  Perception is often viewed as a process that transforms physical variables,
external to an observer, into internal psychological variables. Such a process
can be modeled by a function coined perceptual scale. The perceptual scale can
be deduced from psychophysical measurements that consist in comparing the
relative differences between stimuli (i.e. difference scaling experiments).
However, this approach is often overlooked by the modeling and experimentation
communities. Here, we demonstrate the value of measuring the perceptual scale
of classical (spatial frequency, orientation) and less classical physical
variables (interpolation between textures) by embedding it in recent
probabilistic modeling of perception. First, we show that the assumption that
an observer has an internal representation of univariate parameters such as
spatial frequency or orientation while stimuli are high-dimensional does not
lead to contradictory predictions when following the theoretical framework.
Second, we show that the measured perceptual scale corresponds to the
transduction function hypothesized in this framework. In particular, we
demonstrate that it is related to the Fisher information of the generative
model that underlies perception and we test the predictions given by the
generative model of different stimuli in a set a of difference scaling
experiments. Our main conclusion is that the perceptual scale is mostly driven
by the stimulus power spectrum. Finally, we propose that this measure of
perceptual scale is a way to push further the notion of perceptual distances by
estimating the perceptual geometry of images i.e. the path between images
instead of simply the distance between those.
