Heading Estimation using Centric-Minded Templates

Paolo Cavalleri, Silvio P. Sabatini, Fabio Solari and Giacomo M. Bisio
DIBE - University of Genoa, Via Opera Pia 11a, 16145 Genova, ITALY

As Gibson already observed in 1950 (Gibson, 1950 The perception of the
Visual World), the optic flow plays a relevant role in visual navigation.
In fact, the flow pattern experienced by an observer moving along a straight
line through a static environment contains a singularity (focus of expansion)
that, in the condition of absence of eye movements, represents the direction
towards which the observer is moving. Therefore,
the outflow originating from this point can be used to estimate the observer's
heading direction. Neurophysiological studies evidenced that cortical cells in
the medial superior temporal (MST) area are involved in the analysis of visual
motion and their large receptive fields suggest the idea that navigation is
guided by global properties characterizing large portions of the visual field.
Previous computational models of MST cells (Perrone and Stone, 1994 Vision
Res. 34 2917-2938; Lappe et al., 1998 J. Neuroscience
16 6265-6285) proposed that each cell codes a specific heading direction.

We propose a model for heading estimation in which there are no cardinal cells
for each heading direction and the estimation of global motion parameters
depends on the whole activity of the cell population. The model cells perform
a local analysis of the optic flow characterized with respect to a common
log-polar reference frame centered on the fixation point. The introduction of
a log-polar mapping of the optic flow is indeed a natural way to describe the
visual field with respect to the fovea.

Accordingly, each model cell is a unit selective to an expansion flow
referred to the fixation point and is characterized by a specific
tuning to the mean speed of motion of the optic flow stimuli. From a behavioral
point of view, these cells act as centric-minded templates performing a
vector filter matching (cf. Perrone & Stone, 1994) between cell preferences
and local portions of the optic flow stimuli.

The heading direction is determined with respect to the gaze direction by
analyzing the distribution of the cell response: the peak activity of
the expansion cells locates the portion of the visual field where the optic
flow is maximally radial. Specifically, the peak is located in the region
opposite to the focus of expansion with respect to the fovea and its angular
coordinate represents the direction opposite to the one towards which it is
necessary to turn the gaze to locate the heading direction. When the direction
of gaze coincides with the direction of heading the spatial distribution of
cell activity is uniform along the angular coordinate, whereas the more the two
directions are diverging, the more the activity is concentrated around a
particular angle. Thus, the degree of uniformity of the cells' output provides
an estimate of the distance of the focus of expansion from the fovea.

Extensive simulations validated the approach, evidencing that the global
distribution of the cells response provides "ecological" information about the
heading, useful to guide the gaze towards the translation direction.