# How can one calculate the velocity of an object that appears as a blur?

Around how could you estimate the speed of an object which appears as a blur to the human eye? And by blur I mean to the extent it is hard to trace or make out. I looked this up but the best I could get is people saying it was a "Complicated Formula", I do understand size and distance to the eye are important, but not sure about the formula that keeps getting mentioned.

If not exactly to see blur, around how would it be to where it becomes difficult to process the movement. I am also fine with mere estimations, I do not require an exact number if an exact number cannot be found.

If it is not possible to calculate, I do understand, many things are incalculable. You need simply inform me that it cannot be calculated via a simple formula.

• Are you comfortable with the idea of uncertain measurements and calculations based on them?
– Dan
Commented Dec 18, 2021 at 18:35
• As I believe I said, yeah, estimations or somewhat uncertain measurements are fine as long as they are relatively within an acceptable margin of error. This is mostly just for relative measurements of the speed of a character in a book. It isn't anything important enough to require very precise numbers.
– Zoey
Commented Dec 18, 2021 at 18:37
• scholar.google.com/… Commented Dec 18, 2021 at 21:15

Motion blur in a single image is caused by the finite speed that the camera shutter can open and close when taking pictures. Any object that moves more than 1 pixel distance during this picture-taking process appears blurred.

If this speed is known, the length of the blur (in pixel units) is proportional to how fast the object is moving, and can be tested from experiments using that particular camera.

Motion from a set of images can be also estimated another way, for instance as follows. If a human is around, mark out the object in both photos. Assuming the camera is still, just check one particular identifiable part of the same object in both photos, and note down its difference in pixel coordinates. The object has moved this pixel distance in the time it takes between frames (eg. 1/30 second or 1/60 second).

If we can now estimate how far the object is from the camera, for instance this particular car is probably 2 meters away judging by its appearance and size, we can get an estimate for the 3D distance it has moved between the two frames.

Hope it helps!

PS. In UFO blurred photo cases, sometimes this kind of reasoning is also done, but in this case it is much harder to estimate how far away the unidentified object is, just by the fact that it is "unidentified" so we don't have any experience to draw from, in contrast to the car scenario.

• Sorry but I am not asking about a camera or images, I said that I am doing it for a person. I also don't have a visual, I am just wondering a lower estimation for velocity to appear as a blur within the area of a few feet (perhaps around 10) to a human.
– Zoey
Commented Dec 19, 2021 at 15:59
• @Zoey you mean like estimating the speed of a fan blade by looking at it spinning? I'm but sure about this, there might be a way for doing this though...
– user315366
Commented Dec 19, 2021 at 18:10
• Kind of, yeah. At least have an estimation of a lower bound. The context is just estimating the speed of a character in a book who managed to move fast enough to blur and be untraceable to an ordinary human not that far from him. I am assuming around 10 feet just for ease.
– Zoey
Commented Dec 19, 2021 at 18:18

I assume that what you have in mind is that if an object ("character") has a precise boundary, one can just pick a specific point on the boundary and estimate how fast it moves, but one can't do that when the boundary is blurred. Instead what one can do is to locate roughly where the center of mass of the object is, which can be done even for a blurred object, and then estimate the speed by focusing on the center of mass.