Rephrasing needed (maybe)

First, I would like to thank you for this book, it is really a very good resource in the subject.

I didn't understand this phrase (in chapter 5, p105)

s is the distance of pixels ?! do you mean the depth, the size, or the scaling factor?
What do you mean by the third element of ...

slambook-en/chapters/nonlinearOptimization.tex

Line 37 in ba3a4e2

    
           where $ \mathbf {K} $ is the intrinsic matrix of the camera, and $s$ is the distance of pixels, which is also the third element of $ (\mathbf {R} _k {\mathbf {y} _j} + \mathbf {t} _k) $. If we use  transformation matrix $ \mathbf {T} _k $ to describe the pose, then the points $ \mathbf {y} _j $ must be described in homogeneous coordinates, and then converted to non-homogeneous coordinates afterwards. If you are not familiar with this process, please go back to the previous lectures.

Hi @abougouffa ,

s is the real distance of the pixel. i.e. the distance from the 3D point to the image plane, sometimes it is also mentioned as the scale. Please check the pinhole model in chapter 4 (equation 4.8).

The symbols are slightly different but the meaning is the same.

On the left side of (5.2), s is a scalar, and z_{k,j} is a 3D vector like [u,v,1]^T. When multiplying them together, we get a vector [su, sv, s]^T.
One the right side, K(Ry+t) also gives a 3D vector. By comparing them, we see s is exactly the third element of K(Ry+t).