Fast Realization of Digital Elevation Model

International audienceWe propose an optimization approach to speed up the point matching process underlying the 3D reconstruction of complex urban scenes. We consider the Optical Flow technique for point matching and propose to introduce MMX and SSE2 instructions to accelerate significantly the matching process. Fast point matching allows using sub-pixel image resolution, which provides a more accurate estimation of the Optical Flow by exploiting wider correlation windows, and therefore improves the final quality of urban scenes 3D reconstructions

Hyperfast second-order local solvers for efficient statistically preconditioned distributed optimization

Statistical preconditioning enables fast methods for distributed large-scale empirical risk minimization problems. In this approach, multiple worker nodes compute gradients in parallel, which are then used by the central node to update the parameter by solving an auxiliary (preconditioned) smaller-scale optimization problem. The recently proposed Statistically Preconditioned Accelerated Gradient (SPAG) method [1] has complexity bounds superior to other such algorithms but requires an exact solution for computationally intensive auxiliary optimization problems at every iteration. In this paper, we propose an Inexact SPAG (InSPAG) and explicitly characterize the accuracy by which the corresponding auxiliary subproblem needs to be solved to guarantee the same convergence rate as the exact method. We build our results by first developing an inexact adaptive accelerated Bregman proximal gradient method for general optimization problems under relative smoothness and strong convexity assumptions, which may be of independent interest. Moreover, we explore the properties of the auxiliary problem in the InSPAG algorithm assuming Lipschitz third-order derivatives and strong convexity. For such problem class, we develop a linearly convergent Hyperfast second-order method and estimate the total complexity of the InSPAG method with hyperfast auxiliary problem solver. Finally, we illustrate the proposed method's practical efficiency by performing large-scale numerical experiments on logistic regression models. To the best of our knowledge, these are the first empirical results on implementing high-order methods on large-scale problems, as we work with data where the dimension is of the order of 3 million, and the number of samples is 700 million

3D reconstruction of buildings using the chinese shadows technique

Nous considérons le problème de la reconstruction 3D du bâti à partir d'image(s) de télédétection. Ce problème est classiquement perçu comme un problème inverse puisqu'il s'agit de retrouver la scène qui, à travers le système optique, a produit les images. L'information la plus souvent exploitée est la stéréométrie. Sous réserve de posséder un couple d'images sous des angles différents, il est possible de reconstruitre la troisième dimension. Le problème consiste alors essentiellement à mettre en correspondance les deux images∼\cite{Baillard:1999,Taillandier:2004,Lafarge:2008}. Les ombres ou l'ombrage peuvent également donner une information utile∼\cite{McGlone:1994,Lin:1998}. Dans cet article, nous montrons qu'il est possible de résoudre le problème direct. L'idée consiste à proposer des configurations de bâtiments, puis à simuler les images résultant de ces configurations. Un critère est optimisé pour estimer la solution. C'est le principe des ombres chinoises qui consiste, non pas à calculer l'objet recherché à partir de l'ombre, mais à tester et modifier différentes configurations des mains de sorte que l'ombre produite corresponde à celle de l'objet recherché. Une telle approche est séduisante car elle s'affranchit des difficultés des approches inverses, comme par exemple dans le cas de deux bâtiments tels que l'ombre de l'un se projette sur l'autre. Des exemples de l'approche directe, fondés sur une modélisation par processus ponctuels marqués, ont montré son efficacité pour la reconnaissance d'objets géométriques simples tels que des ellipses ou des rectangles∼\cite{Ortner:2008,Descamps:2008). Néanmoins, la pertinence d'une approche directe peut être mise en doute en raison du temps de calcul. Comment générer des hypothèses et quel temps de calcul est nécessaire à la projection de la scène sur le(s) plan(s) image(s) sont deux questions cruciales. Nous adoptons ici une démarche simple pour la génération d'hypothèses consistant en un algorithme de type glouton. Un objet est modifié aléatoirement à chaque itération et ce changement est accepté si et seulement s'il améliore la configuration au sens du critère adopté. Nous montrons néanmoins qu'il est réaliste d'adopter une approche directe, en nous appuyant sur la puissance de calcul de la carte graphique et le logiciel libre OpenGL pour effectuer la synthèse des images obtenues à partir d'une configuration de bâtiments

