Transcript Altitude Sensor with Optical Flow Math 680 Professor A

Optical Flow
Math 680
Professor A. Hicks
Given by: Bill Green & Rares Stanciu
What is Optical Flow?

Optical flow is the velocity field which warps
one sequential image to another
First Condition

Camera is stationary
– Only objects that are moving have optic flow vectors
Second Condition
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Camera is moving
– Relative to camera, all object appear to be moving
Characteristics
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Objects in close proximity will appear to be
moving faster than far away objects
Optical Flow Formula
OF = w + (v/d) sin q
Other Applications

Conclude if objects are undergoing linear or
rotational motion
 Determine the distance between the camera
and the object
 Tracking moving objects
Challenges with Optical Flow

Correspondence Problem
– Relating pixels in
corresponding images via a
rotation and translation

Aperture Problem
– only able to measure the
component of optical flow
that is in the direction of the
intensity gradient.
Autonomous Landing of UAVs

The UAVs altitude can be calculated from
optical flow
– “Obstacle” is the ground; q = 90
– UAV does not rotate during landing
Our Experiment

Determine distance to obstacle using 2
sequential images
OF = v/d
v
d
Top view
First Attempt

Calculate optic flow
– Threshold and binarize the images
– Find image centroids
– OF value of 110 pixels/sec was calculated
– distance, d, to the target was found
 1 inch (actual dist was 22 ft)
Find the Calibration Constant
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Took 2 sequential images

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Distance from object to
camera was known
Camera’s velocity was also
known
Compute optic flow
 OF = 140; vcam = 12
in/s; d = 163 in
Find K => OF = vcam/dK
K = 5.26 E-4
Redid Calculations

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
Distance from object to camera
was unknown
Camera’s velocity was known
Compute optic flow
 OF = 108; vcam = 15 in/s
Find d => OF = vcam/dK
d = 22 feet
Actual distance was 22’ 6”
Error = 2.22%
Matlab Code
Feature Tracker =>
Load images
centroid
Threshold
Calculate distance
between 2 centroids to
obtain OF vector
Binarize
Compute
centroid
Optic Flow Sensor
References
B.K.P. Horn and B.G. Schunck. “Determining optical flow”,
AI Memo 572. Massachusetts Institute of Technology,
1980.
 Barrows, G., Chahl, J.S., Srinivasan, M.V., "Biomimetic
Visual Sensing and Flight Control", 2002 Bristol UAV
Conference, Bristol, UK April 2002
 Barrows, G., Neely, C., "Mixed-Mode VLSI Optic Flow
Sensors for In-Flight Control of a Micro Air Vehicle", SPIE,
San Diego, CA, July 2000
 Barrows, G., "Future Visual Microsensors for Mini/MicroUAV Applications“

Questions??
Mathematical Background

Assumption: The apparent brightness of moving
objects remains constant between frames
– I(x(t+Dt), y(t+Dt), t+Dt) = I(x(t), y(t), t)

(1)
Taylor expansion of the left term
– I(x(t+Dt), y(t+Dt), t+Dt) =
I(x(t), y(t), t) + Ixu + Iyv + ItDt
where u & v are the optic flow vectors

From (1) and (2), optical flow equation is:
– Ixu + Iyv + ItDt = 0
(2)