Autostereograms can be perceived in different well-defined spatial levels. Therefore they are an excellent tool with which to examine spatiotemporal processes of multistable three-dimensional perception. We study properties of spatial ambiguity such as phase transitions between different spatial levels and hysteresis in perception with and without noise. We show that the perception of physical noise-which is added to the autostereograms in the form of a random dot pattern-is dependent on the perceived spatial level. We demonstrate that noise can be helpful for the perception of depth in some cases. We show that the signal-to-noise ratio of depth perception is enhanced at an intermediate level of noise strength that is the signature of stochastic resonance in depth perception.