1. Optical Flow Based Navigation
Samuel Kim and Vincent Kee
Department of Cognitive and Neural Systems, Boston University, Boston, MA
Department of Electrical and Computer Engineering, Boston University, Boston, MA
This paper deals with the viability of optic flow based navigation as implemented on a robot with a webcam. The
first part discusses the need for such a technology, various filters that may be used to detect optic flow, and their
effectiveness. The second part discusses the results and possible future directions of the project.
!ABSTRACT:
As new technologies continue to develop, more and
more robots are replacing humans in situations
deemed too dangerous. However, current solutions
are not fully automated, requiring offsite human
operators for executing basic actions. The ideal
solution would be a fully autonomous vehicle that
could complete its objectives without any human
intervention. In this project, the viability of optical
flow based navigation was investigated. Optical
flow, or optic flow, is the perception of object
motion due to the object’s pixel shifts as the
viewer moves relative to the environment. First,
motion detection filters were developed and
applied to image sequences in MATLAB. Then,
they were implemented in optic flow based
navigation MATLAB programs for an iRobot
Create with a camera to provide video input. The
robot successfully traversed through a textured
environment but encountered difficulties when
attempting to avoid textured obstacles and
corners. Experiments were developed to compare
the effectiveness of the Correlation and Gabor
filters and to find the relationship between
increased motion detection ability and processing
time per frames. Possible future directions for this
project include implementing GPU (Graphics
Processing Unit), FPGA (Field-Programmable
Gate Array), or even ASIC (Application-Specific
Integrated Circuit) chips to speed up computation
time, utilizing a wide-angle camera or an array of
cameras to get a wider field of view, and
integrating a q learning system.
INTRODUCTION:
In today's technological world, more and more
autonomous machines are being designed to take the
place of their human counterparts, especially in what
are commonly known as dull, dangerous, and dirty
occupations. An especially urgent need for these types
of capabilities exists in military and emergency
response situations. Current solutions such as UAVs
(Unmanned Aerial Vehicle) often require GPS
coordinates and a sophisticated set of sensors to
maintain their position. In addition, they are not fully
autonomous and require a human operator for
executing operations more complex than maintaining a
position. This means that a constant connection with
the operator is required, and this leaves the connection
at the risk of hacking as has happened before.
Furthermore, human operators cannot operate around
the clock at the high performance required of many
missions. A fully autonomous vehicle capable of being
deployed in the midst of a site, adapting to the
environment, and accomplishing its objectives would
be ideal.
This project seeks to determine whether optical
flow is a viable solution for navigation. This will be
accomplished by implementing filters to detect optical
flow via a webcam onboard a moving robot (Fig. 1).
The first part of the paper discusses the development
of filters and implementation of them in generated
image sequences. The second part discusses the
effectiveness of optic flow and the various
relationships between changed parameters of the filters
and performance.
FILTERING IMAGES:
Different filters have been proven to be effective
in detecting motion and optical flow. For this study,
Correlation and Gabor filters were used.
Fig. 1 iRobot Create
with a Microsoft
Lifecam VX-5500!

2. Fig. 3a: Grayscale image of texture
Fig. 3b: Laplacian filter output with kernel from Fig. 2.1.
Fig. 3c: Laplacian filter output with kernel from Fig. 2.2.
Fig. 3d: Gaussian filtered image with kernel from Fig. 2.3.
Filters can be used to detect the edges of images
with texture. Laplacian and Gaussian filters were
written in MATLAB and then applied to grayscale
images. The output displayed edges in a white outline
and the surroundings in black are shown in Fig. 3.
The Laplacian filter is a high-pass filter; thus it
only allows high frequencies to pass and weakens the
signals of the lower frequencies. This filter essentially
sharpens images, emphasizing the edges (see Fig. 3b
and Fig. 3c).
The Gaussian filter is a low-pass filter. Because it
passes low frequencies and weakens and cuts off the
high frequencies, it results in the blurring or
“smoothing” of the image along the edges (Fig. 3d).
Each filter is defined by a kernel, a small array
that is applied to every pixel of the original image.
