1. Object Distance Detection using a Joint Transform
Correlator
Alexander Layton
Dept. of Computer Science
University of Illinois at Urbana-Champaign
Urbana, IL
Dr. Ronald Marsh
Dept. of Computer Science
University of North Dakota
Grand Forks, ND
Abstract—Computer stereo vision makes heavy use of object
distance detection. The primary method to detect object distance
is to compare two images of the same scene taken from different
vantage points. The necessity of comparing two images naturally
leads us to investigate optical correlators.
Since the Fourier transform, on which optical correlators are
based, is lossless, we suppose that distance information encoded in
a stereo image pair is preserved through the correlation process.
We then try to recover that distance by investigating the location
of the correlation peaks.
Initial data indicates that we may plausibly extract distance
information from a correlation result. However, this data was
gathered under very specific and controlled conditions, and
further research is necessary to derive a more general result.
Keywords—computer vision; stereo vision; optics; optical
correlation; joint transform correlator; distance detection
I. INTRODUCTION
A. Optical Correlators
An optical correlator is a device for comparing two images
using Fourier transforms. More specifically, an optical
correlator takes in two input images and outputs their cross-
correlation. We may think of the correlation result as locating
one image inside the other. If the two input images are
sufficiently similar, we will see a bright spot in the correlation
result, hereby referred to as a peak. The location of the peak
indicates the location of one image within the other.
A. VanderLugt developed the first successful optical
correlator, the matched filter correlator, in 1963 [1]. The
matched filter correlator (MFC) pioneered development of
optical correlators and is still in use today. However, the MFC
design requires specialized hardware and is highly sensitive to
the alignment of its instruments.
The MFC was originally designed to locate a particular
image, known as the “reference” or “filter” image, inside many
other images, the “target” or “input” images. As such, the
reference and target image are treated differently within the
correlator, and the MFC is best suited to such asymmetrical
applications.
To overcome the limitations of the matched filter correlator,
Weaver and Goodman invented the joint transform correlator
(JTC) in 1966 [2]. The JTC is much less sensitive to instrument
alignment but is less space-efficient. Additionally, both input
images in a JTC undergo the same transformations, without
regard for a “target” or “reference” image. Thus, the JTC is
better suited to applications without preferential treatment of
either input image. (It should be noted, however, that while the
JTC does not discriminate between input images, the
correlation result depends on each image’s position in the focal
plane. Thus we will not obtain the same result if we swap our
two input images.)
Optical correlation need not be done optically anymore; the
same process can be performed programmatically [3]. Though
the correlation is no longer real-time, one has the opportunity
to post-analyze the correlation result.
B. Application to Object Distance Detection
The root of computer stereo vision is using two or more 2D
images to reproduce a 3D scene. In particular, a computer
detects the distance to an object by measuring the shift in the
object’s 2D location from one vantage point to another [4].
Comparing two images of the same object leads us naturally
to explore optical correlators. Since the Fourier transform is
lossless, we posit that any distance information encoded in the
original images will be preserved in their correlation. In effect,
the correlator automates the process of finding a common pixel
in the algorithm outlined in [5]. Since we use a new pair of
images for each distance measurement, the joint transform
correlator is the appropriate design.
This experiment is entirely exploratory in nature; we are
only concerned with the plausibility of applying optical
correlation to object distance detection, not the practicality. We
hope, however, that this research may find applications in
space, where the background is more or less static.
Nevertheless, to the best of our knowledge, the use of a JTC to
determine distance to an object is a novel approach.
II. EXPERIMENT
A. Setup
Images were generated by two Microsoft LifeCam Cinema
webcams aligned horizontally with 9.5” baseline separation
between cameras (Fig. 1). LifeCam Cinema webcams have a
73° field of view and an autofocusing lens.
This research was made possible by the National Science Foundation,
Award #1359224, with support from the Department of Defense.

2. Fig. 1. Microsoft LifeCam Cinema webcams used for data collection.
Fig. 2. Post-It note on wall from 5ft away.
The subject was a 2”x1.5” Post-It note on a wall (Fig. 2).
We photograph a wall to minimize the confounding effect of
the background on the correlation. To this end, we make sure
the wall is as evenly lit as possible. The Post-It note was chosen
to highly contrast the wall, making it easier for the JTC to
identify the object.
B. Procedure
We measured the distance to the wall with a tape measure,
then took a picture with each camera. We used ImageMagick to
crop each image and then extract the value channel, producing
a black-and-white square image for the correlator. Each input
image served once as the “target” and once as the “filter.” The
correlation program also attempted to detect correlation peaks
using an algorithm developed by Dr. Marsh. The actual distance
and peak data were exported into an Excel spreadsheet.
