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.

A neural model for the integration of stereopsis and motion parallax in structure-from-motion.

We introduce a model for the computation of structure-from-motion based on the physiology of visual cortical areas MT and MST. The model assumes that the perception of depth from motion is related to the firing of a subset of MT neurons tuned to both velocity and disparity. The model's MT neurons are connected to each other laterally to form modulatory receptive-field surrounds that are gated by feedback connections from area MST.

Motion in depth from interocular velocity differences revealed by differential motion aftereffect.

There are two possible binocular mechanisms for the detection of motion in depth. One is based on disparity changes over time and the other is based on interocular velocity differences. It has previously been shown that disparity changes over time can produce the perception of motion in depth.

A reversed structure-from-motion effect for simultaneously viewed stereo-surfaces.

A spatially flat stimulus is perceived as varying in depth if its velocity structure is consistent with that of a three-dimensional (3D) object. This is structure from motion (SFM). We asked if the converse effect also exists.

Seeing motion in depth using inter-ocular velocity differences.

An object moving in depth produces retinal images that change in position over time by different amounts in the two eyes. This allows stereoscopic perception of motion in depth to be based on either one or both of two different visual signals: inter-ocular velocity differences, and binocular disparity change over time. Disparity change over time can produce the perception of motion in depth.

Computing relief structure from motion with a distributed velocity and disparity representation.

Recent psychophysical experiments suggest that humans can recover only relief structure from motion (SFM); i.e., an object's 3D shape can only be determined up to a stretching transformation along the line of sight.