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 an
gles. This observation motivates the development of a regularity based feat
ure vector whose affine invariance is justified theoretically and tested ex
perimentally. 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, i
s shown to be consistent with human judgement on regularity. This feature c
an be implemented as a run filter, allowing for regularity based image filt
ering. 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 locatio
ns of low regularity. (C) 2000 Elsevier Science B.V. All rights reserved.