We discuss how to automatically obtain the metric calibration of an ad-hoc network of cameras with no centralized processor. We model the set of uncalibrated cameras as nodes in a communication network, and propose a distributed algorithm in which each camera performs a local, robust bundle adjustment over the camera parameters and scene points of its neighbors in an overlay "vision graph". We analyze the performance of the algorithm on both simulated and real data, and show that the distributed algorithm results in a fairer allocation of messages per node while achieving comparable calibration accuracy to centralized bundle adjustment.

We propose a decentralized method for obtaining the vision graph for a distributed, ad-hoc camera network, in which each edge of the graph represents two cameras that image a sufficiently large part of the same environment. Each camera encodes a spatially well-distributed set of distinctive, approximately viewpoint-invariant feature points into a fixed-length "feature digest" that is broadcast throughout the network. Each receiver camera robustly matches its own features with the decompressed digest and decides whether sufficient evidence exists to form a vision graph edge. We also show how a camera calibration algorithm that passes messages only along vision graph edges can recover accurate 3D structure and camera positions in a distributed manner. We analyze the performance of different message formation schemes, and show that high detection rates (> 0.8) can be achieved while maintaining low false alarm rates (< 0.05) using a simulated 60-node outdoor camera network.

Recent developments in wireless sensor networks have made feasible distributed camera networks, in which cameras and processing nodes may be spread over a wide geographical area, with no centralized processor and limited ability to communicate a large amount of information over long distances. This paper overviews distributed algorithms for the calibration of such camera networks-that is, the automatic estimation of each camera's position, orientation, and focal length. In particular, we discuss a decentralized method for obtaining the vision graph for a distributed camera network, in which each edge of the graph represents two cameras that image a sufficiently large part of the same environment. We next describe a distributed algorithm in which each camera performs a local, robust nonlinear optimization over the camera parameters and scene points of its vision graph neighbors to obtain an initial calibration estimate.We then show how a distributed inference algorithm based on belief propagation can refine the initial estimate to be both accurate and globally consistent.

We discuss how to obtain the accurate and globally consistent self-calibration of a distributed camera network, in which camera nodes with no centralized processor may be spread over a wide geographical area. We present a distributed calibration algorithm based on belief propagation, in which each camera node communicates only with its neighbors that image a sufficient number of scene points. The natural geometry of the system and the formulation of the estimation problem give rise to statistical dependencies that can be efficiently leveraged in a probabilistic framework. The camera calibration problem poses several challenges to information fusion, including overdetermined parameterizations and nonaligned coordinate systems. We suggest practical approaches to overcome these difficulties, and demonstrate the accurate and consistent performance of the algorithm using a simulated 30-node camera network with varying levels of noise in the correspondences used for calibration, as well as an experiment with 15 real images.

Cooperative game theory is relevant for ensuring reliability of power grid of electricity markets, where central objectives of its transmission sector clash with the private incentive of its players. It is a critical component of market engineering as also is differential pricing, which is used here for pricing of transmission. Another tool used in the model for transmission sector, is a power vector to identify coalition partners. This procedural model is explained in three phases of game theory and is illustrated using a 24 bus power system. The results are significant and show that loss, congestion and total power flow in lines decrease considerably, improving efficiency.