Reflection symmetry

Reflection symmetry is a standard example for the role of perceptual grouping in foreground/background discrimination. The basic relations of reflection symmetric arrangements of oriented parts are given. Hard constraints are replaced by continuous membership assessments. Next to the reflection law, the parts always also need to be in proximity, for which specific continuous assessment functions are discussed. Furthermore, the symmetry is stronger when additionally other features of the parts are similar, such as size, colors, or descriptors. If smaller parts are further away from each other, nested hierarchies of symmetries should be considered. Examples for this are given. Most reflection symmetry recognition procedures use clustering, often implemented in accumulators. A theory for this accumulation is based on a contrario testing. In practice, the reflection symmetry is often distorted due to perspective projection. For this case an algebraic solution using homogeneous coordinates is presented.