Perceptual Coherence : Hearing and Seeing

118 Perceptual Coherence
coupled with changes in illumination, generate the more spread-out distribution
of higher brightness values. The variation of high illumination due to
lighting would create the high-frequency but low-amplitude components,
while the lack of variation in the low-illumination regions would create the
higher-amplitude low-frequency components. Attias and Schreiner (1998)
found a similar result for music, speech, and environmental sounds. There
are more extremely soft sounds than extremely loud sounds in all three
types of sounds, so that the large dynamic range of naturally occurring
sounds is due more to the abundance of soft sounds than the infrequent loud
sounds.
Ruderman (1997) proposed a different but not necessarily competing
explanation. Ruderman started by assuming that the reflection within objects
is basically constant but that the reflection from different objects
varies randomly. Thus the correlation in brightness between points within
an object must be high, but the correlation between points in different objects
must be zero. Furthermore, Ruderman argued that visual images are
made up of independent occluding objects and that the sizes of the objects
in the visual images follow a power law (a function in the form of 1/f c ). If
this is the case, then the correlation in brightness between pixels will follow
a power law function given the constant reflection within objects and
power law function of object size. Balboa, Tyler, and Grzywacz (2001) argued
that the power law spectra will emerge for nearly all scenes simply
due to the fact that objects have different sizes: The sizes of the objects do
not have to follow a power law. The authors claimed that small objects create
exponents close to −3 and big objects create exponents close to 0, so
that in a natural scene the exponent will be close to −1 due simply to the averaging
of the exponents. Balboa et al. made an interesting point about underwater
vision. Underwater blur tends to predominantly reduce the energy
at higher frequencies and thereby make the exponent more negative. Thus,
if the visual system evolved to match the energy distribution in the environment,
then we might expect slightly different sensitivities in underwater
animals.
The variation in illumination across the image can have two opposite effects.
First, if the illumination within one object varies, that variation can
increase the difference between the brightness of two pixels within that object,
which would make the distinction between objects weaker. Second, if
the illumination between objects changes, that variation can increase the
difference in brightness of the pixels in the different objects, which would
make the distinction between objects greater. Depending on the image,
variation in illumination can lead to stronger or weaker object formation.
Overall, variation in illumination tends to reduce the correlation among
pixels, making the exponent closer to 0 (i.e., white noise) for nearly all configurations
of objects.