algorithms for rotating images and preserving high quality. The basis for the approach is a decomposition of a rotation into a sequence of one-dimensional translations. As the accuracy of these operations is critical, we introduce a general theoretical framework that addresses their design and performance. We also investigate the issue of optimality and present an improved least-square formulation of the problem. This approach leads to a separable three-pass implementation of a rotation using one-dimensional convolutions only. We provide explicit filter formulas for several continuous signal models including spline and bandlimited representations. Finally, we present rotation experiments and compare the currently standard techniques with the various versions of our algorithm. Our results indicate that the present algorithm in its higher-order versions outperforms all standard high-accuracy methods of which we are aware, both in terms of speed and quality. Its computational complexity increases linearly with the order of accuracy. The best-quality results are obtained with the sine-based algorithm, which can be implemented using simple one-dimensional FFTs}, author = {Unser, M. and Thevenaz, P. and Yaroslavsky, L.}, booktitle = {Image Processing, IEEE Transactions on}, citeulike-article-id = {5761023}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/83.465102}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=465102}, day = {06}, doi = {10.1109/83.465102}, journal = {Image Processing, IEEE Transactions on}, keywords = {fourier}, month = {August}, number = {10}, pages = {1371--1381}, posted-at = {2009-10-17 18:12:54}, priority = {2}, title = {Convolution-based interpolation for fast, high-quality rotation of images}, url = {http://dx.doi.org/10.1109/83.465102}, volume = {4}, year = {2002} }

TY - JOUR ID - citeulike:5761023 L3 - citeulike-article-id:5761023 N2 - This paper focuses on the design of fast algorithms for rotating images and preserving high quality. The basis for the approach is a decomposition of a rotation into a sequence of one-dimensional translations. As the accuracy of these operations is critical, we introduce a general theoretical framework that addresses their design and performance. We also investigate the issue of optimality and present an improved least-square formulation of the problem. This approach leads to a separable three-pass implementation of a rotation using one-dimensional convolutions only. We provide explicit filter formulas for several continuous signal models including spline and bandlimited representations. Finally, we present rotation experiments and compare the currently standard techniques with the various versions of our algorithm. Our results indicate that the present algorithm in its higher-order versions outperforms all standard high-accuracy methods of which we are aware, both in terms of speed and quality. Its computational complexity increases linearly with the order of accuracy. The best-quality results are obtained with the sine-based algorithm, which can be implemented using simple one-dimensional FFTs IS - 10 JF - Image Processing, IEEE Transactions on EP - 1381 TI - Convolution-based interpolation for fast, high-quality rotation of images VL - 4 T2 - Image Processing, IEEE Transactions on SP - 1371 KW - fourier AU - Unser, M AU - Thevenaz, P AU - Yaroslavsky, L PY - 2002/08/06/ UR - http://dx.doi.org/10.1109/83.465102 ER -