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In dynamical systems, basins of attraction connect a given set of initial conditions in phase space to their asymptotic states. The basin entropy and related tools quantify the unpredictability in the final state of a system when there is an initial perturbation or uncertainty in the initial state. Based on the basin entropy, the $\ln 2$ criterion allows for efficient testing of fractal basin boundaries at a fixed resolution. Here, we extend this criterion into a new test with improved sensitivity that we call the \textit{$S_{bb}$ fractality test}. Using the same single scale information, the $S_{bb}$ fractality test allows for the detection of fractal boundaries in many more cases than the $\ln 2$ criterion. The new test is illustrated with the paradigmatic driven Duffing oscillator, and the results are compared with the classical approach given by the uncertainty exponent. We believe that this work can prove particularly useful to study both high-dimensional systems and experimental basins of attraction.

There has been recently a growing interest for implicit shape representations. Contrary to explicit representations, they have no resolution limitations and they easily deal with a wide variety of surface topologies. To learn these implicit representations, current approaches rely on a certain level of shape supervision (e.g., inside/outside information or distance-to-shape knowledge), or at least require a dense point cloud (to approximate well enough the distance-to-shape). In contrast, we introduce NeeDrop, a self-supervised method for learning shape representations from possibly extremely sparse point clouds. Like in Buffon's needle problem, we "drop" (sample) needles on the point cloud and consider that, statistically, close to the surface, the needle end points lie on opposite sides of the surface. No shape knowledge is required and the point cloud can be highly sparse, e.g., as lidar point clouds acquired by vehicles. Previous self-supervised shape representation approaches fail to produce good-quality results on this kind of data. We obtain quantitative results on par with existing supervised approaches on shape reconstruction datasets and show promising qualitative results on hard autonomous driving datasets such as KITTI., Comment: 22 pages

This paper explores how the modelling of energy systems may lead to undue closure of alternatives by generating an excess of certainty around some of the possible policy options. We exemplify the problem with two cases: first, the International Institute for Applied Systems Analysis (IIASA) global modelling in the 1980s; and second, the modelling activity undertaken in support of the construction of a radioactive waste repository at Yucca Mountain (Nevada, USA). We discuss different methodologies for quality assessment that may help remedy this issue, which include NUSAP (Numeral Unit Spread Assessment Pedigree), diagnostic diagrams, and sensitivity auditing. We demonstrate the potential of these reflexive modelling practices in energy policy making with four additional cases: (i) stakeholders evaluation of the assessment of the external costs of a potential large-scale nuclear accident in Belgium in the context of the ExternE (External Costs of Energy) project; (ii) the case of the ESME (Energy System Modelling Environment) for the creation of UK energy policy; (iii) the NETs (Negative Emission Technologies) uptake in Integrated Assessment Models (IAMs); and (iv) the Ecological Footprint (EF) indicator. We encourage modellers to widely adopt these approaches to achieve more robust and inclusive modelling activities in the field of energy modelling., Comment: 39 pages, 2 tables, 3 figures

We present FacialFilmroll, a solution for spatially and temporally consistent editing of faces in one or multiple shots. We build upon unwrap mosaic [Rav-Acha et al. 2008] by specializing it to faces. We leverage recent techniques to fit a 3D face model on monocular videos to (i) improve the quality of the mosaic for edition and (ii) permit the automatic transfer of edits from one shot to other shots of the same actor. We explain how FacialFilmroll is integrated in post-production facility. Finally, we present video editing results using FacialFilmroll on high resolution videos., Comment: European Conference on Visual Media Production (CVMP '21)

Rigid registration of point clouds with partial overlaps is a longstanding problem usually solved in two steps: (a) finding correspondences between the point clouds; (b) filtering these correspondences to keep only the most reliable ones to estimate the transformation. Recently, several deep nets have been proposed to solve these steps jointly. We built upon these works and propose PCAM: a neural network whose key element is a pointwise product of cross-attention matrices that permits to mix both low-level geometric and high-level contextual information to find point correspondences. These cross-attention matrices also permits the exchange of context information between the point clouds, at each layer, allowing the network construct better matching features within the overlapping regions. The experiments show that PCAM achieves state-of-the-art results among methods which, like us, solve steps (a) and (b) jointly via deepnets. Our code and trained models are available at https://github.com/valeoai/PCAM., Comment: ICCV21

Localizing objects in image collections without supervision can help to avoid expensive annotation campaigns. We propose a simple approach to this problem, that leverages the activation features of a vision transformer pre-trained in a self-supervised manner. Our method, LOST, does not require any external object proposal nor any exploration of the image collection; it operates on a single image. Yet, we outperform state-of-the-art object discovery methods by up to 8 CorLoc points on PASCAL VOC 2012. We also show that training a class-agnostic detector on the discovered objects boosts results by another 7 points. Moreover, we show promising results on the unsupervised object discovery task. The code to reproduce our results can be found at https://github.com/valeoai/LOST.

