ORB-SLAM: A Versatile and Accurate Monocular SLAM System

This paper presents ORB-SLAM, a feature-based monocular simultaneous localization and mapping (SLAM) system that operates in real time, in small and large indoor and outdoor environments. The system is robust to severe motion clutter, allows wide baseline loop closing and relocalization, and includes full automatic initialization. Building on excellent algorithms of recent years, we designed from scratch a novel system that uses the same features for all SLAM tasks: tracking, mapping, relocalization, and loop closing. A survival of the fittest strategy that selects the points and keyframes of the reconstruction leads to excellent robustness and generates a compact and trackable map that only grows if the scene content changes, allowing lifelong operation. We present an exhaustive evaluation in 27 sequences from the most popular datasets. ORB-SLAM achieves unprecedented performance with respect to other state-of-the-art monocular SLAM approaches. For the benefit of the community, we make the source code public

Smoothed Analysis of the Minimum-Mean Cycle Canceling Algorithm and the Network Simplex Algorithm

The minimum-cost flow (MCF) problem is a fundamental optimization problem with many applications and seems to be well understood. Over the last half century many algorithms have been developed to solve the MCF problem and these algorithms have varying worst-case bounds on their running time. However, these worst-case bounds are not always a good indication of the algorithms' performance in practice. The Network Simplex (NS) algorithm needs an exponential number of iterations for some instances, but it is considered the best algorithm in practice and performs best in experimental studies. On the other hand, the Minimum-Mean Cycle Canceling (MMCC) algorithm is strongly polynomial, but performs badly in experimental studies. To explain these differences in performance in practice we apply the framework of smoothed analysis. We show an upper bound of $O(mn^2\log(n)\log(\phi))$ for the number of iterations of the MMCC algorithm. Here $n$ is the number of nodes, $m$ is the number of edges, and $\phi$ is a parameter limiting the degree to which the edge costs are perturbed. We also show a lower bound of $\Omega(m\log(\phi))$ for the number of iterations of the MMCC algorithm, which can be strengthened to $\Omega(mn)$ when $\phi=\Theta(n^2)$. For the number of iterations of the NS algorithm we show a smoothed lower bound of $\Omega(m \cdot \min \{ n, \phi \} \cdot \phi)$.Comment: Extended abstract to appear in the proceedings of COCOON 201

Scheduling data transfers in a network and the set scheduling problem

In this paper we consider the online ftp problem. The goal is to service a sequence of file transfer requests given bandwidth constraints of the underlying communication network. The main result of the paper is a technique that leads to algorithms that optimize several natural metrics, such as max-stretch, total flow time, max flow time, and total completion time. In particular, we show how to achieve optimum total flow time and optimum max-stretch if we increase the capacity of the underlying network by a logarithmic factor. We show that the resource augmentation is necessary by proving polynomial lower bounds on the max-stretch and total flow time for the case where online and offline algorithms are using same-capacity edges. Moreover, we also give poly-logarithmic lower bounds on the resource augmentation factor necessary in order to keep the total flow time and max-stretch within a constant factor of optimum

Self-similar shear-thickening behavior in CTAB/NaSal surfactant solutions

The effect of salt concentration Cs on the critical shear rate required for the onset of shear thickening and apparent relaxation time of the shear-thickened phase, has been investigated systematically for dilute CTAB/NaSal solutions. Experimental data suggest a self-similar behavior of the critical shear rate and relaxation time as functions of Cs. Specifically, the former ~ Cs^(-6) whereas the latter ~ Cs^(6) such that an effective Weissenberg number for the onset of the shear thickened phase is only weakly dependent on Cs. A procedure has been developed to collapse the apparent shear viscosity versus shear rate data obtained for various values of Cs into a single master curve. The effect of Cs on the elastic modulus and mesh size of the shear-induced gel phase for different surfactant concentrations is discussed. Experiments performed using different flow cells (Couette and cone-and-plate) show that the critical shear rate, relaxation time and the maximum viscosity attained are geometry-independent. The elastic modulus of the gel phase inferred indirectly by employing simplified hydrodynamic instability analysis of a sheared gel-fluid interface is in qualitative agreement with that predicted for an entangled phase of living polymers. A qualitative mechanism that combines the effect of Cs on average micelle length and Debye parameter with shear-induced configurational changes of rod-like micelles is proposed to rationalize the self-similarity of SIS formation.Comment: 27 pages, 17 figure

