  When interacting in a three dimensional world, humans must estimate 3D
structure from visual inputs projected down to two dimensional retinal images.
It has been shown that humans use the persistence of object shape over
motion-induced transformations as a cue to resolve depth ambiguity when solving
this underconstrained problem. With the aim of understanding how biological
vision systems may internally represent 3D transformations, we propose a
computational model, based on a generative manifold model, which can be used to
infer 3D structure from the motion of 2D points. Our model can also learn
representations of the transformations with minimal supervision, providing a
proof of concept for how humans may develop internal representations on a
developmental or evolutionary time scale. Focused on rotational motion, we show
how our model infers depth from moving 2D projected points, learns 3D
rotational transformations from 2D training stimuli, and compares to human
performance on psychophysical structure-from-motion experiments.
