Multiview stereo via volumetric Graph-Cuts and occlusion robust photo-consistency.

This paper presents a volumetric formulation for the multi-view stereo problem which is amenable to a computationally tractable global optimisation using Graph-cuts. Our approach is to seek the optimal partitioning of 3D space into two regions labelled as "object" and "empty" under a cost functional consisting of the following two terms: (1) A term that forces the boundary between the two regions to pass through photo-consistent locations and (2) a ballooning term that inflates the "object" region. To take account of the effect of occlusion on the first term we use an occlusion robust photo-consistency metric based on Normalised Cross Correlation, which does not assume any geometric knowledge about the reconstructed object. The globally optimal 3D partitioning can be obtained as the minimum cut solution of a weighted graph.

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.