Particle dynamics in sheared granular matter

The particle dynamics and shear forces of granular matter in a Couette geometry are determined experimentally. The normalized tangential velocity $V(y)$ declines strongly with distance $y$ from the moving wall, independent of the shear rate and of the shear dynamics. Local RMS velocity fluctuations $\delta V(y)$ scale with the local velocity gradient to the power $0.4 \pm 0.05$. These results agree with a locally Newtonian, continuum model, where the granular medium is assumed to behave as a liquid with a local temperature $\delta V(y)^2$ and density dependent viscosity

Prediction of attrition in agitated particle beds

The majority of pharmaceutical powders produced through crystallisation are dried in agitated dryers. The rotation of the impeller causes shear deformation of the bed, which enhances the drying rate, but also leads to particle breakage. A method of predicting the extent of breakage occurring due to agitation is described and applied for Paracetamol in a small-scale dryer. The distributions of stresses and strains in the bed are estimated using the Distinct Element Method (DEM). The information obtained here is then coupled with the measured attrition of Paracetamol in an annular shear cell in order to predict the attrition in the agitated bed. The experiments are carried out on dry material so as to establish purely the effect of stresses and strains on attrition, whilst keeping moisture content and temperature constant.The shear cell provides uniform condition for stresses and strains so that the breakage taking place under relatively well-defined conditions is quantified. In contrast, the prevailing shear stresses and strains in the agitated bed have wide distributions, as little shearing takes place near the impeller shaft, whilst there are considerable shearing stresses near the impeller tip. Therefore, the bed is divided into a number of segments for which the extent of attrition can be evaluated for each segment, based on the shear cell data. A good quantitative agreement is found between the predictions and experimental results obtained for the attrition of Paracetamol in the small scale dryer. The resulting prediction also suggests that, for a given number of impeller rotations, the extent of breakage is independent of impeller speed in the range tested (20-78. rpm). This is expected as the prevailing strain rates are too low for the inertial effects to be dominating and the shear stresses are independent of shear rates within the range investigated. The attrition prediction suggest that over half of the attrition occurs in the bottom third of the bed, with increased attrition at greater radial distances. The attrition is also predicted to occur predominantly within the region extending from 30° in front of to 30° behind the impeller

The history of degenerate (bipartite) extremal graph problems

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version of our survey presented in Erdos 100. In this version 2 only a citation was complete

Chip-Firing and Rotor-Routing on Directed Graphs

We give a rigorous and self-contained survey of the abelian sandpile model and rotor-router model on finite directed graphs, highlighting the connections between them. We present several intriguing open problems.Comment: 34 pages, 11 figures. v2 has additional references, v3 corrects figure 9, v4 corrects several typo

Granular Flow in Silo Discharge: Discrete Element Method Simulations and Model Assessment

Discharge dynamics of granular particles from a flat-bottomed silo is studied using both continuum modeling and three-dimensional (3D) discrete element method (DEM) simulations. Using DEM, the influence of microscopic parameters (interparticle friction coefficient, particle–wall friction coefficient and particle coefficient of restitution) and system parameters (orifice width) on the discharge rate is quantified. The spatial extent of different regimes (quasi-static, intermediate and inertial) of granular rheology are quantified using a regime map previously established from DEM data of homogeneously sheared granular flow. It is shown that all three regimes of granular rheology coexist during silo discharge, and the intermediate regime plays a significant role in discharge dynamics. A quantitative comparison between results of continuum and DEM simulations is performed by computing discharge rates, solid velocities, and solid stresses for a three-dimensional (3D) flat-bottomed silo. It is found that the three constitutive models investigated in this study overpredict the discharge rate when compared to DEM data. Contour plots of the error in solid stress prediction are compared with the spatial extent of different regimes of granular rheology to deduce that it is inaccurate modeling of the intermediate regime that is responsible for overprediction of the discharge rate