Displacement co-occurrence is used to describe the spatial dependence relationships of binary digital images, which in turn are used for disconnectedness detection and texture analysis. A ‘‘m-points-and-M-cells’’ model, in particular, is used to study onedimensional displacement co-occurrence statistics, which then is used for row-wise and column-wise two-dimensional image analysis. A compact state is used to characterize a case for aggregating pixels into a connected region, resulting in a regular straight-line distribution of the displacement co-occurrence histogram. An image pattern is described by a scattering state that usually yields an irregular histogram distribution. With reference to the compact state’s histogram, the vector norms of the scattering states’ histograms can be used to characterize the image’s disconnectedness feature. A connected line along horizontal or vertical orientations results in zero vector norms, and therefore, the nonzero vector norm indicates the presence of disconnectedness. The displacement cooccurrence histogram is invariant under translation, and shear deformation. Using a ‘‘W-points-and-MXN-lattice’’ model and the concept of rectangular rectification, any binary pattern can be considered as one of its scattering states. Two-dimensional displacement co-occurrence matrices yield the statistics of twodimensional displacement configurations, and can be used in texture analysis.