Spectral Solution of Large-Scale Extrinsic Camera Calibration as a Graph Embedding Problem

Extrinsic calibration of large-scale ad hoc networks of cameras is posed as the following problem: Calculate the locations of N mobile, rotationally aligned cameras distributed over an urban region, subsets of which view some common environmental features. We show that this leads to a novel class of graph embedding problems that admit closed-form solutions in linear time via partial spectral decomposition of a quadratic form. The minimum squared error (mse) solution determines locations of cameras and/or features in any number of dimensions. The spectrum also indicates insufficiently constrained problems, which can be decomposed into well-constrained rigid subproblems and analyzed to determine useful new views for missing constraints. We demonstrate the method with large networks of mobile cameras distributed over an urban environment, using directional constraints that have been extracted automatically from commonly viewed features. Spectral solutions yield layouts that are consistent in some cases to a fraction of a millimeter, substantially improving the state of the art. Global layout of large camera networks can be computed in a fraction of a second.