DUST: dual union of spatio-temporal subspaces for monocular multiple object 3D reconstruction

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.We present an approach to reconstruct the 3D shape of multiple deforming objects from incomplete 2D trajectories acquired by a single camera. Additionally, we simultaneously provide spatial segmentation (i.e., we identify each of the objects in every frame) and temporal clustering (i.e., we split the sequence into primitive actions). This advances existing work, which only tackled the problem for one single object and non-occluded tracks. In order to handle several objects at a time from partial observations, we model point trajectories as a union of spatial and temporal subspaces, and optimize the parameters of both modalities, the non-observed point tracks and the 3D shape via augmented Lagrange multipliers. The algorithm is fully unsupervised and results in a formulation which does not need initialization. We thoroughly validate the method on challenging scenarios with several human subjects performing different activities which involve complex motions and close interaction. We show our approach achieves state-of-the-art 3D reconstruction results, while it also provides spatial and temporal segmentation.Peer ReviewedPostprint (author's final draft

Snapshot-Based Methods and Algorithms

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

Méthodes numériques et statistiques pour l'analyse de trajectoire dans un cadre de geométrie Riemannienne.

This PhD proposes new Riemannian geometry tools for the analysis of longitudinal observations of neuro-degenerative subjects. First, we propose a numerical scheme to compute the parallel transport along geodesics. This scheme is efficient as long as the co-metric can be computed efficiently. Then, we tackle the issue of Riemannian manifold learning. We provide some minimal theoretical sanity checks to illustrate that the procedure of Riemannian metric estimation can be relevant. Then, we propose to learn a Riemannian manifold so as to model subject's progressions as geodesics on this manifold. This allows fast inference, extrapolation and classification of the subjects.Cette thèse porte sur l'élaboration d'outils de géométrie riemannienne et de leur application en vue de la modélisation longitudinale de sujets atteints de maladies neuro-dégénératives. Dans une première partie, nous prouvons la convergence d'un schéma numérique pour le transport parallèle. Ce schéma reste efficace tant que l'inverse de la métrique peut être calculé rapidement. Dans une deuxième partie, nous proposons l'apprentissage une variété et une métrique riemannienne. Après quelques résultats théoriques encourageants, nous proposons d'optimiser la modélisation de progression de sujets comme des géodésiques sur cette variété