But perspective projections have the problem that it is difficult to determine the real size of the object from the number of visible pixels alone.
Explain what you mean?
That is the real size of it - multiply by your transfer map for the lobe and then integrate.
If you intend to find some form of radiation through rendering then you’re going to be using a hemicube and a precomputed table for your transfer function (Lambert for radiation/thermal, pivoted around Euler’s for electrical). Render your hemicube, integrate your values multiplied by the transfer map. Repeat until you’ve covered your absorbed surface to whatever resolution.
There is no analytic form-factor for an obscured object like you’ll have in most any render, you have to integrate. Even if you want to query for an infinitely small point you’re still going to be doing integration over several cosine lobes, no different than calculating PMREMs - which are radiation.