Calibrating Distributed Camera Networks Using Belief Propagation

Abstract

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.

Calibrating Distributed Camera Networks

“…In the rest of this section, we summarize our basic approach to the distributed calibration of camera networks, which is more fully described in [8], [9], [66]. Our goal is to design a calibration system in which each camera only communicates with (and possesses knowledge about) those cameras connected to it by an edge in the vision graph.…”

“…We reported detailed results of testing this initial calibration algorithm on synthetic camera/scene configurations in [8], showing that the calibration accuracy was quite good and declined gracefully with additional measurement noise. We also analyzed the algorithm's cost in terms of the numbers of messages each camera would transmit/receive compared to those of a centralized algorithm where one node acts as a "master".…”

“…In Section IV we review approaches for distributed estimation of the calibration parameters of all cameras in the network based on the vision graph. We focus on an efficient method for initializing and refining the calibration estimates we recently proposed in [8], [9]. Throughout Sections III and IV, we illustrate our results on a running example of a set of images acquired from cameras distributed throughout RPI's campus.…”

Distributed calibration of Camera Sensor Networks

“…This has motivated several distributed localization algorithms in the camera sensor networks community such as [12], [13], [14], [15], [16], [17], [18], [19]. Semi-automatic camera network calibration methods use laser printed textures mounted on a board [12] or modulated LED emissions [13], [14].…”

“…Semi-automatic camera network calibration methods use laser printed textures mounted on a board [12] or modulated LED emissions [13], [14]. Automatic methods perform local SfM via robust bundle adjustment [17] and integrate the information using belief propagation [18]. However, these algorithms integrate the information in an ad-hoc fashion and do not provide rigorous proofs of convergence to the centralized solution.…”