  In this paper we address the problem of matching patterns in the so-called
verification setting in which a novel, query pattern is verified against a
single training pattern: the decision sought is whether the two match (i.e.
belong to the same class) or not. Unlike previous work which has universally
focused on the development of more discriminative distance functions between
patterns, here we consider the equally important and pervasive task of
selecting a distance threshold which fits a particular operational requirement
- specifically, the target false positive rate (FPR). First, we argue on
theoretical grounds that a data-driven approach is inherently ill-conditioned
when the desired FPR is low, because by the very nature of the challenge only a
small portion of training data affects or is affected by the desired threshold.
This leads us to propose a general, statistical model-based method instead. Our
approach is based on the interpretation of an inter-pattern distance as
implicitly defining a pattern embedding which approximately distributes
patterns according to an isotropic multi-variate normal distribution in some
space. This interpretation is then used to show that the distribution of
training inter-pattern distances is the non-central chi2 distribution,
differently parameterized for each class. Thus, to make the class-specific
threshold choice we propose a novel analysis-by-synthesis iterative algorithm
which estimates the three free parameters of the model (for each class) using
task-specific constraints. The validity of the premises of our work and the
effectiveness of the proposed method are demonstrated by applying the method to
the task of set-based face verification on a large database of pseudo-random
head motion videos.

Computer Vision and Pattern Recognition