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arXiv · 1811.00863

Principled Design and Implementation of Steerable Detectors

Julien Fageot·Virginie Uhlmann·Zsuzsanna Püspöki·Benjamin Beck·Michael Unser·Adrien Depeursinge
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Abstract

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.

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Julien Fageot, Virginie Uhlmann, Zsuzsanna Püspöki, Benjamin Beck, Michael Unser, Adrien Depeursinge. 2018-10-23. Principled Design and Implementation of Steerable Detectors. https://arxiv.org/abs/1811.00863

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