# Is it possible to transfer a point from one camera to another, given n corresponding points?

I have 2 images of a scene taken at one moment by two identical cameras (similar cameras intrinsic parameters) by to arbitrary locations and at two arbitrary orientations (different cameras poses). On the images n points correspondence p_i1={x_i1, y_i1, z_i1}↔p_i2={x_i2, y_i2, z_i2}, i=1,2,...,n are given. Let for simplicity z_i1=z_i2=f for all the points.

Is it possible at any number of corresponding points n to derive a transformation relation from one camera view to another so that for an additional point p_01 known only at one image to be able to locate it on the second image p_02?

My guess is (due to the fact that projection on a camera sensor plane is 3d-to-2d) it is not possible! And at most one may find a line on the 2nd image on which the additional point could be positioned.

I know that the task is solved with a homography matrix for two cameras having one center. I know it must be solvable for the case of all the points being coplanar.

But is it possible for arbitrary positioned cameras and arbitrary situated (non-coplanar in world frame) corresponding points?

• Please don't add "SOLVED" into the title. It suggests that the question is no longer useful, whereas we want questions to be useful to people in the future, too. The fact that you've accepted an answer already says that the question has been solved to your satisfaction, but there might be an even better answer posted later. – David Richerby Apr 11 '18 at 14:31

Is it possible at any number of corresponding points n to derive a transformation relation from one camera view to another so that for an additional point p_01 known only at one image to be able to locate it on the second image p_02?

The answer is no - it is impossible. Each point on the image1 may in general correspond to an entire line on the image2 (see https://en.wikipedia.org/wiki/Epipolar_geometry). The homography matrix is a projection matrix of one plane on another and, therefore, is useful when you have a plane object ( chessboard, book, painting etc.) pictured on both images.

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