The process of applying the filters, known as
convolution, involves averaging the products of the
values of an array and the corresponding pixels of the
image. This final value that results is the new value
for the original center pixel. This convolution process
continues throughout the entire image. At the edges
of the image and beyond, the values are replicated
from the nearest pixels because they are the most
likely values for the pixels. Depending on the size
and values of the kernel, the image can be altered
drastically (Fig. 2).
1 2 3
a b
c d
There are many filters that can be used for
detecting optical flow. In this project, the
effectiveness of a Correlation Filter and Gabor Filter
were compared. The project started with motion
detection in one dimension and then in two
dimensions.
Correlation Technique:
The Correlation method, combined with the
Laplacian filter, was the first filter combination to be
implemented to compute optic flow and detect
motion. It requires at least two images, one at time t
and another at time t+1, to compute optical flow. It
compares each pixel in the first image with every
potentially corresponding pixel in the second image
and assigns a value based on their correlation factor.
If it correlates, it is assigned a value of one and the
color white. If it is opposite or anti-correlation, it is
assigned a value of negative one and the color black.
If it is not related at all or no correlation, it is
assigned a value of zero and the color gray.
Motion Correlation Algorithm:
!!" !
!!!!!!!!!!!!!
!!!
!!!!!!!!
!!! !!!!!!!!
!!!
!
"where n is the number of measurements of X and Y
and ! and ! are the sample means of X and Y. This
algorithm outputs a single value out of 1 that is the
correlation coefficient, formally known as Pearson’s
product-moment correlation coefficient. It is basically
the covariance (how much X and Y change together)
of X and Y, divided by the product of their standard
deviations.
Gabor Filter:
The Gabor Filter was also implemented for optical
flow based navigation. While the other filters
previously discussed were high pass or low pass
filters, allowing only high and low frequencies,
respectively, the Gabor filter is a band-pass filter.
This means that it allows a specified middle range of
frequencies to pass through. Moreover, it is a
spatiotemporal filter, meaning it can detect
orientation about the temporal and spatial domain.
For higher order motion detection, Gabor filters allow
for higher dimension kernels, which can help detect
motion in more than just the x and y axes.
Fig. 2: Kernel sizes and values for different filters

3. Shifted Image
x (pixel)
10 20
Dot
x (pixel)
10 20
theta = 90 degreestheta = 45 degreestheta = 0 degreestheta = -45 degreestheta = -90 degrees
Fig 4a: Input image and Filtered image at different orientations
Gabor Filter result
x (pixel)
v(pixel/frame)
2 4 6 8 10 12 14 16 18 20
-2
-1
0
1
2 0.05
0.1
0.15
0.2
0.25
0.3
Fig. 6: Motion detection of moving dot results
Input image
Abs Value of Gabor Filter
theta = -45 degrees
The Gabor Filter is defined as the product of a
Gaussian kernel multiplied by a complex sinusoid
and a real component cosine.
Two Dimensional Gabor Filter Algorithm:
! !! !! !! !! ! ! !!!! !!!! ! !!"#!!!!!!"! ! !"!!!
!!!! !!!! !
!
!!!!
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!!!
!
!
"!#!$%&'(!!!!!)!#!$%(*+!!!
$!#!,-.!/0121!.!*(!301!412*'5!'$!301!$6+&3*'+!
!!#!(37+5725!518*73*'+!
!!#!'2*1+373*'+!'$!$*9312!
!
*g(x,y) is the 2D Gaussian envelope. U and V are the
parameters that define the spatial frequency, f. For the
purpose of this project, a frequency of 1/7 and a
sigma value of 2 was used for obtaining optimal
results.
Because the Gabor filter is orientation-based, it is
phase sensitive. The detection of motion in a moving
image depends on how well the orientation of the
Gabor filter lines up with the perceived motion.
!
Motion Detection in One Dimension:
After successfully detecting the edges of images,
filters were applied in order to detect motion in one
dimension. Every two dimensional image can be
represented as many one dimensional lines, a one by
n matrix, shifting in either the left or right direction.
These individual lines represent the motion at
different times. In this case, the temporal domain is
represented by the y axis. Consider a black line with a
white dot on the left. In our experiment, we shifted
the dot until a succession of lines were created,
displaying a two dimensional image.
