3,458 research outputs found
A probabilistic interpretation of set-membership filtering: application to polynomial systems through polytopic bounding
Set-membership estimation is usually formulated in the context of set-valued
calculus and no probabilistic calculations are necessary. In this paper, we
show that set-membership estimation can be equivalently formulated in the
probabilistic setting by employing sets of probability measures. Inference in
set-membership estimation is thus carried out by computing expectations with
respect to the updated set of probability measures P as in the probabilistic
case. In particular, it is shown that inference can be performed by solving a
particular semi-infinite linear programming problem, which is a special case of
the truncated moment problem in which only the zero-th order moment is known
(i.e., the support). By writing the dual of the above semi-infinite linear
programming problem, it is shown that, if the nonlinearities in the measurement
and process equations are polynomial and if the bounding sets for initial
state, process and measurement noises are described by polynomial inequalities,
then an approximation of this semi-infinite linear programming problem can
efficiently be obtained by using the theory of sum-of-squares polynomial
optimization. We then derive a smart greedy procedure to compute a polytopic
outer-approximation of the true membership-set, by computing the minimum-volume
polytope that outer-bounds the set that includes all the means computed with
respect to P
Polyhedral Predictive Regions For Power System Applications
Despite substantial improvement in the development of forecasting approaches,
conditional and dynamic uncertainty estimates ought to be accommodated in
decision-making in power system operation and market, in order to yield either
cost-optimal decisions in expectation, or decision with probabilistic
guarantees. The representation of uncertainty serves as an interface between
forecasting and decision-making problems, with different approaches handling
various objects and their parameterization as input. Following substantial
developments based on scenario-based stochastic methods, robust and
chance-constrained optimization approaches have gained increasing attention.
These often rely on polyhedra as a representation of the convex envelope of
uncertainty. In the work, we aim to bridge the gap between the probabilistic
forecasting literature and such optimization approaches by generating forecasts
in the form of polyhedra with probabilistic guarantees. For that, we see
polyhedra as parameterized objects under alternative definitions (under
and norms), the parameters of which may be modelled and predicted.
We additionally discuss assessing the predictive skill of such multivariate
probabilistic forecasts. An application and related empirical investigation
results allow us to verify probabilistic calibration and predictive skills of
our polyhedra.Comment: 8 page
Visual Odometry and Sparse Scene Reconstruction for UAVs with a Multi-Fisheye Camera System
Autonomously operating UAVs demand a fast localization for navigation, to actively explore unknown areas and to create maps. For pose estimation, many UAV systems make use of a combination of GPS receivers and inertial sensor units (IMU). However, GPS signal coverage may go down occasionally, especially in the close vicinity of objects, and precise IMUs are too heavy to be carried by lightweight UAVs. This and the high cost of high quality IMU motivate the use of inexpensive vision based sensors for localization using visual odometry or visual SLAM (simultaneous localization and mapping) techniques. The first contribution of this thesis is a more general approach to bundle adjustment with an extended version of the projective coplanarity equation which enables us to make use of omnidirectional multi-camera systems which may consist of fisheye cameras that can capture a large field of view with one shot. We use ray directions as observations instead of image points which is why our approach does not rely on a specific projection model assuming a central projection. In addition, our approach allows the integration and estimation of points at infinity, which classical bundle adjustments are not capable of. We show that the integration of far or infinitely far points stabilizes the estimation of the rotation angles of the camera poses. In its second contribution, we employ this approach to bundle adjustment in a highly integrated system for incremental pose estimation and mapping on light-weight UAVs. Based on the image sequences of a multi-camera system our system makes use of tracked feature points to incrementally build a sparse map and incrementally refines this map using the iSAM2 algorithm. Our system is able to optionally integrate GPS information on the level of carrier phase observations even in underconstrained situations, e.g. if only two satellites are visible, for georeferenced pose estimation. This way, we are able to use all available information in underconstrained GPS situations to keep the mapped 3D model accurate and georeferenced. In its third contribution, we present an approach for re-using existing methods for dense stereo matching with fisheye cameras, which has the advantage that highly optimized existing methods can be applied as a black-box without modifications even with cameras that have field of view of more than 180 deg. We provide a detailed accuracy analysis of the obtained dense stereo results. The accuracy analysis shows the growing uncertainty of observed image points of fisheye cameras due to increasing blur towards the image border. Core of the contribution is a rigorous variance component estimation which allows to estimate the variance of the observed disparities at an image point as a function of the distance of that point to the principal point. We show that this improved stochastic model provides a more realistic prediction of the uncertainty of the triangulated 3D points.Autonom operierende UAVs benötigen eine schnelle Lokalisierung zur Navigation, zur Exploration unbekannter Umgebungen und zur Kartierung. Zur Posenbestimmung verwenden viele UAV-Systeme eine Kombination aus GPS-EmpfĂ€ngern und Inertial-Messeinheiten (IMU). Die VerfĂŒgbarkeit von GPS-Signalen ist jedoch nicht ĂŒberall gewĂ€hrleistet, insbesondere in der NĂ€he abschattender Objekte, und prĂ€zise IMUs sind