Perceptual Coherence : Hearing and Seeing

Characteristics of Auditory and Visual Scenes 133
Figure 3.10. Basis functions trained from natural images. Each basis function resembles
a simple spatial frequency × spatial orientation cortical cell. The derived
functions can be roughly categorized into three categories: (A) odd symmetric with
one on- and one off-region; (B) even symmetric with an on-off-on configuration;
and (C) even symmetric with an off-on-off configuration. Each type of function occurs
at different frequencies, orientations, and positions within the 12 × 12 image
patch. Adapted from Olshausen, 2002.
contain objects at many different scales, frequencies, and locations, so that
it is highly unlikely that there is a minimum set of basis functions that
could encode such variability. Simoncelli, Freeman, Adelson, and Heeger
(1992) demonstrated that such an overcomplete set makes each basis function
represent a specific interpretation—the amount of structure at a particular
location, orientation, and scale. Moreover, it creates smooth changes in
the activities of the individual basis functions as a result of small changes
in the input, an obviously desirable outcome. The outcome of this simulation
is a set of basis functions that closely resemble the receptive field properties
of cells in V1, although these basis functions were derived only from
the properties of the images (see figure 3.10).
Bell and Sejnowski (1997) derived a solution similar to that of Olshausen
and Field (1996) using the information theory concept of maximizing
information by making the individual receptive field filters and
basis functions as independent as possible (independent component analysis).
Conceptually, each filter represents the receptive field of one cortical