Is perceptual space inherently non-Euclidean?

It is often assumed that the space we perceive is Euclidean, although this idea has been challenged by many authors. Here we show that, if spatial cues are combined as described by Maximum Likelihood Estimation, Bayesian, or equivalent models, as appears to be the case, then Euclidean geometry cannot describe our perceptual experience. Rather, our perceptual spatial structure would be better described as belonging to an arbitrarily curved Riemannian space.