Measuring image similarity in the presence of noise

Measuring the similarity between discretely sampled intensity values of different images as a function of geometric transformations is necessary for performing automatic image registration. Arbitrary spatial transformations require a continuous model for the intensity values of the discrete images. Because of computation cost most researchers choose to use low order basis functions, such as the linear hat function or low order B-splines, to model the discrete images. Using the theory of random processes we show that low order interpolators cause undesirable local optima artifacts in similarity measures based on the L-2 norm, linear correlation coefficient, and mutual information. We show how these artifacts can be significantly reduced, and at times completely eliminated, by using sine approximating kernels.