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We address the problem of inferring the anatomic skeleton of a person, in an arbitrary pose, from the 3D surface of the body; i.e. we predict the inside (bones) from the outside (skin). This has many applications in medicine and biomechanics. Existing state-of-the-art biomechanical skeletons are detailed but do not easily generalize to new subjects. Additionally, computer vision and graphics methods that predict skeletons are typically heuristic, not learned from data, do not leverage the full 3D body surface, and are not validated against ground truth. To our knowledge, our system, called OSSO (Obtaining Skeletal Shape from Outside), is the first to learn the mapping from the 3D body surface to the internal skeleton from real data. We do so using 1000 male and 1000 female dual-energy X-ray absorptiometry (DXA) scans. To these, we fit a parametric 3D body shape model (STAR) to capture the body surface and a novel part-based 3D skeleton model to capture the bones. This provides inside/outside training pairs. We model the statistical variation of full skeletons using PCA in a pose-normalized space. We then train a regressor from body shape parameters to skeleton shape parameters and refine the skeleton to satisfy constraints on physical plausibility. Given an arbitrary 3D body shape and pose, OSSO predicts a realistic skeleton inside. In contrast to previous work, we evaluate the accuracy of the skeleton shape quantitatively on held-out DXA scans, outperforming the state-of-the-art. We also show 3D skeleton prediction from varied and challenging 3D bodies. The code to infer a skeleton from a body shape is available for research at https://osso.is.tue.mpg.de/, and the dataset of paired outer surface (skin) and skeleton (bone) meshes is available as a Biobank Returned Dataset. This research has been conducted using the UK Biobank Resource., Project page: https://osso.is.tue.mpg.de/. Accepted in CVPR 2022

We describe a novel attribution method which is grounded in Sensitivity Analysis and uses Sobol indices. Beyond modeling the individual contributions of image regions, Sobol indices provide an efficient way to capture higher-order interactions between image regions and their contributions to a neural network's prediction through the lens of variance. We describe an approach that makes the computation of these indices efficient for high-dimensional problems by using perturbation masks coupled with efficient estimators to handle the high dimensionality of images. Importantly, we show that the proposed method leads to favorable scores on standard benchmarks for vision (and language models) while drastically reducing the computing time compared to other black-box methods -- even surpassing the accuracy of state-of-the-art white-box methods which require access to internal representations. Our code is freely available: https://github.com/fel-thomas/Sobol-Attribution-Method, NeurIPS2021

National audience; Few-camera videos Structure from motion Novel depth and RGB Relaxed point reconstruction without temporal consistency Efficient pose estimation robust to dynamic objects Sparse noisy point clouds Camera poses Virtual camera path Variational optimization with temporal consistency Figure 1: Given a set of video sequences from a few cameras only, our method computes camera poses and sparse points, then optimizes those points into a novel video sequence following a user-defined camera path. Our space-time SfM relaxes temporal consistency for points on dynamic objects and instead robustly adds consistency during the novel view synthesis via our variational formulation.

International audience; Modern 3D image recovery problems require powerful optimization frameworks to handle high dimensionality while providing reliable numerical solutions in a reasonable time. In this perspective, asyn-chronous parallel optimization algorithms have received an increasing attention by overcoming memory limitation issues and communication bottlenecks. In this work, we propose a block distributed Majorize-Minorize Memory Gradient (BD3MG) optimization algorithm for solving large scale non-convex differentiable optimization problems. Assuming a distributed memory environment, the algorithm casts the efficient 3MG scheme into smaller dimension subproblems where blocks of variables are addressed in an asynchronous manner. Convergence of the sequence built by the proposed BD3MG method is established under mild assumptions. Application to the restoration of 3D images degraded by a depth-variant blur shows that our method yields significant computational time reduction compared to several synchronous and asynchronous competitors , while exhibiting great scalability potential.

Code available at http://github.com/rfabbri/minus; International audience; We present a method for solving two minimal problems for relative camera pose estimation from three views, which are based on three view correspondences of (i) three points and one line and (ii) three points and two lines through two of the points. These problems are too difficult to be efficiently solved by the state of the art Grobner basis methods. Our method is based on a new efficient homotopy continuation (HC) solver, which dramatically speeds up previous HC solving by specializing HC methods to generic cases of our problems. We show in simulated experiments that our solvers are numerically robust and stable under image noise. We show in real experiment that (i) SIFT features provide good enough point-and-line correspondences for three-view reconstruction and (ii) that we can solve difficult cases with too few or too noisy tentative matches where the state of the art structure from motion initialization fails.

