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Optical Flow Math 680 Professor A. Hicks Given by: Bill Green & Rares StanciuPowerPoint Presentation

Optical Flow Math 680 Professor A. Hicks Given by: Bill Green & Rares Stanciu

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Optical Flow Math 680 Professor A. Hicks Given by: Bill Green & Rares Stanciu

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Optical Flow Math 680 Professor A. Hicks Given by: Bill Green & Rares Stanciu

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Optical FlowMath 680Professor A. HicksGiven by: Bill Green & Rares Stanciu

- Optical flow is the velocity field which warps one sequential image to another

- Camera is stationary
- Only objects that are moving have optic flow vectors

- Camera is moving
- Relative to camera, all object appear to be moving

- Objects in close proximity will appear to be moving faster than far away objects

OF = w + (v/d) sin q

- Conclude if objects are undergoing linear or rotational motion
- Determine the distance between the camera and the object
- Tracking moving objects

- 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.

- The UAVs altitude can be calculated from optical flow
- “Obstacle” is the ground; q = 90
- UAV does not rotate during landing

- Determine distance to obstacle using 2 sequential images

OF = v/d

v

d

Top view

- 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)

- Took 2 sequential images

- 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

- 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%

Load images

Threshold

Binarize

Calculate distance between 2 centroids to obtain OF vector

Compute centroid

- Feature Tracker => centroid

- 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/Micro-UAV Applications“

- 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 (2)

where u & v are the optic flow vectors

- I(x(t+Dt), y(t+Dt), t+Dt) =
- From (1) and (2), optical flow equation is:
- Ixu + Iyv + ItDt = 0