Abstract: A method of characterizing alignment between two images includes receiving a first data set representative of a reference image, receiving a second data set representative of a target image, processing the first and second data sets that includes calculating an autocorrelation of the first data set to obtain a third data set that is substantially absent information representative of a relative shift between the reference image and the target image, and processing the third data set that includes calculating a Radon transform of the autocorrelation of the first data set to obtain a fourth data set that includes information representative of a relative rotational difference between the reference image and the target image.

Abstract: The method identifies a Pixon element, which is a fundamental and indivisible unit of information, and a Pixon basis, which is the set of possible functions from which the Pixon elements are selected. The actual Pixon elements selected from this basis during the reconstruction process represents the smallest number of such units required to fit the data and representing the minimum number of parameters necessary to specify the image. The Pixon kernels can have arbitrary properties (e.g., shape, size, and/or position) as needed to best fit the data.

Abstract: The method identifies a Pixon element, which is a fundamental and indivisible unit of information, and a Pixon basis, which is the set of possible functions from which the Pixon elements are selected. The actual Pixon elements selected from this basis during the reconstruction process represents the smallest number of such units required to fit the data and representing the minimum number of parameters necessary to specify the image. The Pixon kernels can have arbitrary properties (e.g., shape, size, and/or position) as needed to best fit the data.