International audience

International audience; We consider the problem of political redistricting: given the locations of people in a geographical area (e.g. a US state), the goal is to decompose the area into subareas, called districts, so that the populations of the districts are as close as possible and the districts are "compact" and "contiguous," to use the terms referred to in most US state constitutions and/or US Supreme Court rulings.We study a method that outputs a solution in which each district is the intersection of a convex polygon with the geographical area. The average number of sides per polygon is less than six. The polygons tend to be quite compact. Every two districts differ in population by at most one (so we call the solution balanced).In fact, the solution is a centroidal power diagram: each polygon has an associated center in R3 such that• the projection of the center onto the plane z = 0 is the centroid of the locations of people assigned to the polygon, and• for each person assigned to that polygon, the polygon's center is closest among all centers. The polygons are convex because they are the intersections of 3D Voronoi cells with the plane.The solution is, in a well-defined sense, a locally optimal solution to the problem of choosing centers in the plane and choosing an assignment of people to those 2-d centers so as to minimize the sum of squared distances subject to the assignment being balanced.A practical problem with this approach is that, in real-world redistricting, exact locations of people are unknown. Instead, the input consists of polygons (census blocks) and associated populations. A real redistricting must not split census blocks. We therefore propose a second phase that perturbs the solution slightly so it does not split census blocks. In our experiments, the second phase achieves this while preserving perfect population balance. The district polygons are no longer convex at the fine scale because their boundaries must follow the boundaries of census blocks, but at a coarse scale they preserve the shape of the original polygons.

How efficiently can we find an unknown graph using distance or shortest path queries between its vertices? We assume that the unknown graph G is connected, unweighted, and has bounded degree. In the reconstruction problem, the goal is to find the graph G . In the verification problem, we are given a hypothetical graph Ĝ and want to check whether G is equal to Ĝ . We provide a randomized algorithm for reconstruction using Õ( n 3/2 ) distance queries, based on Voronoi cell decomposition. Next, we analyze natural greedy algorithms for reconstruction using a shortest path oracle and also for verification using either oracle, and show that their query complexity is n 1+ o (1) . We further improve the query complexity when the graph is chordal or outerplanar. Finally, we show some lower bounds, and consider an approximate version of the reconstruction problem.

Hierarchical clustering is a recursive partitioning of a dataset into clusters at an increasingly finer granularity. Motivated by the fact that most work on hierarchical clustering was based on providing algorithms, rather than optimizing a specific objective, Dasgupta (2016) framed similarity-based hierarchical clustering as a combinatorial optimization problem, where a `good' hierarchical clustering is one that minimizes some cost function. He showed that this cost function has certain desirable properties, such as in order to achieve optimal cost disconnected components must be separated first and that in `structureless' graphs, i.e., cliques, all clusterings achieve the same cost. We take an axiomatic approach to defining `good' objective functions for both similarity and dissimilarity-based hierarchical clustering. We characterize a set of admissible objective functions (that includes the one introduced by Dasgupta) that have the property that when the input admits a `natural' ground-truth hierarchical clustering, the ground-truth clustering has an optimal value. Equipped with a suitable objective function, we analyze the performance of practical algorithms, as well as develop better and faster algorithms for hierarchical clustering. For similarity-based hierarchical clustering, Dasgupta (2016) showed that a simple recursive sparsest-cut based approach achieves an O(log^3/2 n)-approximation on worst-case inputs. We give a more refined analysis of the algorithm and show that it in fact achieves an O(√log n)-approximation. This improves upon the LP-based O(log n)-approximation of Roy and Pokutta (2016). For dissimilarity-based hierarchical clustering, we show that the classic average-linkage algorithm gives a factor 2 approximation, and provide a simple and better algorithm that gives a factor 3/2 approximation. This aims at explaining the success of this heuristics in practice. Finally, we consider `beyond-worst-case' scenario through a generalisation of the stochastic block model for hierarchical clustering. We show that Dasgupta's cost function also has desirable properties for these inputs and we provide a simple algorithm that for graphs generated according to this model yields a 1 + o(1) factor approximation.

