Guillaume Gautier

Guillaume Gautier, Rémi Bardenet, Michal Valko

The standard Monte Carlo estimator $\widehat{I}_N^{\mathrm{MC}}$ of $\int fdω$ relies on independent samples from $ω$ and has variance of order $1/N$. Replacing the samples with a determinantal point process (DPP), a repulsive distribution, makes the estimator consistent, with variance rates that depend on how the DPP is adapted to $f$ and $ω$. We examine two existing DPP-based estimators: one by Bardenet & Hardy (2020) with a rate of $\mathcal{O}(N^{-(1+1/d)})$ for smooth $f$, but relying on a fixed DPP. The other, by Ermakov & Zolotukhin (1960), is unbiased with rate of order $1/N$, like Monte Carlo, but its DPP is tailored to $f$. We revisit these estimators, generalize them to continuous settings, and provide sampling algorithms.

Guillaume Gautier, Alexandre Mercat, Louis Fréneau et al.

Point cloud compression has become a crucial factor in immersive visual media processing and streaming. This paper presents a new open dataset called UVG-VPC for the development, evaluation, and validation of MPEG Visual Volumetric Video-based Coding (V3C) technology. The dataset is distributed under its own non-commercial license. It consists of 12 point cloud test video sequences of diverse characteristics with respect to the motion, RGB texture, 3D geometry, and surface occlusion of the points. Each sequence is 10 seconds long and comprises 250 frames captured at 25 frames per second. The sequences are voxelized with a geometry precision of 9 to 12 bits, and the voxel color attributes are represented as 8-bit RGB values. The dataset also includes associated normals that make it more suitable for evaluating point cloud compression solutions. The main objective of releasing the UVG-VPC dataset is to foster the development of V3C technologies and thereby shape the future in this field.

Guillaume Gautier, Mousa FarajAllah, Wassim Hamidouche et al.

Versatile video coding (VVC) is the next generation video coding standard developed by the joint video experts team (JVET) and released in July 2020. VVC introduces several new coding tools providing a significant coding gain over the high efficiency video coding (HEVC) standard. It is well known that increasing the coding efficiency adds more dependencies in the video bitstream making format-compliant encryption with the standard more challenging. In this paper we tackle the problem of selective encryption of the VVC standard in format-compliant and constant bitrate. These two constraints ensure that the encrypted bitstream can be decoded by any VVC decoder while the bitrate remains unchanged by the encryption. The selective encryption of all possible VVC syntax elements is investigated. A new algorithm is proposed to encrypt in format-compliant and constant bitrate the transform coefficients (TCs) together with other syntax elements at the level of the entropy encoder. The proposed solution was integrated and assessed under the VVC reference software model version 6.0. Experimental results showed that the encryption drastically decreases the video quality while the encryption is robust against several types of attacks. The encryption space is estimated in the range of 15% to 26% of the bitstream size resulting in a lightweight encryption process. The web page of this work is available at https://gugautie.github.io/sevvc/.

Guillaume Gautier, Guillermo Polito, Rémi Bardenet et al.

Determinantal point processes (DPPs) are specific probability distributions over clouds of points that are used as models and computational tools across physics, probability, statistics, and more recently machine learning. Sampling from DPPs is a challenge and therefore we present DPPy, a Python toolbox that gathers known exact and approximate sampling algorithms for both finite and continuous DPPs. The project is hosted on GitHub and equipped with an extensive documentation.

Guillaume Gautier, Rémi Bardenet, Michal Valko

Determinantal point processes (DPPs) are distributions over sets of items that model diversity using kernels. Their applications in machine learning include summary extraction and recommendation systems. Yet, the cost of sampling from a DPP is prohibitive in large-scale applications, which has triggered an effort towards efficient approximate samplers. We build a novel MCMC sampler that combines ideas from combinatorial geometry, linear programming, and Monte Carlo methods to sample from DPPs with a fixed sample cardinality, also called projection DPPs. Our sampler leverages the ability of the hit-and-run MCMC kernel to efficiently move across convex bodies. Previous theoretical results yield a fast mixing time of our chain when targeting a distribution that is close to a projection DPP, but not a DPP in general. Our empirical results demonstrate that this extends to sampling projection DPPs, i.e., our sampler is more sample-efficient than previous approaches which in turn translates to faster convergence when dealing with costly-to-evaluate functions, such as summary extraction in our experiments.