Role of noise in image processing by the human perceptive system
M. Piana
INFM, Unita ` di Ricerca di Genova, I-16146 Genova, Italy
M. Canfora
Dipartimento di Fisica, Universita ` di Genova, Genova, Italy
M. Riani
INFM and Dipartimento di Fisica, Universita ` di Genova, Genova, Italy
Received 9 February 2000
Two psychophysics experiments are described, pointing out the significant role played by stochastic reso-
nance in recognition of capital stylized noisy letters by the human perceptive apparatus. The first experiment
shows that an optimal noise level exists at which the letter is recognized for a minimum threshold contrast. A
simple two-parameter model that best fits the experimental data is also discussed. In the second experiment we
show that a dramatically increased ability of the visual system in letter recognition occurs in an extremely
narrow range of increasing noise. Possible interesting future investigations suggested by these experimental
results and based on functional imaging techniques are discussed.
PACS numbers: 87.10.+e, 05.20.-y, 89.70.+c
I. INTRODUCTION
Stochastic resonance SR is a statistical phenomenon as-
sociated with nonlinear systems 1; for a large class of such
systems, an increase in the noise affecting the input signal
may induce an increase in the signal-to-noise ratio SNR in
the system’s output. The basic ingredients for SR to show up
are a coherent small signal, a form of energetic threshold,
and the possibility of varying the amount of noise affecting
the signal either by external addition or by some inherent
process. In this situation it can be shown 2,3 that there
exists an optimal level of noise maximizing the response of
the system in a resonancelike behavior. Experimental verifi-
cations of this effect have been performed in many areas of
applied physics and in biology 4,5see, for example, 6,7
for recent and rather complete reviews. The interest of such
a phenomenon in the processing of information by the bio-
logical neural system is evident at all levels from the lower
‘‘physiological’’ levels to the higher ‘‘cognitive’’ ones. For
sensory systems SR effects have been explored, for example,
in experiments on single mechanoreceptors from crayfish
tails 8, crayfish 9 and cricket 10 ganglion cells, rat hip-
pocampal cells 11, and human muscle spingles 12. At
higher levels of complexity in cognitive systems, SR effects
have been found in a neural network modeling the phenom-
enon of perceptual alternation occurring in the observation of
the so-called ambiguous pattern 13, in the human tactile
system 14, and in human visual perception 15,16. An
interesting behavioral experiment is described in 17, and in
18 the role of noise in the auditory system is reported. Both
these experiments may link stochastic resonance to evolu-
tion, that is, the use of SR can obviously have a survival
value and thus was selected for. The results of our experi-
ments may also point in the same direction. We are inter-
ested in the key question whether and how the human brain
exploits noise in order to enhance the quality of external
stimuli. This problem has been addressed in 15 with a psy-
chophysics experiment concerning visual perception of noisy
patterns. This experiment shows quantitatively that the hu-
man brain is helped by noise in detecting small details in
stationary images and that this visual enhancement is satis-
factorily modeled by a one-parameter SR curve obtained
from level-crossing detector theory 19.
In the present paper we discuss two experiments con-
cerned with the visual perception of noisy letters. More pre-
cisely, in experiment I, characterized by an experimental
paradigm similar to the one in 15, we produce images con-
taining one letter each that we painted over a uniform back-
ground and depressed under a fixed threshold, i.e., pixels
with gray level lower than the threshold are painted with the
same gray level as the background. Then we affect each
letter with noise of different standard deviations, and for
each presentation we smoothly increase the contrast between
the letter signal and the background until the subject recog-
nizes the letter. By plotting the contrast value for which the
letter is recognized by the subject versus the value of the
standard deviation characterizing the presentation, we can
show that an optimal noise level, where the recognition con-
trast value is minimum, can be detected. As the main results
of this experiment we obtain the following.
1 SR occurs when the human perceptive apparatus is
asked to recognize rather big stylized noisy capital letters
previously depressed under a fixed threshold.
2 A quantitative estimate of the optimal noise level can
be produced for all the subjects. Knowledge of the corre-
sponding contrast threshold is helpful for the realization of
the second experiment in this paper.
3 The theoretical model describing the detection of
small details in the experiment in 15 is here able to follow
only coarsely the trend of the noise effect on the contrast
threshold of the human visual system. However, we can pro-
vide a two-parameter modification of that model fitting our
data in a more reliable fashion.
In a second experiment experiment II each subject is
PHYSICAL REVIEW E JULY 2000 VOLUME 62, NUMBER 1
PRE 62 1063-651X/2000/621/11046/$15.00 1104 ©2000 The American Physical Society