Large scale heterogeneous networks, the Davis-Wielandt shell, and graph separation

We consider a large scale network of interconnected heterogeneous dynamical components. Scalable stability conditions are derived that involve the input/output properties of individual subsystems and the interconnection matrix. The analysis is based on the Davis-Wielandt shell, a higher dimensional version of the numerical range with important convexity properties. This can be used to allow heterogeneity in the agent dynamics while relaxing normality and symmetry assumptions on the interconnection matrix. The results include small gain and passivity approaches as special cases, with the three dimensional shell shown to be inherently connected with corresponding graph separation arguments. © 2012 Society for Industrial and Applied Mathematics.

High-level scene structure using visibility and occlusion

We demonstrate a new method for extracting high-level scene information from the type of data available from simultaneous localisation and mapping systems. We model the scene with a collection of primitives (such as bounded planes), and make explicit use of both visible and occluded points in order to refine the model. Since our formulation allows for different kinds of primitives and an arbitrary number of each, we use Bayesian model evidence to compare very different models on an even footing. Additionally, by making use of Bayesian techniques we can also avoid explicitly finding the optimal assignment of map landmarks to primitives. The results show that explicit reasoning about occlusion improves model accuracy and yields models which are suitable for aiding data association. © 2011. The copyright of this document resides with its authors.