How to extract velocity in mm unit using Optical Flow

I am using Optical Flow to extract metrics as velocity and angle of a moving object. The output of Optical Flow is (u,v) which are the velocities (in pixel unit I assume) in x and y axes. My question is how to convert the resultant u and v (pixel) into mm?

I saw that different techniques can be applied as taking an image of a ruler and evaluate how many pixels in i.e. mm. I think this is not a good solution beause it depends on the intrinsic and extrinsic parameters of the camera.

Answer 1

[Prakhar Rai]

Using this you could calculate it for your situation/dpi :

dpi is the pixel density or dots per inch.

96 dpi means there are 96 pixels per inch.

1 inch is equal to 25.4 millimeters.

1 inch = 25.4 mm

dpi = 96 px / in

96 px / 25.4 mm

Therefore one pixel is equal to

1 px = 25.4 mm / 96

1 px = 0.26458333 mm

[Fahad Aljehani]

Thank you @Prakhar Rai for your useful response. I have one concern regrading the radial distortion of an image or some projective geometry. I believe and correct if I am wrong that the camera calibration is a must task to do before mapping the pixels to some real distance mm. Do you think using the pixel density can deal with such images/video?

[Prakhar Rai]

Yess camera calibration can deal with radial distortion of an image.

The radial distortion coefficients model this type of distortion. The distorted points are denoted as (xdistorted, ydistorted):

xdistorted = x(1 + k1*r2 + k2*r4 + k3*r6)

ydistorted= y(1 + k1*r2 + k2*r4 + k3*r6)

• x, y — Undistorted pixel locations. x and y are in normalized image coordinates. Normalized image coordinates are calculated from pixel coordinates by translating to the optical center and dividing by the focal length in pixels. Thus, x and y are dimensionless.
• k1, k2, and k3 — Radial distortion coefficients of the lens.
• r2: x2 + y2

Typically, two coefficients are sufficient for calibration. For severe distortion, such as in wide-angle lenses, you can select 3 coefficients to include k3.

You could refer this link : calibration calibrator radialDistortion

Specialized software packages as Photomodeler or Camera Calibration toolbox for Matlab are designed for the calibration of non-metric cameras.

Calibration is the solution of radial distortion and pixel density won't help you much.

[Fahad Aljehani]

Thanks @Prakhar Rai