Here, we propose an ecological and perceptual form of the untangling hypothesis: naturally occurring image sequences follow perceptually linear trajectories. We estimated the perceptual linearity of image sequences by asking observers to discriminate between all pairs of frames. We then used signal detection theory to estimate the perceptual distances between these frames, and combined these to yield an estimate of the perceptual length and curvature of the entire sequence.

Consistent with our hypothesis, we find that a natural image sequence containing complex motion is nearly perceptually flat. That is, although the trajectory of the image pixels is highly nonlinear, the estimated perceptual curvature is not significantly different from zero. In contrast, an artificial sequence that follows a straight-line path between the end-frames of the same movie (i.e., "fading" from the first frame to the last) yields a perceptual path whose length is approximately twice the distance between the end frames, and thus highly curved. But not all sequences that follow straight-line paths in pixel space yield large perceptual curvature. For example, we find that an image sequence generated by gradually altering the contrast of the initial frame (as would occur when fog lifts) is also perceptually linear. Finally, consistent with previous physiological tests of untangling, we find that sequences generated by translating, dilating, or rotating an initial image produce minimal perceptual curvature.

These results provide direct evidence that image trajectories that occur in natural videos are linearized by the visual system, an ecological version of the "untangling" hypothesis. These results also suggest the possibility that the transformations of the ventral stream arise through an unsupervised learning process that aims to minimize the curvature of neural population response trajectories.