The main purpose of visual perception is to enable action in the physical world. Processing of visual input is done in neuronal circuits where little more than neighbouring relations may be taken for granted. Veridical notions of geometric concepts such as straightness of lines or distance between objects need to be established.

Mathematician Felix Klein postulated that each geometry is the study of invariants under certain groups of movements (Erlanger Programm 1872). The euclidean geometry is generated by the euclidean group of motions in space. The translation subgroup is generated by infinitesimally small movements. In visual perception, the nearest physiologically possible realization are microsaccades, which may be thought as generating the group homomorphism from physical translations into the geometry of visual space. If visual geometry is built up at demand, certain phenomena may be better understood. Human vision is able to detect the nonius alignment of straight lines with a hyperacuity down to 5 arcseconds. When the lines are separated by a gap, however, a much larger nonius error of some arcminutes may be observed. The need for continuously refreshing of the metric in visual space may be the reason why microsaccades occur regularly and frequently.