This paper is an extension of a conference paper presented by the second two authors [1]. The authors consider the problem of how to fill in the blank pixel values that result from an affine rotation of a 2D image.

Given an angle of rotation θ = tan^-1p/q, the pixel located at (x,y) is mapped to the point (x’,y’) = (qx-py,px+qy). This rotation maps a unit square to a square with area p²+q² and gives rise to a sparse matrix, called a p:q lattice, in which the pixel values are separated by p rows and q columns. All other positions contain zeros. Area-based methods for filling vacant pixel positions depend on the fraction of each pixel area that lies within the p:q lattice. The authors claim that these asymmetric masks have certain disadvantages, including a property that enables one to detect the angle of rotation. To overcome these difficulties, they describe, in general terms, an in-filling symmetric mask algorithm that involves the solution of a linear system of Diophantine equations.

This could be a good idea for improving the quality of image rotations.