What does the absolute scale mean? In this context, scale refers to
what property related to an image?
Essentially scale refers to the size of the object/scene that the camera sees.
As a projective sensor the camera can't know the depth/size of the object it is viewing. Look at the below image. While we might know that the big and small boxes are different sizes the camera/image can't tell the difference.
The same reason is why people are always doing the optical illusion of holding up the leaning tower of pisa. A purely projective sensor can't tell the actual size of the object.
Note that the actual equation for using scale is typically something like this.
$$size_{true} = scale_{absolute} * size$$
In your case absolute scale is just the true size/ or the scalar multiple needed to get the true size of the object.
2- What is the meaning of the statement stretching and compressing the
estimation of motion in the 3D world?
3- What does a scaled trajectory mean?
These can be answered with the same example.
In the image below you have 3 cases of the robot trajectory generated from a monocular visual odometry algorithm. In reality they are just stretched(bigger) or compressed(smaller) versions of the same trajectory. This is because we can't tell the size of the world. These trajectories would be equally valid for a robot the size of an ant, or one as large as a truck.
A scaled trajectory generally means a trajectory that is scaled to the correct size. Generally used for evaluation purposes. As we want to compare our visual odometry algorithm against something like GPS poses.
