Question

I was reading about pixel per foot but can someone teach how can i calculate the pixel per foot?
If given the resolution 640(horizontal) x 480(vertical), lens range from 2.8 mm – 12 mm, distance = 16ft (around 5 meter) and pixel per foot equals to?

Anyone?

Answer 1

I think I understand what you mean – you want to calculate how wide an image is in real-world units?

If you know the angle of the field of view f, and the distance to the target d, you can calculate the width w of plane visible at that distance with a bit of trig.

    <------------------w-------------------->                                               
    *****************************************                    
     *                ^ * <-----o------>   *                          
      *               | *                 *                           
       *              | *                *                            
        *             | *               *                             
         *            | *              *                              
          *           | *             *                               
           *          | *            *                                
            *         d *           *                                 
             *        | *          *                                  
              *       | *         *                                   
               *      | *        *                                    
                *     | *       *                                     
                 *    | * f/2  *                                      
                  *   | *     *                                       
                   *  | *    *                                        
                    * v *   *                                         
                     *  *  *                                          
                      * * *                                           
                       ***                                            
                        *                                             

So, remember the old school SOH CAH TOA? tan(angle) = opposite / adjacent. We want to calculate the opposite dimension o, and we know that the adjacent is d and the angle is is f/2, so we get o = tan(f/2) * d

o is half the width, so we double it to give our final calculation of w = d * tan(f/2) * 2

So, now you know the real-world width w of the plane d units from the camera, and you know your image is p pixels wide, the pixels-per-unit is simply p/w

The only problem that remains is calculating the field of view angle f from the focal length of the lens – that’s a little more specialised. This depends on the camera, particularly the size of the image sensor. You can generate a table for many popular cameras here http://www.howardedin.com/articles/fov.html.

If you know the size of the image sensor, or are using 36mmx24mm film negatives, you can use this formula to calculate the FOV for a “normal” rectilinear lens:

fieldOfView = 2 * arctan (sensorWidth / (2 * focalLength))