Abstract
In the present work the problem of reconstructing locations of events in an arbitrary scene, or "world" (for example 3D scene in real applications) from an over-complete set of measurements, typically of lower dimension each (such as multiple 2D images obtained from different cameras) is addressed. A non-parametric approach based on Principal Component Analysis (PCA) has been developed where a training set of points with known world-coordinates is used to reconstruct the forward and inverse transformation matrices from the scene to the measurement space. The technique does not use any a priori information about the data acquisition geometry or its parameters and can also identify degenerate cases where either the training or the measurement sets are insufficient to perform robust reconstruction. As a first illustration a simple test-set of objects and their 2D images has been presented in order to illustrate the validity of the method. The next realistic application involves a data set of explosions recorded from two high-speed cameras. The method successfully reconstructs the positions of the explosions and in addition their intensities were also quantified.