then..
> And finally, they have resisted the temptation to do “neural” anything ;)
So, they are doing something similar to NeRF, in a sense, but using a different basis function, and a slightly different target. The whole "neural" or not "neural" is just about what you are optimizing, but it's not that different, conceptually -- they are optimizing a data-driven approximator of a 3d scene-related variable based on images.
The big difference of course, based on reading this, is that NeRF models the whole light transmission function ("radiance field") whereas this seems to model only the boundary conditions (what the light "hits"). So given the different modelling target, then yes, a different, and perhaps simpler, representation basis definitely seems warranted, and is shown here to give good results. But the comment, "they avoided neural anything" feels a bit smug, as if "avoiding the hype" is a laudable goal on its own merits. As if people are using neural networks for no reason but because they're cool, and not because they're actually an appropriate solution that are shown to work really well in practice. They surely are cool, don't get me wrong, but the hype is so often justified, because neural networks are really good function approximators. They are also not just one thing -- the choice and breadth of architectures that we happen to call "neural networks" is huge, so explicitly avoiding this huge potential solution space for some reason without good reason feels pretty specious; heck you could even consider having a Gaussian "output layer" to a neural network, which is called an RBF, being something like this "splat" approach. (This is in response to the blog post, not the paper -- I'm sure the paper has plenty of justification for modeling choices.) Having said that, of course it's interesting to also explore simpler, perhaps more efficient approaches, but I don't see "resisting using neural anything" as a good thing, just because they are popular. It ignores that they are popular for a reason.
(nb: This assessment is just based on the blog post and giving my impression from the tone of the introduction, I haven't read the paper yet, so might not be accurate with respect to the paper contents. I just found this off-hand comment in the post worth reflecting on.)