A top-list is a possibly incomplete ranking of elements: only a subset of the elements are ranked, with all unranked elements tied for last. Top-list aggregation, a generalization of the well-known rank aggregation problem, takes as input a collection of top-lists and aggregates them into a single complete ranking, aiming to minimize the number of upsets (pairs ranked in opposite order in the input and in the output). In this paper, we give simple approximation algorithms for top-list aggregation. * We generalize the footrule algorithm for rank aggregation. * Using inspiration from approval voting, we define the score of an element as the frequency with which it is ranked, i.e. appears in an input top-list. We reinterpret Ailon's RepeatChoice algorithm for top-list aggregation using the score of an element and its average rank given that it is ranked. * Using average ranks, we generalize and analyze Borda's algorithm for rank aggregation. * We design a simple 2-phase variant of the Generalized Borda's algorithm, roughly sorting by scores and breaking ties by average ranks. * We then design another 2-phase variant in which in order to break ties we use, as a black box, the Mathieu-Schudy PTAS for rank aggregation, yielding a PTAS for top-list aggregation. * Finally, we discuss the special case in which all input lists have constant length., Comment: To appear in SODA'20

In an asynchronous distributed system where any number of processes may crash, a process may have to run solo, computing its local output without receiving any information from other processes. In the basic shared memory system where the processes communicate through atomic read/write registers, at most one process may run solo. This paper introduces the family of d-solo models, where d-processes may concurrently run solo, 1 ≤ d ≤ n (the 1-solo model is the basic read/write model). The paper then studies distributed colorless computations in the d-solo models, where process ids are not used, either in task specifications or during computation. It presents a characterization of the colorless tasks that can be solved in each d-solo model. Colorless tasks include consensus, set agreement and many other previously studied tasks. It shows that colorless algorithms have limited computational power for solving tasks, only when d > 1 . When d = 1 , colorless algorithms can solve the same tasks as algorithms that may use ids. It is well-known that, while consensus is not wait-free solvable in a model where at most one process may run solo, ϵ-approximate agreement is solvable. In a d-solo model, the fundamental solvable task is ( d , ϵ ) -solo approximate agreement, a generalization of ϵ-approximate agreement. Indeed, ( d , ϵ ) -solo approximate agreement can be solved in the d-solo model, but not in the ( d + 1 ) -solo model. Finally, the paper studies a link between the solvability of d-set agreement and ( d , ϵ ) -solo approximate agreement in asynchronous wait-free message-passing systems, which provides an insight on the “maximal partitioning” allowed to solve an approximate agreement task.

International audience; The stated goal for visual data exploration is to operate at a rate that matches the pace of human data analysts, but the ever increasing amount of data has led to a fundamental problem: datasets are often too large to process within interactive time frames. Progressive analytics and visualizations have been proposed as potential solutions to this issue. By processing data incrementally in small chunks, progressive systems provide approximate query answers at interactive speeds that are then refined over time with increasing precision. We study how progressive visualizations affect users in exploratory settings in an experiment where we capture user behavior and knowledge discovery through interaction logs and think-aloud protocols. Our experiment includes three visualization conditions and different simulated dataset sizes. The visualization conditions are: (1) blocking, where results are displayed only after the entire dataset has been processed; (2) instantaneous, a hypothetical condition where results are shown almost immediately; and (3) progressive, where approximate results are displayed quickly and then refined over time. We analyze the data collected in our experiment and observe that users perform equally well with either instantaneous or progressive visualizations in key metrics, such as insight discovery rates and dataset coverage, while blocking visualizations have detrimental effects.

International audience; We give the first polynomial-time approximation schemes (PTASs) for the following problems: (1) uniform facility location in edge-weighted planar graphs; (2) $k$-median and $k$-means in edge-weighted planar graphs; and (3) $k$-means in Euclidean space of bounded dimension. Our first and second results extend to minor-closed families of graphs. All our results extend to cost functions that are the $p$th power of the shortest-path distance. The algorithm is local search, where the local neighborhood of a solution $S$ consists of all solutions obtained from $S$ by removing and adding $1/\varepsilon^{\Theta(1)}$ centers.

