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# Optical Flow Math 680 Professor A. Hicks Given by: Bill Green & Rares Stanciu - PowerPoint PPT Presentation

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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### 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%

Threshold

Binarize

Calculate distance between 2 centroids to obtain OF vector

Compute centroid

Matlab Code

• 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

• From (1) and (2), optical flow equation is:

• Ixu + Iyv + ItDt = 0