APPLYING FILTERS IN ONE DIMENSION:
Motion of pixels can be measured as velocities. In
our previous one dimensional pixel shift example, we
created a white dot in a black line and shifted it to the
right, showing the motion of the dot for fifteen
frames. When applying the Gabor filter, only one
frame is necessary in order to detect the continuous
motion of the image. In our case, the middle frame
was chosen as it is the most accurate measure of
detecting the average velocity. When the correlation
method was used, the two middle frames were chosen
to detect motion. In order to determine the velocity,
we set a range of velocities that we knew the speed of
the dot would be in.
In our experiment, a range of -10 to +10 in
increments of one velocity was used because the
motion we were dealing with fit within this range.
Moreover, moving at slower velocities in smaller
increments allows for more accurate results and
calculations of optic flow.
In the Moving Dot example, the dot speed was set
to +1 pixel/frame.
Moving Dot
x (pixel)
t(frame)
10 20
5
10
15
Fig. 5: A dot shifting to the right for 15 frames
Abs Value of Gabor Filter
theta = 45 degrees
Abs Value of Gabor
Filter
! = -45˚
Abs Value of Gabor
Filter
! = -45˚
!!! ! !!"!!!!!!!!! ! !!"!!!!!!!!!! ! !"!!!!!!!!!!!!! ! !"#!!!!!!!!! ! !"˚
Fig 4b: Different orientations of Gabor filter

4. input
x (pixel)
y(pixel)
10 20
10
20
shifted image
x (pixel)
y(pixel)
10 20
10
20
X-T Plane
x (pixel)
t(frame)
5 10 15 20
2
4
6
8
10
12
14
16
18
20
Fig 8: A line was shifted only the x direction. The X-T plane is
shown of the motion and the correct corresponding gabor filter
orientation.
theta = -45 degrees
The color bar to the right of the graph indicates
how well the orientation of the filter matches the
velocity of the pixelated dot. Because the filters
matches best with the velocity at +1pixel/frame, we
can conclude the velocity of the moving dot is
+1pixel/frame.
In the image, the Gabor filter seems to pick up
more velocities than just +1 pixel/frame. However,
when dealing with larger velocities and images, the
neighboring the velocities the Gabor filter picks up can
be disregarded and are insignificant.
For the motion correlation, it is clear that the
motion it detected was +1 pixel/frame, although the
results are random elsewhere.
MOTION DETECTION IN TWO DIMENSIONS:
As one dimensional motion can be displayed in a
two dimensional image, two dimensional motion can
be pictured in a three dimensional space. Motion is
nothing but a succession of moving frames at t time.
Because the time between each frame is infinitely
short, pixel movement is viewed as a continuous
motion.
To start simple, motion was generated only in the x
direction of a two dimensional image. In Fig. 7a, a
white two dimensional image with a vertical black
line was created, shifting one pixel to the right.
Within this sequence of frames (Fig. 7c), the frames
appear as a solid figure along the temporal domain
(Fig. 7b). Although dealing with a few frames can
cause pixelated motion to be very noticeable, there
little difference between pixelated and smooth motion
in the resulting filtered image.
Because this is a two-dimensional image, the
velocity can be seen as a vector with x and y
components. This moving line example has a velocity
of +1pixel/frame in the x direction and a velocity of 0
pixels/frame in the y direction.
APPLYING FILTERS IN TWO DIMENSIONS:
As seen from the two dimensional Gabor filter
algorithm, a new variable is introduced, theta. Theta
is the orientation or angle of the filter. With theta
being added to the equation, it makes the two
dimensional Gabor filter more accurate than other
two dimensional filters when analyzing motion. But
because motion is defined in terms of velocity rather
than angle, we defined the relationship between
theta and velocity V. Since this is a basic relationship
between angle and pixel/frame, the equation for
conversion is:
theta = atan(-V).
(Note that the negative velocity is to correct the
orientation of the image)
As stated before, since the Gabor filter now
detects orientation, it is phase sensitive, which means
it detects motion when the orientation fits the
perceived motion. In the moving line example, when
the line was shifted only in the x axis moving at a
velocity of +1pixel/frame, the motion could be seen
from the top surface of the three dimensional space.
