This paper gives a summary of our research on pattern regularity. Periodic structures are perceived by humans as regular in a wide range of viewing angles. This observation motivates the development of a regularity based feature vector whose affine invariance is justified theoretically and tested experimentally. The vector is derived from the interaction map of a pattern. Several alternative but closely related definitions of the interaction map are discussed. The maximal regularity, a component of the feature vector, is shown to be consistent with human judgement on regularity. This feature can be implemented as a run filter, allowing for regularity based image filtering. Three applications of the regularity approach are presented. First, it is used for affine-invariant texture classification. Then, detection of periodic structures in aerial images is demonstrated. Finally, the texture inspection problem is addressed and structural defects are found as locations of low regularity.