Improved sampling for gradient-domain metropolis light transport

Abstract

We present a generalized framework for gradient-domain Metropolis rendering, and introduce three techniques to reduce sampling artifacts and variance. The first one is a heuristic weighting strategy that combines several sampling techniques to avoid outliers. The second one is an improved mapping to generate offset paths required for computing gradients. Here we leverage the properties of manifold walks in path space to cancel out singularities. Finally, the third technique introduces generalized screen space gradient kernels. This approach aligns the gradient kernels with image structures such as texture edges and geometric discontinuities to obtain sparser gradients than with the conventional gradient kernel. We implement our framework on top of an existing Metropolis sampler, and we demonstrate significant improvements in visual and numerical quality of our results compared to previous work.

Gradient-domain path tracing

“…In practice, however, robust sampling of gradients is challenging because of this very sparsity. Recently, Manzi et al [2014] introduced improved gradient sampling techniques for GMLT that make unbiased reconstruction practical. An important insight of this work is that there is considerable freedom in how to sample gradients, which indicates that there is more room for future improvements.…”

“…In contrast to gradient-domain Metropolis light transport [Lehtinen et al 2013;Manzi et al 2014], we use a regular Monte Carlo sampling strategy to evaluate gradients. While a standard path tracer evaluates only the image contribution function for each sampled path, we evaluate, in addition, a path difference function defined by a shift mapping that maps each base path to a "similar" offset path through the neighbor pixel, as shown in Figure 2, and returns the difference between the contribution of the base and offset path.…”

“…While the basic mathematical formulation follows previous work [Lehtinen et al 2013;Manzi et al 2014], we will use fundamentally different sampling strategies. We denote the difference between two pixels i and j by ∆i,j.…”

“…Recent advances [Lehtinen et al 2013;Manzi et al 2014] take advantage of Metropolis sampling to distribute samples according not only to pixel values (or path throughput), but also finitedifference image gradients. This reduces costs by focusing computing resources onto areas of high variations.…”

“…In order to simplify implementation, we propose a new shift mapping that does not rely on manifold perturbations like the original shift by Lehtinen et al [2013], and whose Jacobian, which is necessary to account for the change of path densities introduced by the shift [Lehtinen et al 2013;Manzi et al 2014], is also simple to evaluate. Finally, we observe that the difference between two pixels can be sampled according to either a forward or an inverse shift, and we show that applying multiple importance sampling between these two strategies significantly improves quality.…”