This book presents a geometric framework for the efficient detection of regular repetitions of planar (but not necessarily coplanar ) patterns in images. At the heart of the system lie the fixed structures of the transformations that describe these regular configurations. The approach detects a number of configurations that have traditionally dealt with separately, in that all configurations corresponding to planar homologies are detected. These include important cases such as periodicities, mirror-symmetries and reflections about points. The approach can handle perspective distortions and avoids to get trapped in combinatorics through invariant-based hashing for pattern matching and through Hough transforms for the detection of fixed structures. The performance of the system is demonstrated with several examples.