Calculating object position from image processing

Question

I am looking for an efficient way to calculate the position of an oject on a surface based on an image taken from a certain perspective.

Let me explain a little further. There is an object on a rectangular flat surface. I have a picture taken of this setup with the camera positioned at one of the corners of the surface area at a rather low angle. On the picture I will thus see a somewhat distorted, diamond-shaped view of the surface area and somewhere on it the object.

Through some image processing I do have the coordinates of the object on the picture but now have to calculate the actual position of the object on the surface.

So I do know that the center of the object is at the pixel-coordinates (x/y) on the picture and I know the coordinates of the 4 reference points that represent the corners of the area.

How can I now calculate the "real world" position of the object most efficiently (x and y coordinates on the surface)?

Any input is highly appreciated since I have worked so hard on this I can't even think straight anymore.

Best regards, Tom

Answer 1

You have to find a perspective transformation.

Here you may find an explanation and code in Matlab

HTH!

Answer 2

How good is your linear algebra? A perspective transformation can be described by a homography matrix. You can estimate that matrix using the four corner points, invert it and the calculate the world coordinates of every pixel in your image.

Or you can just let OpenCV do that for you.