  We propose a template matching method for the detection of 2D image objects
that are characterized by orientation patterns. Our method is based on data
representations via orientation scores, which are functions on the space of
positions and orientations, and which are obtained via a wavelet-type
transform. This new representation allows us to detect orientation patterns in
an intuitive and direct way, namely via cross-correlations. Additionally, we
propose a generalized linear regression framework for the construction of
suitable templates using smoothing splines. Here, it is important to recognize
a curved geometry on the position-orientation domain, which we identify with
the Lie group SE(2): the roto-translation group. Templates are then optimized
in a B-spline basis, and smoothness is defined with respect to the curved
geometry. We achieve state-of-the-art results on three different applications:
detection of the optic nerve head in the retina (99.83% success rate on 1737
images), of the fovea in the retina (99.32% success rate on 1616 images), and
of the pupil in regular camera images (95.86% on 1521 images). The high
performance is due to inclusion of both intensity and orientation features with
effective geometric priors in the template matching. Moreover, our method is
fast due to a cross-correlation based matching approach.
