kram1032

@rohansawhney
@keenancrane

Just had an odd idea for an application of Monte Carlo geometry processing and am wondering whether it makes any sense at all:

There is this rendering technique called Gradient-Domain Path Tracing (and various extensions thereof)

https://onlinelibrary.wiley.com/doi/abs/10.1111/cgf.13652

This method basically tries to find similar paths on nearby pixels to estimate the local gradient of the image and adaptively sample where there is a large gradient, thereby hopefully using samples more where they actually are needed.

You then take those gradients to reconstruct the actual image.

This, as I understand it, relies on a usually discrete pixel-space shift-operator.

It occurred to me, that images are basically like discretized geometry. It's highly regular of course, but still: It's inherently discrete and scale-dependent.

Now I wonder whether it would be possible to do this same sort of sampling but in an unbiased, continuous manner using the methods you worked on

Nov 25, 2022 at 11:01amWeb
Show threadKeenan CraneDec 11, 2022
@kram1032 @rohansawhney Nice idea. Walk on spheres is most appropriate in situations where your domain has very complex geometry—here your domain is a square! But you could still indeed use Monte Carlo to recover the image. In particular if you could estimate the divergence of the gradient, then you could convolve it (via Monte Carlo) with the harmonic Green's function—avoiding discretization, and enabling local evaluation (e.g., just in a region of interest).