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Topic: 3D Rotation Matrix not coming out to be Orthonormal
Replies: 0

 maria Posts: 1 Registered: 11/19/13
3D Rotation Matrix not coming out to be Orthonormal
Posted: Nov 19, 2013 1:35 PM

Hey,
I am trying to implement 3D Augmented Reality using 4 marker points(plane).
So far I am only dealing with two image frames.One I consider my base view which is a rectangle in the centre of the image plane.Another is a plane which is rotated translated and scaled in real world.

I am using the following approach for solving this problem.
In order to place the 3D object on the plane,we need the 3D orientation of the plane in a frame.

The 3D orientation comprises of Rotation(along the three axis),translation (along x and y axis) and scaling(along z axis or translation along z axis tz).

The Rotation(in 3D world) of the plane is simply the inverse of the rotation(R) of the camera from the relation

H=KRKinverse

So if we compute the Homography H between the two frames,we are good to go.

Now the translations tx and ty (in real 3D world) can be computed by simply applying rotation (Rinverse) on the 3D object,applying K on it (taking its image) and moving it according to the distance between the two images(take any one corner as reference e.g the top most left corner or even the center).

The problem that I am facing is that my R doesnt come out to be orthonormal and its not a minute difference.the determinant is almost close to zero.I have verified my H and it is correct.