  We provide a complete pipeline for the detection of patterns of interest in
an image. In our approach, the patterns are assumed to be adequately modeled by
a known template, and are located at unknown positions and orientations that we
aim at retrieving. We propose a continuous-domain additive image model, where
the analyzed image is the sum of the patterns to localize and a background with
self-similar isotropic power-spectrum. We are then able to compute the optimal
filter fulfilling the SNR criterion based on one single template and background
pair: it strongly responds to the template while being optimally decoupled from
the background model. In addition, we constrain our filter to be steerable,
which allows for a fast template detection together with orientation
estimation. In practice, the implementation requires to discretize a
continuous-domain formulation on polar grids, which is performed using
quadratic radial B-splines. We demonstrate the practical usefulness of our
method on a variety of template approximation and pattern detection
experiments. We show that the detection performance drastically improves when
we exploit the statistics of the background via its power-spectrum decay, which
we refer to as spectral-shaping. The proposed scheme outperforms
state-of-the-art steerable methods by up to 50% of absolute detection
performance.
