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

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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 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

### 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

• Camera is moving

• Relative to camera, all object appear to be moving

### Characteristics

• 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

• 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

### Redid Calculations

• 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

### 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/Micro-UAV Applications“

### 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 (2)

where u & v are the optic flow vectors

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

• Ixu + Iyv + ItDt = 0