  We present an approach to computing spatial information based on Fourier
coefficient distributions. The Fourier transform (FT) of an image contains a
complete description of the image, and the values of the FT coefficients are
uniquely associated with that image. For an image where the distribution of
pixels is uncorrelated, the FT coefficients are normally distributed and
uncorrelated. Further, the probability distribution for the FT coefficients of
such an image can readily be obtained by Parseval's theorem. We take advantage
of these properties to compute the spatial information in an image by
determining the probability of each coefficient (both real and imaginary parts)
in the FT, then using the Shannon formalism to calculate information. By using
the probability distribution obtained from Parseval's theorem, an effective
distance from the completely uncorrelated or most uncertain case is obtained.
The resulting quantity is an information computed in k-space (kSI). This
approach provides a robust, facile and highly flexible framework for
quantifying spatial information in images and other types of data (of arbitrary
dimensions). The kSI metric is tested on a 2D Ising ferromagnet, and the
temperature-dependent phase transition is accurately determined from the
spatial information in configurations of the system.