fĂŒr leichtgewichtige UAVs zu schwer. Auch die hohen Kosten qualitativ hochwertiger IMUs motivieren den Einsatz von kostengĂŒnstigen bildgebenden Sensoren zur Lokalisierung mittels visueller Odometrie oder SLAM-Techniken zur simultanen Lokalisierung und Kartierung. Im ersten wissenschaftlichen Beitrag dieser Arbeit entwickeln wir einen allgemeineren Ansatz fĂŒr die BĂŒndelausgleichung mit einem erweiterten Modell fĂŒr die projektive KollinearitĂ€tsgleichung, sodass auch omnidirektionale Multikamerasysteme verwendet werden können, welche beispielsweise bestehend aus Fisheyekameras mit einer Aufnahme einen groĂen Sichtbereich abdecken. Durch die Integration von Strahlrichtungen als Beobachtungen ist unser Ansatz nicht von einem kameraspezifischen Abbildungsmodell abhĂ€ngig solange dieses der Zentralprojektion folgt. Zudem erlaubt unser Ansatz die Integration und SchĂ€tzung von unendlich fernen Punkten, was bei klassischen BĂŒndelausgleichungen nicht möglich ist. Wir zeigen, dass durch die Integration weit entfernter und unendlich ferner Punkte die SchĂ€tzung der Rotationswinkel der Kameraposen stabilisiert werden kann. Im zweiten Beitrag verwenden wir diesen entwickelten Ansatz zur BĂŒndelausgleichung fĂŒr ein System zur inkrementellen PosenschĂ€tzung und dĂŒnnbesetzten Kartierung auf einem leichtgewichtigen UAV. Basierend auf den Bildsequenzen eines Mulitkamerasystems baut unser System mittels verfolgter markanter Bildpunkte inkrementell eine dĂŒnnbesetzte Karte auf und verfeinert diese inkrementell mittels des iSAM2-Algorithmus. Unser System ist in der Lage optional auch GPS Informationen auf dem Level von GPS-TrĂ€gerphasen zu integrieren, wodurch sogar in unterbestimmten Situation - beispielsweise bei nur zwei verfĂŒgbaren Satelliten - diese Informationen zur georeferenzierten PosenschĂ€tzung verwendet werden können. Im dritten Beitrag stellen wir einen Ansatz zur Verwendung existierender Methoden fĂŒr dichtes Stereomatching mit Fisheyekameras vor, sodass hoch optimierte existierende Methoden als Black Box ohne Modifzierungen sogar mit Kameras mit einem Gesichtsfeld von mehr als 180 Grad verwendet werden können. Wir stellen eine detaillierte Genauigkeitsanalyse basierend auf dem Ergebnis des dichten Stereomatchings dar. Die Genauigkeitsanalyse zeigt, wie stark die Genauigkeit beobachteter Bildpunkte bei Fisheyekameras zum Bildrand aufgrund von zunehmender UnschĂ€rfe abnimmt. Das KernstĂŒck dieses Beitrags ist eine VarianzkomponentenschĂ€tzung, welche die SchĂ€tzung der Varianz der beobachteten DisparitĂ€ten an einem Bildpunkt als Funktion von der Distanz dieses Punktes zum Hauptpunkt des Bildes ermöglicht. Wir zeigen, dass dieses verbesserte stochastische Modell eine realistischere PrĂ€diktion der Genauigkeiten der 3D Punkte ermöglicht
Active and Physics-Based Human Pose Reconstruction
Perceiving humans is an important and complex problem within computervision. Its significance is derived from its numerous applications, suchas human-robot interaction, virtual reality, markerless motion capture,and human tracking for autonomous driving. The difficulty lies in thevariability in human appearance, physique, and plausible body poses. Inreal-world scenes, this is further exacerbated by difficult lightingconditions, partial occlusions, and the depth ambiguity stemming fromthe loss of information during the 3d to 2d projection. Despite thesechallenges, significant progress has been made in recent years,primarily due to the expressive power of deep neural networks trained onlarge datasets. However, creating large-scale datasets with 3dannotations is expensive, and capturing the vast diversity of the realworld is demanding. Traditionally, 3d ground truth is captured usingmotion capture laboratories that require large investments. Furthermore,many laboratories cannot easily accommodate athletic and dynamicmotions. This thesis studies three approaches to improving visualperception, with emphasis on human pose estimation, that can complementimprovements to the underlying predictor or training data.The first two papers present active human pose estimation, where areinforcement learning agent is tasked with selecting informativeviewpoints to reconstruct subjects efficiently. The papers discard thecommon assumption that the input is given and instead allow the agent tomove to observe subjects from desirable viewpoints, e.g., those whichavoid occlusions and for which the underlying pose estimator has a lowprediction error.The third paper introduces the task of embodied visual active learning,which goes further and assumes that the perceptual model is notpre-trained. Instead, the agent is tasked with exploring its environmentand requesting annotations to refine its visual model. Learning toexplore novel scenarios and efficiently request annotation for new datais a step towards life-long learning, where models can evolve beyondwhat they learned during the initial training phase. We study theproblem for segmentation, though the idea is applicable to otherperception tasks.Lastly, the final two papers propose improving human pose estimation byintegrating physical constraints. These regularize the reconstructedmotions to be physically plausible and serve as a complement to currentkinematic approaches. Whether a motion has been observed in the trainingdata or not, the predictions should obey the laws of physics. Throughintegration with a physical simulator, we demonstrate that we can reducereconstruction artifacts and enforce, e.g., contact constraints
A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning
We present a tutorial on Bayesian optimization, a method of finding the
maximum of expensive cost functions. Bayesian optimization employs the Bayesian
technique of setting a prior over the objective function and combining it with
evidence to get a posterior function. This permits a utility-based selection of
the next observation to make on the objective function, which must take into
account both exploration (sampling from areas of high uncertainty) and
exploitation (sampling areas likely to offer improvement over the current best
observation). We also present two detailed extensions of Bayesian optimization,
with experiments---active user modelling with preferences, and hierarchical
reinforcement learning---and a discussion of the pros and cons of Bayesian
optimization based on our experiences
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