4.7 Article

Principled Design and Implementation of Steerable Detectors

Journal

IEEE TRANSACTIONS ON IMAGE PROCESSING
Volume 30, Issue -, Pages 4465-4478

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2021.3072499

Keywords

Detectors; Signal to noise ratio; Splines (mathematics); Estimation; Pipelines; Computational modeling; Biomedical imaging; Steerable filters; pattern detection; orientation estimation; SNR criterion; isotropic self-similar Gaussian model; radial B-spines

Funding

  1. Swiss National Science Foundation [200020-162343/1, PZ00P2_154891, 205320_179069]
  2. European Bioinformatics Institute (EMBL)

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A pipeline for pattern detection in images is presented, utilizing a continuous-domain additive image model and optimal filter computation method. The approach involves discretization on polar grids and improving detection performance by exploiting the power-spectrum decay of background statistics.
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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