International audience; Roundness and cylindricity evaluations are among the most important problems in computational metrology, and are based on sets of surface measurements (input data points). A recent approach to such evaluations is based on a linear-programming approach yielding a rapidly converging solution. Such a solution is determined by a fixed-size subset of a large input set. With the intent to simplify the main computational task, it appears desirable to cull from the input any point that cannot provably define the solution. In this note we present an analysis and an efficient solution to the problem of culling the input set. For input data points arranged in cross-sections under mild conditions of uniformity, this algorithm runs in linear time.

National audience; Understanding the dynamics of evolving social or infrastructure networks is a challenge in applied areas such as epidemiology, viral marketing, and urban planning. During the past decade, data has been collected on such networks but has yet to be analyzed fully. We propose to use information on the dynamics of the data to find stable partitions of the network into groups. For that purpose, we introduce a time-dependent, dynamic version of the facility location problem, which includes a switching cost when a client's assignment changes from one facility to another. This might provide a better representation of an evolving network, emphasizing the abrupt change of relationships between subjects rather than the continuous evolution of the underlying network. We show for some realistic examples that this model yields better hypotheses than its counterpart without switching costs, where each snapshot can be optimized independently. For our model, we present an $O(\log nT)$-approximation algorithm and a matching hardness result, where $n$ is the number of clients and $T$ is the number of timesteps. We also give another algorithm with approximation ratio $O(\log nT)$ for a variant model where the decision to open a facility is made independently at each timestep.

We improve complexity bounds for energy-efficient speed scheduling problems for both the single processor and multi-processor cases. Energy conservation has become a major concern, so revisiting traditional scheduling problems to take into account the energy consumption has been part of the agenda of the scheduling community for the past few years. We consider the energy minimizing speed scaling problem introduced by Yao et al. where we wish to schedule a set of jobs, each with a release date, deadline and work volume, on a set of identical processors. The processors may change speed as a function of time and the energy they consume is the $\alpha$th power of its speed. The objective is then to find a feasible schedule which minimizes the total energy used. We show that in the setting with an arbitrary number of processors where all work volumes are equal, there is a $2(1+\varepsilon)(5(1+\varepsilon))^{\alpha -1}\tilde{B}_{\alpha}=O_{\alpha}(1)$ approximation algorithm, where $\tilde{B}_{\alpha}$ is the generalized Bell number. This is the first constant factor algorithm for this problem. This algorithm extends to general unequal processor-dependent work volumes, up to losing a factor of $(\frac{(1+r)r}{2})^{\alpha}$ in the approximation, where $r$ is the maximum ratio between two work volumes. We then show this latter problem is APX-hard, even in the special case when all release dates and deadlines are equal and $r$ is 4. In the single processor case, we introduce a new linear programming formulation of speed scaling and prove that its integrality gap is at most $12^{\alpha -1}$. As a corollary, we obtain a $(12(1+\varepsilon))^{\alpha -1}$ approximation algorithm where there is a single processor, improving on the previous best bound of $2^{\alpha-1}(1+\varepsilon)^{\alpha}\tilde{B}_{\alpha}$ when $\alpha \ge 25$.

The assumption of real-number arithmetic, which is at the basis of conventional geometric algorithms, has been seriously challenged in recent years, since digital computers do not exhibit such capability. A geometric predicate usually consists of evaluating the sign of some algebraic expression. In most cases, rounded computations yield a reliable result, but sometimes rounded arithmetic introduces errors which may invalidate the algorithms. The rounded arithmetic may produce an incorrect result only if the exact absolute value of the algebraic expression is smaller than some (small) varepsilon, which represents the largest error that may arise in the evaluation of the expression. The threshold varepsilon depends on the structure of the expression and on the adopted computer arithmetic, assuming that the input operands are error-free. A pair (arithmetic engine,threshold) is an "arithmetic filter". In this paper we develop a general technique for assessing the efficacy of an arithmetic filter. The analysis consists of evaluating both the threshold and the probability of failure of the filter. To exemplify the approach, under the assumption that the input points be chosen randomly in a unit ball or unit cube with uniform density, we analyze the two important predicates "which-side" and "insphere". We show that the probability that the absolute values of the corresponding determinants be no larger than some positive value V, with emphasis on small V, is Theta(V) for the which-side predicate, while for the insphere predicate it is Theta(V^(2/3)) in dimension 1, O(sqrt(V)) in dimension 2, and O(sqrt(V) ln(1/V)) in higher dimensions. Constants are small, and are given in the paper., Comment: 22 pages 7 figures Results for in sphere test inproved in cs.CG/9907028