An accelerated second-order method for distributed stochastic optimization

We consider distributed stochastic optimization problems that are solved with master/workers computation architecture. Statistical arguments allow to exploit statistical similarity and approximate this problem by a finite-sum problem, for which we propose an inexact accelerated cubic-regularized Newton's method that achieves lower communication complexity bound for this setting and improves upon existing upper bound. We further exploit this algorithm to obtain convergence rate bounds for the original stochastic optimization problem and compare our bounds with the existing bounds in several regimes when the goal is to minimize the number of communication rounds and increase the parallelization by increasing the number of workers

Hyperfast second-order local solvers for efficient statistically preconditioned distributed optimization

Statistical preconditioning enables fast methods for distributed large-scale empirical risk minimization problems. In this approach, multiple worker nodes compute gradients in parallel, which are then used by the central node to update the parameter by solving an auxiliary (preconditioned) smaller-scale optimization problem. The recently proposed Statistically Preconditioned Accelerated Gradient (SPAG) method has complexity bounds superior to other such algorithms but requires an exact solution for computationally intensive auxiliary optimization problems at every iteration. In this paper, we propose an Inexact SPAG (InSPAG) and explicitly characterize the accuracy by which the corresponding auxiliary subproblem needs to be solved to guarantee the same convergence rate as the exact method. We build our results by first developing an inexact adaptive accelerated Bregman proximal gradient method for general optimization problems under relative smoothness and strong convexity assumptions, which may be of independent interest. Moreover, we explore the properties of the auxiliary problem in the InSPAG algorithm assuming Lipschitz third-order derivatives and strong convexity. For such problem class, we develop a linearly convergent Hyperfast second-order method and estimate the total complexity of the InSPAG method with hyperfast auxiliary problem solver. Finally, we illustrate the proposed method's practical efficiency by performing large-scale numerical experiments on logistic regression models. To the best of our knowledge, these are the first empirical results on implementing high-order methods on large-scale problems, we work with data where the dimension is of the order of~3 million, and the number of samples is~700 million

Design of materials for solid oxide fuel cells cathodes and oxygen separation membranes based on fundamental studies of their oxygen mobility and surface reactivity

Design of materials for solid oxide fuel cells cathodes and oxygen separation membranes and studying their oxygen transport characteristics are important problems of modern hydrogen energy. In the current work, fundamentals of such materials design based on characterization of their oxygen mobility by oxygen isotope exchange with C18O2 and 18O2 in flow and closed reactors for samples of Ruddlesden – Popper-type oxides Ln2-xCaxNiO4+δ, perovskite-fluorite nanocomposites PrNi0.5Co0.5O3-δ – Ce0.9Y0.1O2-δ, etc. are presented. Fast oxygen transport was demonstrated for PNC – YDC (DO ~10-8 cm2/s at 700°C) nanocomposites due to domination of the fast diffusion channel involving oxygen of the fluorite phase with incorporated Pr cations and developed perovskite-fluorite interfaces. For LnCNO materials a high oxygen mobility (DO ~10-7 cm2/s at 700°C) provided by the cooperative mechanism of its migration was demonstrated. Depending on Ca dopant content and Ln cation nature, in some cases 1–2 additional channels of the slow diffusion appear due to decreasing the interstitial oxygen content and increasing the energy barrier for oxygen jumps due to cationic size effect. Optimized by the chemical composition and nanodomain structure materials of these types demonstrated a high performance as SOFC cathodes and functional layers in asymmetric supported oxygen separation membranes