The main objective here is to computer pose of a real camera in the subsequent frames of a video (after I compute it in the first frame using a PnP algorithm) without the need of solving PnP again and again.
I have two rotation matrices. One is that of the rotation matrix of a real webcam which I got by solving the PnP problem. I have a world coordinate frame and I know the locations of each and every point in world coordinates in the world space.
As far as I understand, a rotation matrix transforms points in world coordinates to camera frame coordinates (not considering translation here). This means that, R1 gives you the orientation of world coordinate frame with respect to camera coordinate frame.
My second rotation matrix is that of a sensor which is also in world coordinates. ie, this rotation matrix gives you the orientation of world coordinate frame with respect to sensor coordinate frame.
I want to find the orientation of real webcam coordinate frame with respect to sensor coordinate frame.
Lets name the first rotation matrix Rw1 and the second rotation matrix Rw2, with the subscripts w1 denoting world with respect to real webcam and w2 denoting world with respect to sensor (1 and 2 can be considered denoting real webcam and sensor respectively).
So my aim is to find R12. (and not R21)
- R12 = R1w * Rw2 = (Rw1)' * Rw2
I am assuming that this R12 remains constant throughout (in the subsequent frames of the video) because sensor and webcam position will not be disturbed relative to each other and they always move together. Is my assumption valid?
If it is valid, then my ultimate objective is to compute the rotation matrix of real webcam in the subsequent frames. I can calculate the rotation matrix of sensor in subsequent frames which is Rw2 for the subsequent frames. I have to find out Rw1 and I can not use any PnP algorithms. I want to compute it from the currently available information.
Let's consider the second frame for now.
I know R12 (which I am assuming is constant and I computed it in first frame) and Rw2 (sensor rotation matrix for the second frame). I have to find Rw1 for the second frame.
- Rw1 = Rw2 * R21 = Rw2 * (R12)'
And then I repeat the same process for all the subsequent frames using the above formula. The only thing which is changing is Rw2 and I have it for all the frames. R12 matrix will not be changing according to my assumption.
Is my method and assumption valid ?
PS: (R)' means the transpose of R.
Intuitively your logic looks OK. I don't know much about the PnP so can't comment on that. If you know your relation R12 (and thus R21), then it's a really easy problem (assuming you know Rw2 in all frames). The equation looks fine.
Intuitively your logic looks OK. I don't know much about the PnP so can't comment on that. If you know your relation R12 (and thus R21), then it's a really easy problem (assuming you know Rw2 in all frames). The equation looks fine.
The mathematical model explained above clearly articulates the conjectures of relative frames of reference. However, if you extend your research into the nature of light you can understand that light itself is a three dimensional tensor and way beyond the normative projections of conventional topology. Only the quantum of light can be plotted while you try a controlled experiment and use a model of circulation based matrices.
Dear Heng,
I am using EPnP for the first frame. But since the input points (from the image and from the object) have to be selected manually it is only possible for the first frame. You can try using feature based image matching for doing EPnP in subsequent frames, but this will be a big burden in terms of computational complexity. So my objective is to compute extrinsic matrices (of the real camera) in a rather semi-automatic way in the subsequent frames using a sensor which is attached to the camera.
https://math.stackexchange.com/questions/2113634/comparing-two-rotation-matrices
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