In a wait-free model any number of processes may crash. A process runs solo when it computes its local output without receiving any information from other processes, either because they crashed or they are too slow. While in wait-free shared-memory models at most one process may run solo in an execution, any number of processes may have to run solo in an asynchronous wait-free message-passing model. This paper is on the computability power of models in which several processes may concurrently run solo. It first introduces a family of round-based wait-free models, called the d-solo models, 1 ≤ d ≤ n, where up to d processes may run solo. The paper gives then a characterization of the colorless tasks that can be solved in each d-solo model. It also introduces the (d, ǫ)-solo approximate agreement task, which generalizes ǫ-approximate agreement, and proves that (d, ǫ)-solo approximate agreement can be solved in the d-solo model, but cannot be solved in the (d + 1)-solo model. The paper studies also the relation linking d-set agreement and (d, ǫ)-solo approximate agreement in asynchronous wait-free message-passing systems. These results establish for the first time a hierarchy of wait-free models that, while weaker than the basic read/write model, are nevertheless strong enough to solve non-trivial tasks.; Dans un modèle wait-free, un nombre quelconque de processus peut arrêter de fonctionner. Un processus s'exécute en solo lorsqu'il calcule sa sortie sans communiquer avec les autres processus. Dans les modèles wait-free avec des processus communicant par mémoire partagée, au plus un processus peut s'exécuter en solo, alors que, dans les modèles wait-free ou ils échangent des messages, un nombre quelconque d'entre eux peut avoir à s'exécuter en solo. Cet article étudie la calculabilité dans des modèles intermédiaires, appelés d-solo modèles, dans lesquels au plus d processus s'exécutent en solo.

International audience; We address the problem of upper-body human pose estimation in uncontrolled monocular video sequences, without manual initialization. Most current methods focus on isolated video frames and often fail to correctly localize arms and hands. Inferring pose over a video sequence is advantageous because poses of people in adjacent frames exhibit properties of smooth variation due to the nature of human and camera motion. To exploit this, previous methods have used prior knowledge about distinctive actions or generic temporal priors combined with static image likelihoods to track people in motion. Here we take a different approach based on a simple observation: Information about how a person moves from frame to frame is present in the optical flow field. We develop an approach for tracking articulated motions that "links" articulated shape models of people in adjacent frames through the dense optical flow. Key to this approach is a 2D shape model of the body that we use to compute how the body moves over time. The resulting "flowing puppets" provide a way of integrating image evidence across frames to improve pose inference. We apply our method on a challenging dataset of TV video sequences and show state-of-the-art performance.

International audience; Although action recognition in videos is widely studied, current methods often fail on real-world datasets. Many recent approaches improve accuracy and robustness to cope with challenging video sequences, but it is often unclear what affects the results most. This paper attempts to provide insights based on a systematic performance evaluation using thoroughly-annotated data of human actions. We annotate human Joints for the HMDB dataset (J-HMDB). This annotation can be used to derive ground truth optical flow and segmentation. We evaluate current methods using this dataset and systematically replace the output of various algorithms with ground truth. This enables us to discover what is important - for example, should we work on improving flow algorithms, estimating human bounding boxes, or enabling pose estimation? In summary, we find that highlevel pose features greatly outperform low/mid level features; in particular, pose over time is critical, but current pose estimation algorithms are not yet reliable enough to provide this information. We also find that the accuracy of a top-performing action recognition framework can be greatly increased by refining the underlying low/mid level features; this suggests it is important to improve optical flow and human detection algorithms. Our analysis and JHMDB dataset should facilitate a deeper understanding of action recognition algorithms.

We study the online clustering problem where data items arrive in an online fashion. The algorithm maintains a clustering of data items into similarity classes. Upon arrival of v, the relation between v and previously arrived items is revealed, so that for each u we are told whether v is similar to u. The algorithm can create a new cluster for v and merge existing clusters. When the objective is to minimize disagreements between the clustering and the input, we prove that a natural greedy algorithm is O(n)-competitive, and this is optimal. When the objective is to maximize agreements between the clustering and the input, we prove that the greedy algorithm is .5-competitive; that no online algorithm can be better than .834-competitive; we prove that it is possible to get better than 1/2, by exhibiting a randomized algorithm with competitive ratio .5+c for a small positive fixed constant c., 12 pages, 1 figure

We consider a stochastic version of the $k$-server problem in which $k$ servers move on a circle to satisfy stochastically generated requests. The requests are independent and identically distributed according to an arbitrary distribution on a circle, which is either discrete or continuous. The cost of serving a request is the distance that a server needs to move to reach the request. The goal is to minimize the steady-state expected cost induced by the requests. We study the performance of a greedy strategy, focusing, in particular, on its convergence properties and the interplay between the discrete and continuous versions of the process.