The cameras would frequently fail to focus on the wall; this
led to blurry input images that would not produce a strong
correlation peak. These correlation results were thrown out.
Frequently, a peak would be plainly visible but not strong
enough for the algorithm to detect it. For example, a peak that
occupies two pixels in the output image would slip through the
detector since neither pixel has sufficient contrast with its
neighbor, despite being clearly enough resolved to be a useful
data point. In these cases, the peaks locations were entered
manually.
III. DATA
Each stereo pair of input images (Fig. 3) produced a pair of
correlation results (Fig. 4).
Fig. 3. A pair of input images.
Fig. 4. A pair of correlation results. The peak is the cross-shaped mark.
Fig. 5. Coordinates of the peak vs. distance from wall.
We plot the location of the peak versus the distance to the
wall to find a clear relation (Fig. 5). Coordinates of the peak are
measured from center, since distance to the wall should not
depend on the size of the image. Note that we take the absolute
value of the coordinates since swapping the input images
negates the peak’s coordinates.
A. Wrapping and Flipping Effect
As distance to the object decreases, the X coordinate of the
peak increases, up to a maximum of half the image size. With
our testing environment, this occurs at around 1.5 feet. If actual
distance to the object decreases beyond that, the peak will wrap
around the image and then get both coordinates flipped:
0
50
100
150
0 2 4 6 8 10 12
|PeakX,Y|
Distance
Distance vs. |Peak X,Y|
|Peak X| |Peak Y|

3. Fig. 6. Effects of an off-image peak.
B. Regression
If we restrict our analysis to distances that do not produce
the above “flipping” effect, we may invert the data and a
regression becomes quite obvious (Fig. 7). Excel gives the
following logarithmic model:
. | | .
It is important to note that this formula was generated under
the specific conditions, including a 73° field of view and a 9.5
in baseline, but it is expected to lay the groundwork for a more
general formula. With this formula we were able to determine
distances from 2 ft to 5 ft, with an accuracy of ±3 in.
Fig. 7. Absolute value of peak x vs distance.
IV. CONCLUSIONS
The work to date achieved its goal of proving that distance
can be recovered from a joint transform correlation peak. While
this work shows promise, further work is needed to elucidate and
generalize the relationship between peak location and distance.
This will move us closer to the ultimate goal of finding a formula
relating Peak X, Peak Y, field of view, baseline, and distance.
The wrapping and flipping effect presents a formidable
challenge to this goal, and will likely be the next target of
investigation. Another obvious direction future research will
take is to test the effect of varying baseline on the location of the
correlation peak.
Finally, at this time the method has not been tested for
practical applications like the CubeSat platform (for which this
research was originally conceived). The work to date and near-
future work is entirely proof of concept, and we may expect that
applications follow once a strong foundation is laid.
ACKNOWLEDGMENT
This material is based upon work supported by the National
Science Foundation Research Experience for Undergraduates
under Grant No. (NSF 1359244).
REFERENCES
[1] A. Vander Lugt, "Signal detection by complex spatial filtering," IEEE
Transactions on Information Theory, vol. 10, pp. 139-145. 1964.
[2] C. S. Weaver and J. W. Goodman, "A Technique for Optically
Convolving Two Functions," Applied Optics vol. 5, pp. 1248-1249. 1966.
[3] A. J. Barry and R. Tedrake, "Pushbroom stereo for high-speed navigation
in cluttered environments," Robotics and Automation (ICRA), 2015 IEEE
International Conference on, Seattle, WA, 2015, pp. 3046-3052.
[4] Jernej Mrovlje and Damir Vrančić, “Distance measuring based on
stereoscopic pictures,” 9th International PhD Workshop on Systems and
Control: Young Generation Viewpoint. 2008.
[5] E. Tjandranegara, “Distance Estimation Algorithm for Stereo Pair
Images,” Purdue ECE Tech. Rep., West Lafayette, IN, Rep. 64, 2005.
[6] R. Mandelbaum, L. McDowell, L. Bogoni, B. Reich and M. Hansen,
"Real-time stereo processing, obstacle detection, and terrain estimation
from vehicle-mounted stereo cameras," Applications of Computer Vision,
1998. WACV '98. Proceedings., Fourth IEEE Workshop on, Princeton,
NJ, 1998, pp. 288-289.
y = -2.059ln(x) + 11.529
R² = 0.9812
0
2
4
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0 20 40 60 80 100 120
Distance
|Peak X|
|Peak X| vs. Distance