For the Gabor filter, a velocity of the +1
pixel/frame corresponds to a -45 degree angle as
shown in Fig. 8.
For the Correlation method, the y-axis motion can
be detected with the two-dimensional motion version.
In the one dimensional motion version, the y-axis
motion velocity was kept at zero. However, in the case
of the moving line, motion in the y axis remains zero.
OPTIC FLOW:
After testing filters in the image sequences
generated, the filters were then implemented into
optic flow based navigation MATLAB programs with
Perception of Motion [1]
Fig 7: Displaying motion of a 2D image in three dimensions
! ! !!"!!!!!

5. the iRobot Create. Optic flow is the perception of
object motion due to the object’s pixel shifts as the
viewer moves relative to the environment. As the
pixels shift from frame to frame, they form vectors.
As a result, optic flow can be represented by a vector
field. The pixels shift outward in increasing
magnitude as they move further from the center.
MATERIALS AND METHODS:
Image Acquisition:
In this investigation, a webcam was mounted onto
the iRobot Create to stream the images via an active
USB extension to be processed off the robot. The
frames required for image processing were acquired
with a Microsoft Lifecam VX-5500. The webcam has
a resolution up to 640 by 320 and a frame rate of
twenty frames per second. It also has a relatively
narrow 55º field of view, which later proved to be a
problem.
Through a USB to Serial adaptor and another
active USB extension cable, the iRobot Create
received commands from the laptop running
programs through the MATLAB Toolbox. The
programs for the Correlation and the Gabor filter
were slightly different because of the way the filters
function.
In the Correlation filter implementation, an image
was taken, the robot moved forward 0.1 meter, and
then another image was taken (Fig. 10). In the Gabor
filter implementation, it was necessary to create a
stream of images to detect motion. An Audio Video
Interleave (.avi) video file consisting of 15 frames
taken at 20 frames per second was created as the
iRobot moved forward. In both implementations, the
resulting images were fed into the optic flow
function, which output the optic flow values.
Image Acquired from Robot
Optic Flow
Velocity Field
Fig. 9: An image of a textured wall was acquired as the iRobot
moved forward. Optic flow results are shown where the
velocity vectors are represented by the color wheel.
The difference between the
optic flow on the left and right
half was then computed.
Based on this value, the robot
either continued moving
forwards or turned left or right
at an angle dependent on the
magnitude of the overall optic
flow value. The robot was
programmed to turn to the
side with less optic flow
because theoretically, this was
the side the robot was farther
from. However, as we later
discovered, this was not
always true due to imperfect
conditions, equipment, and
possible errors with our
functions.
!
Fig. 10: Flow Chart of optic flow based navigation MATLAB
program for Correlation method. The Gabor filter implementation
was the same except that a stream of images was taken instead of two
frames.!

6. Program Parameters:
We predicted that the increase in motion detection
range directly correlates with an increase in
processing times. To get the fastest performance, the
range of velocities to detect for were set to be
relatively small (11 pixels) and the robot was to move
in small increments (0.1 meters) each time it stopped
to take a frame. This way, the robot would start and
stop in many small and relatively fast increments. In
addition to this, we did not detect for vertical pixel
shifts because we found that pixels did not move as
noticeably in the y axis. Only horizontal motion was
observed. This was also to speed up the processing
time.
In addition to varying the range of detected
velocities, parts of image center were cut out where
there was not much optic flow in order to speed up
processing times. Like the range of pixel shifts, we
tested and found that it too was directly correlated to
processing time. To speed up the program, 320 pixels
from the center were removed. We believed cutting
out the center pixels would not significantly affect
optical flow because the pixels in that spread had low
pixel shifts that didn’t amount to much. By doing
this, the size of the image was cut in half,
theoretically doubling the speed of processing
between each set of frames.
TESTING:
Although we assumed the relationships between
various factors of our factors and processing time, we
created tests to determine the exact correlations
between different parameters and processing time.
Both filters require a predefined range of pixel shifts
or velocities to detect for. The larger the range, the
more velocities can be detected. Because time is a
huge factor in real time navigation, time was
measured based on different parameters in the filters
in order to identify their relationships.