While there has been a number of studies on Zero-Shot Learning (ZSL) for 2D images, its application to 3D data is still recent and scarce, with just a few methods limited to classification. We present the first generative approach for both ZSL and Generalized ZSL (GZSL) on 3D data, that can handle both classification and, for the first time, semantic segmentation. We show that it reaches or outperforms the state of the art on ModelNet40 classification for both inductive ZSL and inductive GZSL. For semantic segmentation, we created three benchmarks for evaluating this new ZSL task, using S3DIS, ScanNet and SemanticKITTI. Our experiments show that our method outperforms strong baselines, which we additionally propose for this task., Comment: For the published code, see https://github.com/valeoai/3DGenZ

The R package "sensobol" provides several functions to conduct variance-based uncertainty and sensitivity analysis, from the estimation of sensitivity indices to the visual representation of the results. It implements several state-of-the-art first and total-order estimators and allows the computation of up to third-order effects, as well as of the approximation error, in a swift and user-friendly way. Its flexibility makes it also appropriate for models with either a scalar or a multivariate output. We illustrate its functionality by conducting a variance-based sensitivity analysis of three classic models: the Sobol' (1998) G function, the logistic population growth model of Verhulst (1845), and the spruce budworm and forest model of Ludwig, Jones and Holling (1976)., Comment: The paper has been accepted for publication in the Journal of Statistical Software (expected for 2022)

Learning image representations without human supervision is an important and active research field. Several recent approaches have successfully leveraged the idea of making such a representation invariant under different types of perturbations, especially via contrastive-based instance discrimination training. Although effective visual representations should indeed exhibit such invariances, there are other important characteristics, such as encoding contextual reasoning skills, for which alternative reconstruction-based approaches might be better suited. With this in mind, we propose a teacher-student scheme to learn representations by training a convolutional net to reconstruct a bag-of-visual-words (BoW) representation of an image, given as input a perturbed version of that same image. Our strategy performs an online training of both the teacher network (whose role is to generate the BoW targets) and the student network (whose role is to learn representations), along with an online update of the visual-words vocabulary (used for the BoW targets). This idea effectively enables fully online BoW-guided unsupervised learning. Extensive experiments demonstrate the interest of our BoW-based strategy which surpasses previous state-of-the-art methods (including contrastive-based ones) in several applications. For instance, in downstream tasks such Pascal object detection, Pascal classification and Places205 classification, our method improves over all prior unsupervised approaches, thus establishing new state-of-the-art results that are also significantly better even than those of supervised pre-training. We provide the implementation code at https://github.com/valeoai/obow., Comment: Accepted to CVPR2021. Code at https://github.com/valeoai/obow

The Variogram Analysis of Response Surfaces (VARS) has been proposed by Razavi and Gupta as a new comprehensive framework in sensitivity analysis. According to these authors, VARS provides a more intuitive notion of sensitivity and it is much more computationally efficient than Sobol' indices. Here we review these arguments and critically compare the performance of VARS-TO, for total-order index, against the total-order Jansen estimator. We argue that, unlike classic variance-based methods, VARS lacks a clear definition of what an "important" factor is, and show that the alleged computational superiority of VARS does not withstand scrutiny. We conclude that while VARS enriches the spectrum of existing methods for sensitivity analysis, especially for a diagnostic use of mathematical models, it complements rather than substitutes classic estimators used in variance-based sensitivity analysis., Comment: Currently under review in Environmental Modelling & Software

