What does the normalized image coordinates imply?

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?