  We propose an approach to the problem of global reconstruction of an
orientation field. The method is based on a geometric model called "bisector
line fields", which maps a pair of vector fields to an orientation field,
effectively generalizing the notion of doubling phase vector fields. Endowed
with a well chosen energy minimization problem, we provide a polynomial
interpolation of a target orientation field while bypassing the doubling phase
step. The procedure is then illustrated with examples from fingerprint
analysis.
