Can a digital image be considered as a tensor ? or have a tensor like structure?
An isotropic tensor is one invariant under rotations. An isotropic kernel is also invariant under rotations, but the way the rotation acts on the object is very different.

Tensors transform as linear forms, whereas images are just rotated like a scalar function of coordinates and the coordinates are rotated. So if you come from continuum mechanics, the image/kernel transforms like the pressure field.