how to calculate camera extrinsic parameters from three known dimensions in the target plane

Question

My question is as follows.

A single camera (constant in both position and orientation) is applied to monitor the motion of a far-away planar target. The intrinsic parameters including focal length, sensor resolution, principal point, are known. The lens distortion is not considered.

In the world system, three dimensions about the target (in a plane) are known. I wonder whether it is enough to determine the camera extrinsic parameters. If it is, how to calculate it?

Many thanks.

Answer 1

I think you can first use corresponding points x(image points) and X(object points) to determine the projection matrix P:

    x = PX

then run interpretation of P to derive interior and exterior matrix:

    P = H1 [I|0] H2

where H1 is 3x3 interior matrix and H2 is 4x4 exterior matrix.

Since you already know interior parameters, I think you can use them to adjust H2 to get a proper result.

Anyway, this method is still lack of high accuracy and need further improvement.