When we are rendering a 3D objects on a computer screen, we turn this object into a 2D picture, a.k.a a set of colored pixels. We call Rendering the process of computing the color to associate to each pixel. Computing this color sums up as integrating the amount of light that reaches this pixel from any directions. Unfortunately, a computer can't compute an integrand, so we instead approximate it with Monte Carlo methods. Those methods uses a set of samples in the domain, evalute the function on those samples, and approximate the integrand through a weighted average of those evalutations.
In rendering, it is mandatory that the sampler used to generates the samples generates a point set that covers the domain uniformly. This limits the apparition of noise in the final image. We also wish that the sampling pattern do not present any visible structure, wich would lead to aliasing artefacts.
Usually, sampler that have an optimal uniformity are highly structured, causing aliasing, whereas samplers that do not create aliasing are not optimal for uniformity.
During this PhD, we try to develop a new category of samplers that are both optimal in terms of uniformity and in terms of noise reduction.