Firefly Eindhoven - Remaining Sensors

Optical flow

Optical flow refers to estimation of apparent velocities of certain objects in an image. This is done by measuring the optical flow of each frame using which velocities of objects can be estimated. It is 2D vector field where each vector is a displacement vector showing the movement of points from first frame to second. By estimating the flow of points in a frame, the velocity of the moving camera can be calculated.

Working Principle

If [math]\displaystyle{ I(x,y,t) }[/math] is the intensity of a pixel in an image then after some time [math]\displaystyle{ dt }[/math], as the pixel moves some distance [math]\displaystyle{ dx }[/math] and [math]\displaystyle{ dy }[/math] then as the pixel intensity is consistent, it can be said that;

[math]\displaystyle{ I(x,y,t) = I(x+dx, y+dy, t+dt) }[/math]

Using taylor series, it is possible to write

[math]\displaystyle{ \frac{\partial I}{\partial x} \frac{\partial x}{\partial t} + \frac{\partial I}{\partial y} \frac{\partial y}{\partial t} + \frac{\partial I}{\partial t} = 0 }[/math]

In the above equation, the space differentials of intensity are refereed to as image gradients and the above equation is termed as Optical flow Equation. The time differentials of the pixel position [math]\displaystyle{ x, y }[/math] are the unknowns which determine the optical flow.

There are multiple algorithms in order to solve this problem, the most popular ones being:

• Lucas Kanade Method
• Phase Correlation