International audience; Ce papier décrit AEON, un système dédié à la synthèse d'algorithmes d'ordonnancement à partir de modèles de haut niveau. AEON, qui est entièrement écrit en COMET, prend en entrée le modèle de haut niveau d'un problème d'ordonnancement et l'analyse pour générer un algorithme dédié et qui exploite la structure du problème. AEON oeure une variété de synthétiseurs pour générer des algorithmes complets ou heuristiques. En outre, ces synthétiseurs peuvent être composés, permettant de générer naturellement des algorithmes hybrides complexes. Les premiers résultats montrent que cette approche peut être compétitive avec l'état de l'art des algorithmes de recherche.

We propose certified reduced basis methods for the efficient and reliable evaluation of a general output that is implicitly connected to a given parameterized input through the harmonic Maxwell's equations. The truth approximation and the development of the reduced basis through a greedy approach is based on a discontinuous Galerkin approximation of the linear partial differential equation. The formulation allows the use of different approximation spaces for solving the primal and the dual truth approximation problems to respect the characteristics of both problem types, leading to an overall reduction in the off-line computational effort. The main features of the method are the following: (i) rapid convergence on the entire representative set of parameters, (ii) rigorous a posteriori error estimators for the output, and (iii) a parameter independent off-line phase and a computationally very efficient on-line phase to enable the rapid solution of many-query problems arising in control, optimization, and design. The versatility and performance of this approach is shown through a numerical experiment, illustrating the modeling of material variations and problems with resonant behavior.

A permutation $a_1a_2 \ldots a_n$ is $\textit{indecomposable}$ if there does not exist $p \lt n$ such that $a_1a_2 \ldots a_p$ is a permutation of $\{ 1,2, \ldots ,p\}$. We compute the asymptotic probability that a permutation of $\mathbb{S}_n$ with $m$ cycles is indecomposable as $n$ goes to infinity with $m/n$ fixed. The error term is $O(\frac{\log(n-m)}{ n-m})$. The asymptotic probability is monotone in $m/n$, and there is no threshold phenomenon: it degrades gracefully from $1$ to $0$. When $n=2m$, a slight majority ($51.1 \ldots$ percent) of the permutations are indecomposable. We also consider indecomposable fixed point free involutions which are in bijection with maps of arbitrary genus on orientable surfaces, for these involutions with $m$ left-to-right maxima we obtain a lower bound for the probability of being indecomposable., Une permutation $a_1a_2 \ldots a_n$ est $\textit{indécomposable}$, s’il n’existe pas de $p \lt n$ tel que $a_1a_2 \ldots a_p$ est une permutation de $\{ 1,2, \ldots ,p\}$. Nous calculons la probabilité pour qu’une permutation de $\mathbb{S}_n$ ayant $m$ cycles soit indécomposable et plus particulièrement son comportement asymptotique lorsque $n$ tend vers l’infini et que $m=n$ est fixé. Cette valeur décroît régulièrement de $1$ à $0$ lorsque $m=n$ croît, et il n’y a pas de phénomène de seuil. Lorsque $n=2m$, une faible majorité ($51.1 \ldots$ pour cent) des permutations sont indécomposables. Nous considérons aussi les involutions sans point fixe indécomposables qui sont en bijection avec les cartes de genre quelconque plongées dans une surface orientable, pour ces involutions ayant $m$ maxima partiels (ou records) nous obtenons une borne inférieure pour leur probabilité d’êtres indécomposables.

