The section titled "Log-polar Mapping in 3D" is, as you say, simply adapting the same map to 3D. The section "Log-spherical Mapping" is about the proper 3D equivalent.
However, while maps in 2D space can be neatly represented with complex numbers, there is no equivalent for 3D space, so things can't be as neat. But the geometric properties are there: using the log-spherical map, translation along one axis maps to uniform scaling (in all 3 axes).
However, while maps in 2D space can be neatly represented with complex numbers, there is no equivalent for 3D space, so things can't be as neat. But the geometric properties are there: using the log-spherical map, translation along one axis maps to uniform scaling (in all 3 axes).