Unfortunately, computation of appropriate registration parameters
is complicated. Even the simplest models must first nominate
features that are invariant between known-match images. Clearly
minutiae coordinates (x, y) will vary between misregistered
known-matches, so automated algorithms must seek alternative
features (or alternative means) of deducing correspondences. One
approach to this problem is to generate Delaunay triangles using
minutiae as vertices (Fig. 1) [12]. Ideally, minutia triplets generate
triangles that possess invariant features (inner angles and ratio of
sides) which in turn nominate a series of candidate control points
that can be used to compute the registration parameters that
maximize the similarity between two images [11,12].
The success associated with using triangulation as a means of
determining appropriate affine transformation parameters hinges
on the fact that the Delaunay triangulation of a set of points is both
unique, and possess high local stability [19]. However, the stability
has a limit; extreme low quality prints with a large number of
missing or spurious minutiae can result in triangulation maps that
lack any correspondence when compared to maps associated with
high quality known-match prints [11]. The result is an automated
registration procedure that will result in a low match score, despite
the presence of matching (but spatially distant and dispersed)
minutiae. In other words, the algorithm is sensitive to the number
of corresponding minutiae in a localized area, rather than the total
number of matching minutiae between two prints. However, the
match score that results from registration using triangulation is
actually a good measure of local correspondence and the presence of
minutiae with a compact spatial configuration (as opposed to
distant matching minutiae separated by unknown blocks of low
quality ridge detail).
Given the value of a cluster of corresponding minutiae (versus
spatially dispersed matching minutiae separated by voids in
clarity), the automated registration employed for this study was
based on Delaunay triangulation to extract invariant features in
both high quality and low quality fingerprints. The invariant
features were used to nominate candidate matching control points
(minutiae) allowing computation of affine transformation variables
of rotation and translation