CONVOLUTION-BASED INTERPOLATION FOR FAST, HIGH-QUALITY ROTATION OF IMAGES

This paper focuses on the design of fast algorithms for rotating image s and preserving high quality, The basis for the approach is a decompo sition of a rotation into a sequence of one-dimensional translations, As the accuracy of these operations is critical, we introduce a genera l theoretical framework that addresses their design and performance. W e also investigate the issue of optimality and present an improved lea st-square formulation of the problem, This approach leads to a separab le three-pass implementation of a rotation using one-dimensional convo lutions only, We provide explicit filter formulas for several continuo us signal models including spline and bandlimited representations. Fin ally, we present rotation experiments and compare the currently standa rd techniques with the various versions of our algorithm, Our results indicate that the present algorithm in its higher-order versions outpe rforms 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 obta ined with the sine-based algorithm, which can be implemented using sim ple one-dimensional FFT's.