Division happens, indirectly, in cases where the image formation model is multiplicative. Concepts behind background varies on whether one only considers smooth fluctuations, or one includes noise. For the later, there is a lot of literature on multiplicative noise.
important example(s]: speckle noise [...] proper shadows due to
undulations on the surface of the imaged objects, shadows cast by
complex objects like foliage and Venetian blinds, dark spots caused by
dust in the lens or image sensor, and variations in the gain of
individual elements of the image sensor array.
For a combined case, the principle of homomorphic filtering considers a nonlinear transformation on the image $f$ to cope with two main components (one slow, illumination $i$ and one fast, reflection $r$). In the most basic case, $f=i\times r$ is passed through a logarithm before some linear filtering (and an inverse exponential on the results).This allows to reduce the noise without compressing the dynamic range too much.
It is suitable for instance to shading effects on surfaces, where one end is darker than the other, for instance, from Homomorphic filtering – part 2 (Mathworks):
In the mathematical morphology community, you can also find the LIP concept, for Logarithm Image Processing.