How to change world space camera orientation and position vectors to the camera space?

0
votes

My problem is exactly the reverse of How to determine world coordinates of a camera?.

If R and t are the vector of orientation and position of the camera in the world space? How do I transform easily back to the same space like the rvec and tvec?

1
opencvmathcomputer-vision
do you want to transform some real world point coordinates to local camera coordinares? have a look at computer graphics theory. afair it should be just to multiply the 3D point by the inverse of the camera matrix. – Micka
look here Understanding 4x4 homogenous transform matrices just keep in mind that camera matrix is Inverse – Spektre
@Micka, because I made a mistake about what's [R|t] in the projection matrix. I calculated the R and t of the camera in the world space. So now I wish to transform them back to the camera space without coding too much. – tomriddle_1234
in my understanding from "camera space" R is unit mat and t is zero everywhere for a camera in its own "camera space" (if points are given in camera space you can perform standard projection), but I might be wrong there... – Micka

1 Answers

2
votes

If you say you do have an R and t in world space, then this is not very accurate.

However, let us assume that R and t (a 3x3 rotation matrix and 3x1 translation vector) represent the orientation and translation which are used to transform a point Xw in world space to a point in camera space Xc (no homogeneuos coordinates) :

Xc = R*Xw + t

These are the R and t, which are part of your projection matrix P (which is applicable with homogeneous coordinates) and the result of solvePnP (see Note at the bottom):

P = K[R|t]

The t is the world origin in camera space.

The other way round, to transform a point in camera space to world space, can be easily derived since the inverse of the orthogonal matrix R is R' (R transposed):

 Xw = R'*Xc - R't

As you can see R' (3x3 matrix) and - R't (3x1 vector) are now the orientation matrix respectively translation vector to transform from camera to world space (more precise - R't is the camera origin/center in world space often referred to as C).

Note: rvec is in the form of rotation vectors, as you may know Rodrigues() is used to switch between the two representations.