Invariants and Fixed Structures Lead the Way to Change

The use of invariants quickly gained impetus in the computer vision community. The paper recapitulates why this strand of research has become so influential by summarizing the traditional advantages often highlighted in the context of object recognition. Then, however, the paper moves on to corroborate the importance of certain geometrical entities, called “fixed structures”. It is argued that looking at these entities forms a core idea, that can be considered central to several applications. These include as diverse subjects as grouping and three-dimensional scene reconstruction. A careful and systematic study of fixed structures, the corresponding subgroups, and their invariants is advocated.