The mechanisms underlying conscious visual perception are often studied with either binocular rivalry or perceptual rivalry stimuli. Despite existing research into both types of rivalry, it remains unclear to what extent their underlying mechanisms involve common computational rules. Computational models of binocular rivalry mechanisms are generally tested against Levelt's four propositions, describing the psychophysical relation between stimulus strength and alternation dynamics in binocular rivalry. Here we use a bistable rotating structure-from-motion sphere, a generally studied form of perceptual rivalry, to demonstrate that Levelt's propositions also apply to the alternation dynamics of perceptual rivalry. Importantly, these findings suggest that bistability in structure-from-motion results from active cross-inhibition between neural populations with computational principles similar to those present in binocular rivalry. Thus, although the neural input to the computational mechanism of rivalry may stem from different cortical neurons and different cognitive levels the computational principles just prior to the production of visual awareness appear to be common to the two types of rivalry.