Eric Heitz

Thomas Chambon, Eric Heitz, Laurent Belcour

Our objective is to compute a textural loss that can be used to train texture generators with multiple material channels typically used for physically based rendering such as albedo, normal, roughness, metalness, ambient occlusion, etc. Neural textural losses often build on top of the feature spaces of pretrained convolutional neural networks. Unfortunately, these pretrained models are only available for 3-channel RGB data and hence limit neural textural losses to this format. To overcome this limitation, we show that passing random triplets to a 3-channel loss provides a multi-channel loss that can be used to generate high-quality material textures.

Eric Heitz, Kenneth Vanhoey, Thomas Chambon et al.

We address the problem of computing a textural loss based on the statistics extracted from the feature activations of a convolutional neural network optimized for object recognition (e.g. VGG-19). The underlying mathematical problem is the measure of the distance between two distributions in feature space. The Gram-matrix loss is the ubiquitous approximation for this problem but it is subject to several shortcomings. Our goal is to promote the Sliced Wasserstein Distance as a replacement for it. It is theoretically proven,practical, simple to implement, and achieves results that are visually superior for texture synthesis by optimization or training generative neural networks.

Jacopo Pantaleoni, Eric Heitz

In this manuscript, we derive optimal conditions for building function approximations that minimize variance when used as importance sampling estimators for Monte Carlo integration problems. Particularly, we study the problem of finding the optimal projection $g$ of an integrand $f$ onto certain classes of piecewise constant functions, in order to minimize the variance of the unbiased importance sampling estimator $E_g[f/g]$, as well as the related problem of finding optimal mixture weights to approximate and importance sample a target mixture distribution $f = \sum_i α_i f_i$ with components $f_i$ in a family $\mathcal{F}$, through a corresponding mixture of importance sampling densities $g_i$ that are only approximately proportional to $f_i$. We further show that in both cases the optimal projection is different from the commonly used $\ell_1$ projection, and provide an intuitive explanation for the difference.