Are my Points coplanar?

asked 2016-01-28 04:14:56 -0500

RVQ gravatar image

Hi,

A while ago I worked on pose estimation. I also asked a question about it to make it work. (old question)

Today I read the following about POSIT (solvePNP) in Learning OpenCV 1st Edition

POSIT (aka “Pose from Orthography and Scaling with Iteration”) is an algorithm originally proposed in 1992 for computing the pose (the position T and orientation R described by six parameters [DeMenthon92]) of a 3D object whose exact dimensions are known. To compute this pose, we must find on the image the corresponding locations of at least four non-coplanar points on the surface of that object.

This is my image

Example

For me this points appear to be coplanar, since they are all in the same plane? Could someone explain to me why it works anyway?

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In this document, it says:

For the case of coplanar feature points, researchers have formulated closed form solutions for configurations of three feature points and four feature points. The P3P problem (with three noncollinear points) can have as many as four possible solutions. On the other hand, the P4P problem has a single theoretical solution when the coplanar points are in an ordinary configuration (no three collinear scene points, non collinear image points).

You can read the original Posit paper if you want more information and the litterature on PnP problem.

Eduardo gravatar imageEduardo ( 2016-01-28 07:25:57 -0500 )edit

Thanks for the sources. Am I understanding you correct, that you say, that my Points are coplanar but it works anyway because of a closed form solution?

RVQ gravatar imageRVQ ( 2016-01-28 11:38:49 -0500 )edit
1

Your points are coplanar (the 4 points lie more or less on the same plane) and as long as you are not in a degenerate configuration (3 collinear scene points for example), you can estimate the pose.

Eduardo gravatar imageEduardo ( 2016-01-28 12:26:29 -0500 )edit

Thank you!

RVQ gravatar imageRVQ ( 2016-01-29 02:26:25 -0500 )edit