2009 IEEE 8TH INTERNATIONAL CONFERENCE ON DEVELOPMENT AND LEARNING 1
Learning independent causes in natural images
explains the spacevariant oblique effect
Constantin A. Rothkopf, Thomas H. Weisswange, and Jochen Triesch
Frankfurt Institute for Advanced Studies, Frankfurt, Germany.
Email: {rothkopf, weisswange, triesch}@fias.uni-frankfurt.de
Abstract—The efficient coding hypothesis posits that sensory
processing increases independence between neural responses to
natural stimuli by removing their statistical redundancy reflective
of the structure present in the natural environment. While there
is consensus on the role of the statistical structure of the physical
environment in shaping the natural input to the sensory system,
it is not well understood how the sensory apparatus itself and its
active use during behavior determine the statistics of the input. To
explore this issue, a virtual human agent is simulated navigating
through a wooded environment under full control of its gaze
allocation during walking. Independent causes for the images
obtained during navigation are learned with algorithms that have
been shown to extract computationally useful representations
similar to those encountered in the primary visual cortex of
the mammalian brain. The distributions of properties of the
learned simple cell like units are in good agreement with a wealth
of data on the visual system including the oblique effect, the
meridional effect, properties of neurons in the macaque visual
cortex, and functional Magnetic Resonance Imaging (fMRI)
data on orientation selectivity in humans and monkeys. Finally,
this analysis sheds new light on the discussion on orientation
anisotropies based on carpented environments. Thus, when learn-
ing computational representations it is not sufficient to consider
only the regularities of the environment but also the regularities
imposed by the sensory apparatus and its use during behavior
need to be taken into account.
I. INTRODUCTION
It has been proposed that a fundamental principle for the un-
derstanding of neuronal computations involving sensory data is
that they have been shaped on evolutionary and developmental
timescales by the regularities in the environment [1], [2].
Theories of the encoding of natural stimuli based on their
statistical regularities have been successful at reproducing a
number of properties of neurons in visual cortical areas in
humans and animals [3], [4]. However, the dependence of
these statistics on the sensory apparatus and its active use have
been considered to a much lesser degree. This is surprising,
given that the active character of vision is well established [5],
[6], [7], [8]. Moreover, there is ample empirical data showing
that this active selection process is much less involuntary
and reactive as suggested by some experimental paradigms, if
vision is studied in its ecologically valid context of extended,
goal-directed, visuomotor behavior [9], [10], [11], [12].
Statistical models have been proposed in the past, which
aim at reducing the statistical redundancy of the brain’s repre-
sentation of natural images by considering their higher order
dependencies. Such models also can be viewed as generative
models, in which latent variables cause images according to
probabilistic formulations of the image generation process.
Applying such models to natural image ensembles has been
shown to learn receptive field like units as hidden causes [13].
But such learning has usually assumed stationary statistics
across the visual field and implicitly also independence from
the active selection process due to eye movements as well as
the imaging geometry. Such models therefore cannot explain
that visual performance on a wide variety of tasks depends on
the position within the visual field. As an example, perceptual
studies in humans have d reduced discrimination ability for
obliquely oriented patterns as compared to horizontal and
vertical ones in the central area of the visual field [14]. This
so called oblique effect varies with the position within the
visual field in that with increasing eccentricity sensitivity to
meridionally oriented stimuli increases [15].
A wealth of data on these psychophysical effects has
been collected not only in humans, but across species [14].
The attenuation in performance for obliquely oriented stimuli
compared to horizontal and vertical ones close to the fovea has
its correspondence in a non-uniform distribution of preferred
orientations in simple and complex cells in the primary visual
cortices of several species including ferrets [16], cats [17],
and monkeys [18]. These studies have also reported subtle
differences in orientation selectivity across species and even
across humans who have been raised in carpented versus
non-carpented environments [19]. Furthermore, fMRI studies
in monkeys and humans have shown a correlation between
the blood-oxygen-level-dependent (BOLD) activation in V1
during orientation discrimination tasks and the performance
on these tasks across different orientations [20].
While some aspects of the oblique effect can be understood
in terms of the second order statistics of natural images, as
quantified by their power spectrum [21], [22], the present
study investigates the role of higher order dependencies and
task behavior on properties of receptive fields across the
visual field. The dependencies that go beyond second order
are important, as removing the dependencies up to second
order leaves the spatial structure such as edges intact and
images with only correlational, i.e. second order structure
such as that of natural images, do not contain features such
as edges or contours. Indeed, receptive field like units that
are spatially localized, oriented, and band-pass in different
spatial frequency bands have been extracted from natural
images by maximizing higher-order moments. Thus, receptive
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