The following tests were conducted:
- Range of Velocities versus Time
- Size of Image Center versus Time
- Resolution Size versus Time
- Gabor Filter Size versus Time
- Navigating an arena without bumping into
walls
Besides measuring Range of Velocities vs. Time,
we measured the time based on how much of the
center of the image was cut out. As explained earlier,
often little to no optic flow is detected at the center.
All the large pixel shifts are at the edges of the image.
Therefore, cutting out the image center would
decrease the processing time without significantly
affecting our optical flow values.
For the resolution size, the area of the image taken
by the camera versus processing time per frame was
tested to determine how great the trade-off was
between higher resolution and time.
One test that was exclusive to the Gabor filter was
its size versus processing time per frame. Because the
number of frames the robot needs to capture depends
on the Gabor filter size, the time was measured for
the parameters of the filter.
In addition to time, the optic flow at different
angles from the wall was tested to see if the
computation of optic flow was correct. The angle was
measured in terms of how far it strayed off its course.
We predicted that greater the angle, the greater the
resulting absolute difference in optic flow.
For real time navigation, robot was to move about
an arena without bumping into walls. Later, obstacles
were introduced and the robot was to avoid them
accordingly.
!
Fig. 11: Diagram showing how the angle was measured!
Fig. 12: CAD of the robot arena

7. RESULTS:
Fig. 13a: Graph showing Velocity Range versus Processing
Time per frame for the Correlation method. The increase in
range directly correlates with the processing time as predicted.!
Fig. 13b: Graph showing Velocity Range versus Processing
Time per frame for the Gabor Filter. Just like the Correlation
method, there is a direct relationship between the two.
However, processing time was 3-4x times longer for the same
range of the velocities. !
Fig. 13c: An inverse relationship exists between the number of
pixels removed from the center of the image and the processing
time per frame for the Correlation Filter. The Gabor Filter had
same relationship, but with a longer processing time. Because
more of the center was cut out where there was little optic flow,
images took less time to process.!
Fig. 13d: A direct correlation was found between the Area
of Image processed and the processing time as predicted.
With Correlation filter, the tradeoff for a higher resolution is
only a few seconds. For the Gabor filter, however, the
tradeoff was a few minutes.!
Fig. 13e: The relationship between the Gabor Filter Size and
processing time is quadratic. The size of the Gabor is defined by
[Y X] = ndgrid(-len:+len,-len:+len) where len = length
Since doubling the length quadruples the size of the Gabor filter,
their relationship between the two is quadratic.
!!!
Fig. 13f: This shows a graph of the Optic Flow value versus the
Optical Angle for the Gabor Filter. The outliers of the graph
indicate an incorrect computation of optic flow from the
theoretical value. Furthermore, the optic flow values for given
angles were not consistent. The Correlation Method had even less
consistent results.!

8. Fig. 14 Obstacle Avoidance Dilemna
1 2 3 4
5 6 7
Note: Robot is represented by the circle with the inscribed isosceles triangle. Cylindrical textured
obstacle is represented by the red circle. Field of view is represented by the blue dotted line coming from
the vertex of the isosceles triangle.
Fig. 14.1: Robot moves forward,
detects more optic flow on the left
because textured obstacle is closer
than the back wall and left of center
line.
Fig. 14.2: Robot turns 15°
right, away from the obstacle.
Obstacle at edge of field of
view and more optic flow on
left side.
Fig. 14.3: Robot continues to
turn away from obstacle until
out of field of view.
Fig. 14.3: Robot detects optic flow
only on right side from the textured
wall so it turns left 15°, back
towards the obstacle.
Fig. 14.5: Obstacle appears in field
of view, possibly as rightward
motion. Another possible theory is
that the particles on the back wall
may appear as noise and may cause
more optic flow to be detected on
the right side.
Fig. 14.6: Robot turns another 15°
left towards the obstacle. Obstacle
of view.
Fig. 14.7: Robot directly facing the
textured cylinder detects
symmetrical optic flow so
continues going straight until it
collides into obstacle.

