Mathematical correctness of equation (4) in Camera Models

[scimad]

In equation 3 (Camera Models), the dimension of the terms are some real world image distance units (say cm for example). However, in equation 4, new terms i.e. k and l; whose units are pixel/cm are introduced, which makes the addition between two terms in equation 4 mathematically incorrect, though intuitively okay. Should there be some more rigorous approach to this?