Quantifying the information content of lattice images

Quantitative information may be extracted from local areas of images that consist of one or more types of unit cell. Fourier-space analysis, real-space intensity analysis, and real-space vector pattern recognition are discussed. The pattern recognition approach efficiently exploits the available information by representing the intensity distribution within each unit cell of the image as a multidimensional vector. Thus, the amount and the effect of noise present are determined, statistically significant features are identified, and quantitative comparisons are made with model images. In the case of chemical lattice images, the position of a vector can be directly related to the atomic composition of the unit cell it represents, allowing quantitative chemical mapping of materials at near-atomic sensitivity and resolution. More generally, the vector approach allows the efficient and quantitative extraction of information from images, which consist of mosaics of unit cells.