Visual Odometry terminology: Scale, Relative scale, absolute scale

I'm watching a MOOC about Machine Vision for Robotics, but I really do not know the meaning of some vocabulary of this domain.

For example, What does the professor mean when he says this:

However, we usually cannot estimate the absolute scale from a single camera. What this means is that estimation of motion produced from one camera can be stretched or compressed in the 3D world without affecting the pixel feature locations by adjusting the relative motion estimate between the two images.

1- What does the absolute scale mean? In this context, scale refers to what property related to an image?

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?

• Look at this question to put the idea of scale into a little more context. It doesn't answer your questions directly, but I am sure will be of interest to you; – JJB_UT Feb 3 at 18:40

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.

• Thank you very much for this pretty excellent answer. – sci9 Feb 4 at 5:21