Hey there I try to do a realtime visual odometry system for a monocular camera. Now I'm looking for an equation to describe 3d points movement in 2d vectors. While researching I came across a very interesting looking equation. I'm refering to page 22. It basically makes a simplification under the assumption of a relatively small time step. But now I'm struggeling about the image coordinates x and y. It's said that x would be sth like x=(px-px0) and y=(py-py0). When I understand it right p0 is the center of rotation. But if this is the case the whole formular would make no sense for my case cause I would need a prior knowledge of the center of rotation. Which is based on the translation again.
So maybe can help understanding it or maybe point me to a better way to do it.
To use this equation, you must have calibrated your camera (with a pinhole model), so you have a set of distortion coefficients, a focal distance and the principal point, which is the intersection of the optical axis with the image plane, as illustrated here: http://docs.opencv.org/2.4/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.html.
In the equation you mention, x and y coordinates are in pixels after distortion correction and relative to the center of projection, not the center of rotation. So, the px0 and py0 you are looking for, are the coordinates of the principal point, that is, cx0 and cy0 using the naming convention of the link above.