Perimetric complexity is a measure of the complexity of binary pictures. It is defined as the sum of inside and outside perimeters of the foreground, squared, divided by the foreground area, divided by 4p . Difficulties arise when this definition is applied to digital images composed of binary pixels. In this paper we identify these problems and propose solutions. Perimetric complexity is often used as a measure of visual complexity, in which case it should take into account the limited resolution of the visual system. We propose a measure of visual perimetric complexity that meets this requirement.