Sensitivity analysis helps identify which model inputs convey the most uncertainty to the model output. One of the most authoritative measures in global sensitivity analysis is the Sobol' total-order index, which can be computed with several different estimators. Although previous comparisons exist, it is hard to know which estimator performs best since the results are contingent on the benchmark setting defined by the analyst (the sampling method, the distribution of the model inputs, the number of model runs, the test function or model and its dimensionality, the weight of higher order effects or the performance measure selected). Here we compare several total-order estimators in an eight-dimension hypercube where these benchmark parameters are treated as random parameters. This arrangement significantly relaxes the dependency of the results on the benchmark design. We observe that the most accurate estimators are Razavi and Gupta's, Jansen's or Janon/Monod's for factor prioritization, and Jansen's, Janon/Monod's or Azzini and Rosati's for approaching the "true" total-order indices. The rest lag considerably behind. Our work helps analysts navigate the myriad of total-order formulae by reducing the uncertainty in the selection of the most appropriate estimator., Comment: Previous versions of this manuscript were titled "The Battle of Total-Order Sensitivity Indices". The version with the title "A comprehensive comparison of total-order estimators for global sensitivity analysis" has been accepted for publication in the International Journal for Uncertainty Quantification. Please kindly cite the journal version

We propose and study a method called FLOT that estimates scene flow on point clouds. We start the design of FLOT by noticing that scene flow estimation on point clouds reduces to estimating a permutation matrix in a perfect world. Inspired by recent works on graph matching, we build a method to find these correspondences by borrowing tools from optimal transport. Then, we relax the transport constraints to take into account real-world imperfections. The transport cost between two points is given by the pairwise similarity between deep features extracted by a neural network trained under full supervision using synthetic datasets. Our main finding is that FLOT can perform as well as the best existing methods on synthetic and real-world datasets while requiring much less parameters and without using multiscale analysis. Our second finding is that, on the training datasets considered, most of the performance can be explained by the learned transport cost. This yields a simpler method, FLOT$_0$, which is obtained using a particular choice of optimal transport parameters and performs nearly as well as FLOT., Comment: Accepted at ECCV20

Face age editing has become a crucial task in film post-production, and is also becoming popular for general purpose photography. Recently, adversarial training has produced some of the most visually impressive results for image manipulation, including the face aging/de-aging task. In spite of considerable progress, current methods often present visual artifacts and can only deal with low-resolution images. In order to achieve aging/de-aging with the high quality and robustness necessary for wider use, these problems need to be addressed. This is the goal of the present work. We present an encoder-decoder architecture for face age editing. The core idea of our network is to create both a latent space containing the face identity, and a feature modulation layer corresponding to the age of the individual. We then combine these two elements to produce an output image of the person with a desired target age. Our architecture is greatly simplified with respect to other approaches, and allows for continuous age editing on high resolution images in a single unified model.

We address the problem of style transfer between two photos and propose a new way to preserve photorealism. Using the single pair of photos available as input, we train a pair of deep convolution networks (convnets), each of which transfers the style of one photo to the other. To enforce photorealism, we introduce a content preserving mechanism by combining a cycle-consistency loss with a self-consistency loss. Experimental results show that this method does not suffer from typical artifacts observed in methods working in the same settings. We then further analyze some properties of these trained convnets. First, we notice that they can be used to stylize other unseen images with same known style. Second, we show that retraining only a small subset of the network parameters can be sufficient to adapt these convnets to new styles.

Recent state-of-the-art methods for point cloud processing are based on the notion of point convolution, for which several approaches have been proposed. In this paper, inspired by discrete convolution in image processing, we provide a formulation to relate and analyze a number of point convolution methods. We also propose our own convolution variant, that separates the estimation of geometry-less kernel weights and their alignment to the spatial support of features. Additionally, we define a point sampling strategy for convolution that is both effective and fast. Finally, using our convolution and sampling strategy, we show competitive results on classification and semantic segmentation benchmarks while being time and memory efficient.

We consider the problem of identifying people on the basis of their walk (gait) pattern. Classical approaches to tackle this problem are based on, e.g., video recordings or piezoelectric sensors embedded in the floor. In this work, we rely on acoustic and vibration measurements, obtained from a microphone and a geophone sensor, respectively. The contribution of this work is twofold. First, we propose a feature extraction method based on an (untrained) shallow scattering network, specially tailored for the gait signals. Second, we demonstrate that fusing the two modalities improves identification in the practically relevant open set scenario., Comment: Published at IEEE GlobalSIP 2017

De Graaf et al. (2019) suggest that groundwater pumping will bring 42--79\% of worldwide watersheds close to environmental exhaustion by 2050. We are skeptical of these figures due to several non-unique assumptions behind the calculation of irrigation water demands and the perfunctory exploration of the model's uncertainty space. Their sensitivity analysis reveals a widespread lack of elementary concepts of design of experiments among modellers, and can not be taken as a proof that their conclusions are robust., Comment: Comment on the paper by De Graaf et al. 2019. Environmental flow limits to global groundwater pumping. Nature 574 (7776), 90-94