Special issue on sketch based modeling; International audience; We present a new method for interactively creating garments for dressing virtual characters. The user draws an outline of the front and back of the garment, and the system makes reasonable geometric inferences about the overall shape of the garment (ignoring constraints arising from physics). Both the garment's shape and the way the character is wearing it are determined at once. We use the distance from the 2D garment silhouette to the character model to infer the variations of the distance between the remainder of the garment and the character in 3D. The garment surface is generated from the silhouette and border lines and this varying distance information, using a distance field to the character's body. This method is integrated in an interactive system in which the user sketches the garment over the 3D model of the character. Our results show that the system can be used to create a broad range of clothes that may be worn in a variety of ways.

International audience; We present a method for simply and interactively creating basic garments for dressing virtual characters in applications like video games. The user draws an outline of the front or back of the garment, and the system makes reasonable geometric inferences about the overall shape of the garment (ignoring constraints arising from physics and from the material of the garment). Thus both the garment's shape and the way the character is wearing it are determined at once. We use the distance from the 2D garment silhouette to the character model to infer the variations of the distance between the remainder of the garment and the character in 3D. The garment surface is generated from the silhouette and border lines and this varying distance information, thanks to a data-structure that stores the distance field to the character's body. This method is integrated in an interactive system in which the user sketches the garment over the 3D model of the character. Our results show that the system can be used to create both standard clothes (skirts, shirts) and other garments that may be worn in a variety of ways (scarves, panchos).

International audience; This paper proposes a solution for the automatic detection and tracking of human motion in image sequences. Due to the complexity of the human body and its motion, automatic detection of 3D human motion remains an open, and important, problem. Existing approaches for automatic detection and tracking focus on 2D cues and typically exploit object appearance (color distribution, shape) or knowledge of a static background. In contrast, we exploit 2D optical flow information which provides rich descriptive cues, while being independent of object and background appearance. To represent the optical flow patterns of people from arbitrary viewpoints, we develop a novel representation of human motion using low-dimensional spatio-temporal models that are learned using motion capture data of human subjects. In addition to human motion (the foreground) we probabilistically model the motion of generic scenes (the background); these statistical models are defined as Gibbsian fields specified from the first-order derivatives of motion observations. Detection and tracking are posed in a principled Bayesian framework which involves the computation of a posterior probability distribution over the model parameters (i.e., the location and the type of the human motion) given a sequence of optical flow observations. Particle filtering is used to represent and predict this non-Gaussian posterior distribution over time. The model parameters of samples from this distribution are related to the pose parameters of a 3D articulated model (e.g. the approximate joint angles and movement direction). Thus the approach proves suitable for initializing more complex probabilistic models of human motion. As shown by experiments on real image sequences, our method is able to detect and track people under different viewpoints with complex backgrounds.

An efficient technique to solve precision problems consists in using exact computations. For geometric predicates, using systematically expensive exact computations can be avoided by the use of filters. The predicate is first evaluated using rounding computations, and an error estimation gives a certificate of the validity of the result. In this note, we studies the statistical efficiency of filters for cosphericity predicate with an assumption of regular distribution of the points. We prove that the expected value of the polynomial corresponding to the in sphere test is greater than epsilon with probability O(epsilon log 1/epsilon) improving the results of a previous paper by the same authors., Comment: 7 pages 2 figures presented at the 15th European Workshop Comput. Geom., 113--116, 1999 improve previous results (in other paper)

International audience; This paper considers the problem of verifying the correctness of geometric structures. In particular, we design simple optimal checkers for convex polytopes in two and higher dimensions, and for various types of planar subdivisions, such as triangulations, Delaunay triangulations, and convex subdivisions. Their performance is analyzed also in terms of the algorithmic degree, which characterizes the arithmetic precision required.

International audience; Given is a set \s\ of $n$ points, each colored with one of $k \geq 3$ colours. We say that a triangle defined by three points of \s\ is 3-colored if its vertices have distinct colours. We prove in this paper that the problem of constructing the boundary of the union \ts\ of all such 3-colored triangles can be done in optimal $O(n \log n)$ time.

International audience; We study a family of implementations for linked lists using fine-grain synchronisation. This approach enables greater concurrency, but correctness is a greater challenge than for classical, coarse-grain synchronisation. Our examples are demonstrative of common design patterns such as lock coupling, optimistic, and lazy synchronisation. Although they are are highly concurrent, we prove that they are linearisable, safe, and they correctly implement a high-level abstraction. Our proofs illustrate the power and applicability of rely-guarantee reasoning, as well of some of its limitations. The examples of the paper establish a benchmark challenge for other reasoning techniques.