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How does the size/length of an object vary with distance?

Is it a logarithmic relationship? exponential? linear?

I plotted a curve of the size/length of an object for different distances from the camera, and the curve looked exponential/logarithmic. I was trying to understand the reasoning behind that.

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3 Answers 3

The relationship is a simple inverse, i.e.

 object size in image = Object size * focal length / object distance from camera

If you keep the same object and the same focal length you get: size = 1/ distance (the =-sign should be proportional-sign).

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Thanks. How is that different when it's object size vs object location image in terms of pixel (x,y) coordinates –  fmvpsenior Jul 17 '13 at 16:48
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It's not different, pixels are just a different unit than say meters. You can change units by knowing the size of one pixel. –  Unapiedra Jul 17 '13 at 17:02

I'm sure this is a duplicate, but I can't find a good answer to the question in the archives so here goes.

The relationship between object size and distance is an inverse linear relationship, i.e. size is 1 / distance. This makes sense when you think about it as if you double the distance the size halves.

This is why you appear to be observing an exponential: the exponent is -1, if you take the reciprocal of the size, your graph should be a straight line.

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Thanks. I am actually plotting the size of the object vs distance in pixels (or location). So I start with the object being on the far left of the image (pixel coord x = 0) and end with the object being on the far right of the image along the same line (pixel coord x=3000). I wonder if the relationship is the same in that case. –  fmvpsenior Jul 17 '13 at 16:47

Inversely linear is a good approximation. Imagine a 1,7m tall girl at 1 m distance b. Her head is at point B. triangle that name corners and sides

How does the size/length of an object vary with distance?

Let the girl walk away from you. Her size stays the same. She appears smaller, because she is appearing under a smaller angle. Her angular size changes.

Using arctangent to calculate her angular size is the right way. For small angles you can simplify:

Angular size is inversely proportional to its object distance, without using optical devices.

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