Perceptual problems in aeronautics were studied. The mechanism by which color constancy is achieved in human vision was examined. A computable algorithm was developed to model the arrangement of retinal cones in spatial vision. The spatial frequency spectra are similar to the spectra of actual cone mosaics. The Hartley transform as a tool of image processing was evaluated and it is suggested that it could be used in signal processing applications, GR image processing

Wandell, B. A.

English

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Computational models of
human vision with applications
Final close out, October 1985
Prepared by
Professor Brian A. Wandell
Department of Psychology
Stanford University
Stanford, CA 94305
(NASA—CR- 176413) COMFUTATICNAL MODELS OF
HU!!AN VISION IITH APPLICATIta^ 
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Report, Oct. 1985 (Stanford ULiv.) 7 1; 06P
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N86-15858
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G3/52 16357
•'	 September-12, 1985	 1
Final Report for NW-44
Brief Background
The initial program program of research studies on perceptual problems in
aeronautics was initiated in 1977 by the Joint Institute for Aeronautics and
Acoustics of the Department of Aeronautics and Astronautics at Stanford
University. The last three year period of this program, which terminating in
October, has been supported under NASA grant 2-44. Prof. Brian Wandell of the
Stanford University Department of Psychology has acted as co-principal
investigator with Prof. Karamcheti and Prof. Roberts of the Department of
Aeronautics and Astronautics. 'Ile program has also enjoyed the active
participation of several members of the present staff at NASA-Ames Aerospace
Human Factors Research Divison. Specifically, Dr. David C. Nagel, Dr. Albert
Ahumada, Dr. Andrew Watson and Dr. Ken Nielsen have all participated in the
ongoing research acitivities of the grant over the last several years. On the basis of
discussions between Drs. Nagel, Ahumada and Watson and Prof. Wandell, it was
decided to initiate a new program of research studies for a period of three years
from November 1984 to October 1987. This new program is under the auspices of
the Stanford University Department of Psychology with Prof. Brian Wandell acting
as principal investigator. The new award replaces the function of NC 2-44 which
we now are closing out.
J,)	 September 12, 1985
In the past we have submitted annual progress reports describing tl
ongoing research activities supported by NC 2-44. In this final close-out 1
describe the research supported during the past year.
Human color vision
When working in a room illuminated by the sun during the day an
fluorescent or tungsten light during the evening, we notice almost no change ,n Lne
colors of objects. The perceptual ability to discount spectral variation of the
illumination -- thereby maintaining the appearance of object colors -- is called color
constancy. The mechanism by which color constancy is achieved remains the
outstanding problem in the analysis of human color vision.
A solution to the problem of how color constancy is achieved is also
essential to correct color rendering in photography, television, and the construction
of artificial visual systems for robotics. In photography such a process will make
possible the use of only a single type of color film for most different lighting
conditions, ranging from daylight to fluorescent. In professional video and TV
recordings the transmitted signal can be corrected for distortions arising from the
ambient light, reducing the need for precise control of lighting within the studio.
A similar advantage can be gained in the processing of color film in the movie
industry. It will not be necessary to use intense lighting in order to overcome the
natural lighting present: rather one can compensate and correct for the ambient
1	 September. 12, 1985	 3
lighting during the development process. And finally, this method can serve as an
important means of discriminating different surfaces -- such as fruit sorting --
under conditions in which the ambient light cannot be perfectly controlled. •
Spatial Vision
Allen Poirson has spent part of his time working on aspects of spatial vision.
In collaboration with Dr. A. Ahumada of the Ames Research Center 's Aerospace
Human Factors Research Division, Allen has been developing a computable
algorithm to model the arrangement of the retinal cones. The spacing of the
retinal cones -- and the match or mis-match of this spacing compared with the
resolution of the lens -- is an important determinant of the visual system's ability
to resolve small targets and to avoid aliasing artificats.
Ahumada and Poirson have been working on a model of how the spacing of
photoreceptors occurs in across the retina For the central foveal region of viewing
they have developed a random -size, hard-disk, close-packing model of receptor
spacing. For the parafovea and periphery they have developed a simpler, non.
overlapping Poisson-distributed hard -disk model that gives a fair approximation to
the anatomically observed cone mosaic. The spatial frequency spectra of the
sampling functions generated by the models are similar to the spectra of actual
cone mosaics.
41
t^ f
September 12, 1985	 4
Other models, such as jittered lattice models, have striking differences
between their spectra and the observed spectra. This rules out a large class of
potential models. The work on sampling lattice arrays has interesting application
for the presentation of high resolution images on video displays.
Hartley transform
In addition to working on the sampling distribution of the photoreceptor
mosaic, Poirson has collaborated with A. B. Watson and B. Wandell on
implementing and evaluating the performance of the Hartley Transform as a tool
in image processing.
The Hartley transform was originally defined and analyzed by Hartley at the
Bell Labs. It represents an alternative transform to the Fourier transform with
many of the same properties but a few potential advantages. First, like the Fourier
transform, the Hartley transform represents signals with respect to the sinusoidal
and cosinusoidal basis functions. Unlike the Fourier transform, the Hartley
transform maps real signals into real signals and it is its own inverse. The Fourier
transform, of course, maps complex signals into complex signals and a sign change
in the complex exponential is required in order to compute the inverse Fourier
transform.
Two years ago R. Bracewell discovered a method for computing the Fast
Hartley Transform (FHT'), which parallels the method for computing the Fast
September-12, 1985
	 5
Fourier Transform ( FFT). This means that the Hartley transform could become
quite practicable in various signal processing applications, and in particular in image
lb
processing applications. Indeed, through Stanford Unversity Bracewell has applied
for a patent based on the Hartley Transform.
Poirson and Wandell have implemented the FHT on a VAX 780 running
UNIX BSD 4.2 in the C programming language. They have begun to evaluate the
performance of the FHT with the conventional FFT. In addition, Poirson, Watson
and Wandell have begun to analyze the extension of the Hartley transform from a
one-dimensional transform -- the case completely worked out by Bracewell -- to a
two-dimensional transform that could be applied to image data. The initial results
of the simulations and corresponding convolution theorems for two-dimensional
image processing have been disappointing. Based on their simulations there is
little reason to believe that the Hartley transform will outperform the Fourier
transform.
The principal advantage of the Hartley transform at this point appears to be
	 .
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its logical simplicity in mapping real signals into a real transform output. This may
prove to be of some value in teaching, but it is not likely to offer significant
improvement as a tool for research over conventional signal processing algorithms
based on the FFT.
September 12, 1985	 6
Conclusions
The several years of support through NC-2-44 have been very productive.
•
A number of fine young scientists have been supported at Stanford, and in some
cases (such as Dr. Nielsen) these scientists have gone on to become valued
members of the staff at the Ames Research Center. Poirson is presently working
at Ames and plans to return to graduate school at Stanford. I think we can be
proud of the contribution that this project has made not only in terms of new
research, but also in terms of training productive scientists who will continue to be
contributing members of the scientific and engineering communities.
30


Computational models of human vision with applications

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