A note on the KP hierarchy

Given the two boson representation of the conformal algebra \hat W_\infty, the second Hamiltonian structure of the KP hierarchy, I construct a bi-Hamiltonian hierarchy for the two associated currents. The KP hierarchy appears as a composite of this new and simpler system. The bi-Hamiltonian structure of the new hierarchy gives naturally all the Hamiltonian structures of the KP system.Comment: 12 pages, no figure

A framework for forensic face recognition based on recognition performance calibrated for the quality of image pairs

Recently, it has been shown that performance of a face recognition system depends on the quality of both face images participating in the recognition process: the reference and the test image. In the context of forensic face recognition, this observation has two implications: a) the quality of the trace (extracted from CCTV footage) constrains the performance achievable using a particular face recognition system; b) the quality of the suspect reference set (to which the trace is matched against) can be judiciously chosen to approach optimal recognition performance under such a constraint. Motivated by these recent findings, we propose a framework for forensic face recognition that is based on calibrating the recognition performance for the quality of pairs of images. The application of this framework to several mock-up forensic cases, created entirely from the MultiPIE dataset, shows that optimal recognition performance, under such a constraint, can be achieved by matching the quality (pose, illumination, and, imaging device) of the reference set to that of the trace. This improvement in recognition performance helps reduce the rate of misleading interpretation of the evidence