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We provide a complete pipeline for the detection of patterns of interest inan image. In our approach, the patterns are assumed to be adequately modeled bya known template, and are located at unknown positions and orientations that weaim at retrieving. We propose a continuous-domain additive image model, wherethe analyzed image is the sum of the patterns to localize and a background withself-similar isotropic power-spectrum. We are then able to compute the optimalfilter fulfilling the SNR criterion based on one single template and backgroundpair: it strongly responds to the template while being optimally decoupled fromthe background model. In addition, we constrain our filter to be steerable,which allows for a fast template detection together with orientationestimation. In practice, the implementation requires to discretize acontinuous-domain formulation on polar grids, which is performed usingquadratic radial B-splines. We demonstrate the practical usefulness of ourmethod on a variety of template approximation and pattern detectionexperiments. We show that the detection performance drastically improves whenwe exploit the statistics of the background via its power-spectrum decay, whichwe refer to as spectral-shaping. The proposed scheme outperformsstate-of-the-art steerable methods by up to 50% of absolute detectionperformance.

Principled Design and Implementation of Steerable Detectors