Accurate Image Rotation using Hermite Expansions - Park, Wooram (2009)
In this paper we propose an approach for the accurate rotation of a digital image using Hermite expansions. This exploits the fact that if a 2D continuous band-limited Hermite expansion is rotated, the resulting function can be expressed as a Hermite expansion with the same band limit. Furthermore, the Hermite coefficients of the initial 2D expansion and the rotated expansion are mapped through an invertible linear relationship. Two efficient methods to compute the mapping between Hermite coefficients during rotation are proposed. We also propose a method for connecting the Hermite expansion and a discrete image. Using this method, we can obtain the Hermite expansion from a discrete image and vice versa. Combining these techniques, we propose new methods for the rotation of discrete images. We assess the accuracy of our methods and compare with existing FFT-based methods implementing three shears. We find that the method proposed here consistently has better accuracy than FFT-based methods.