find speed from object size growth in video

Question

if I have a video of a car coming at me, can I find the speed it is traveling by the growth of the car over time. for example, if it takes two seconds for the height of the car (from my perspective) to double, can I find out how fast it is coming at me? I figure it would be something about if it doubles in size, it is twice as close. And if it took 2 seconds to get twice as close....????

Sorry if this has already been asked but I couldn't find it.

thanks

Mark

Answer 1

No.

In this picture

you don't have enough information to determine the distance covered in $2$ seconds, even with an estimate of the height of the car. You'd need to know the angle too.

Arguing from similar triangles shows you are right that the distance to the car halves when its apparent height doubles (my sketch isn't accurate).

Answer 2

Unless you know how big the object is, you can't determine how fast it is moving.

As proof of that, consider a real car moving at some speed towards a camera from some initial distance, and a model car moving similarly - where the speed and initial distance of the model (from the camera) are scaled by the ratio of the dimensions of the model to the dimensions of the real car. The two videos would look identical (allowing for possible inaccuracies in the model and focusing limits in the camera), but the speed of the car and model are obviously different.

But even if you know the object you still cant determine speed unless you know teh viewing angle.

As proof of that, consider a car moving at 10 m/s initially 20 m away and travelling for 1 second until it is 10 m away, and a second car moving at 100 m/s initially 200 m away and traveling for 1 second until it is 100 m away. Both cars will double in size over that second, but if the first is photographed using a wide angle lens and the second with a telephoto lens then the two videos could look identical.

So you need to know the size of the object, and the magnification of the lens before you can calculate the objects speed. (Even then you could be fooled if the video is played back at the wrong speed.)