In VSLAM or visual odometry, we use a camera matrix P to transform 3D scene points to 2D image points. When using homogeneous representation, we may choose the image coordinates as the normalized image coordinates $(x, y, 1)^T$, which means the image plane is placed at $Z = 1$ measured in 3D Euclidean coordinate system.

My question is, after normalized the image coordinates, are the x and y components of the image coordinates also measured in 3D Euclidean coordinate system?

  • $\begingroup$ Technically the normalized image coordinates are in the projective space($\mathbb{P}^n$), which can be considered embedded in the 3D Euclidean space. I don't know exactly what else you want to know. $\endgroup$
    – edwinem
    Jul 10 '20 at 18:02
  • $\begingroup$ @edwinem If an image point is expressed as (x, y, 1) in homogeneous representation, what is the unit for x and y coordinates? $\endgroup$
    – lzx071021
    Jul 11 '20 at 13:20
  • $\begingroup$ They are unitless. You can see this from the projection equation. To get from a 3D point to normalized coordinates it is $(X/Z,Y/Z,Z/Z) \rightarrow (x,y,1)$. The Units of a 3D point could be meters so it is $\frac{m}{m}$ which cancels out. $\endgroup$
    – edwinem
    Jul 11 '20 at 16:42

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