9. GABOR FILTER VS. CORRELATION:
The main difference between the Gabor filter and
the Correlation method was the quality of the output of
the optic flow field. For the Gabor filter, the velocity
vectors were clearly seen in the flow field, but at the
expense of significantly longer processing time. When
using the Correlation technique, the direction of flow
was in some cases hard to distinguish, but processing
time was much quicker. However, in terms of
navigation, the results were similar. Both methods
could not replicate a successful navigation through the
arena multiple times. Because many other factors were
changing and had to be considered when computing
the overall optic flow, each trial could not be
replicated in the same way.
CONCLUSION:
Although our implementation of the optic flow
based navigation program did successful traverse
through a textured environment, many aspects of the
application must change for optic flow to become a
feasible method of navigation.
First and foremost, the processing time per frame
must be exponentially cut down. The processing time
of the relatively faster Correlation method was
anywhere from two to over ten seconds depending on
the parameters. For real-time navigation, where a
typical camera captures frames at 30 frames per
second or higher, those frames must be all processed
as the robot is moving and constantly receiving new
frames. In addition, the two seconds achieved were
with detecting pixel shifts from -10 to +10. For real
world application, where drones such as the MQ-9
Reaper may be flying at up to 300 mph, the pixel
shifts being detected must be much larger. The
conclusion that the processing speed must be
exponentially increased is perhaps an understatement.
The next largest issue is the narrow field of view
of the camera (55!!. This problem often led to
incorrect computation of optic flow, sometimes even
in the wrong direction, which all compounded into
poor obstacle, wall, and corner avoidance. With a
narrow field of view, the obstacle does not enter the
view unless the iRobot is almost directly facing it.
Once the robot is partway past the obstacle, it loses
track of where the obstacle is until it reenters the field
of view. At that point, as depicted in the Fig. 14.6, the
obstacle fills the field of view and causes the robot to
continue moving forward until it collides into the
obstacle. In addition, there were problems when the
iRobot encountered walls and corners face on. If the
iRobot moves towards walls and corners
symmetrically, it computed equal but opposite values
of optic flow from the left and right side, which
resulted in little to no overall flow. Depending on the
distance from the wall, this would not be considered a
problem if the distance was far. However, when
dealing with close proximities, the iRobot has trouble
deciding whether to turn or go straight.
If these two issues can be solved, the lofty goal of
a fully autonomous and adaptable vehicle will be
much closer to being accomplished.
FUTURE DIRECTIONS:
There are many possible future directions for this
project. First and foremost, the biggest issue is the
slow image processing time. This is due in part to
running the programs through MATLAB.
Implementing the algorithms on a FPGA (Field-
Programmable Gate Array) or even ASIC
(Application-Specific Integrated Circuit) chip would
significantly speed up the computations. Another
possible solution would be to write code that would
take advantage of GPUs with their parallel processing
to do the optic flow computations.
To solve the issues with the narrow field of view,
a wide angle webcam could be used. Another
possible solution would be to use an array of
webcams and then stitch the frames together to form
one high quality panoramic image. This would allow
the robot to keep obstacles in the field of view and
allow the robot to avoid them more proficiently. The
same would apply for wall navigation.
Perhaps the most intriguing future direction for
this project is to develop a robot q learning system. It
would be a points reward system to 'teach' the robot
to navigate using optic flow. The robot should be able
to eventually avoid obstacles after many trial runs.
For example, if the robot is navigating under certain
conditions and it runs into an obstacle, it would get a
negative point. Whenever the robot makes the correct
decision and avoids the collision, the robot gets a
positive point. Eventually, after repeatedly
committing the same error, it would learn to avoid the
obstacle. Ultimately, the robot would learn to adapt
on its own. This feature, if successfully developed,
would definitely get us closer to having robots that
could function and adapt to new situations without
human operators.

10. ACKNOWLEDGEMENTS
We would like to thank Schuyler Eldridge, Florian
Raudies, and Dr. Ajay Joshi for helping us immensely
with this project.
We could not have gone as far as we did without
the help of Florian Raudies with the filters and optic
flow concepts. Even sacrificing some of his work
time to help us, he was a main driving force in our
project.
We would like to thank Schuyler Eldridge for
helping us troubleshoot some of the key interfacing
and performance issues with the iRobot Create
implementations.
We would like to thank Dr. Ajay Joshi for being
our mentor and supporting us every step of the way.
Even though he was extremely busy, he would
always meet up and arrange time to check up on our
progress.
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