Good Continuation in Rows or Frieze Symmetry

Abstract

Repetition of similar objects in equal spacing along a straight line is very salient to the human eye. This kind of symmetry is known as frieze or row symmetry and present in many environments, in particular in the man-made world, such as arts or architecture. A selection of published methods and models for the recognition of such symmetry is reviewed. This chapter also presents a corresponding operation. It differs from the reflection symmetry operation of the previous chapter in its arity: Input is an n-tupel of parts where n is at least two. Given a set of objects of non-trivial size an enumeration of all n-tupels for search for salient friezes is intractable. Accordingly, the chapter presents greedy search methods of low computational complexity. Actually, the parts should also be in proximity, and all kinds of similarity laws can be fused in the assessment of the constructed row.