# Principled Design and Implementation of Steerable Detectors

arXiv: https://arxiv.org/abs/1811.00863 · HTML: https://mlsanity.com/paper/1811.00863/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2018.

## Built on by (most cited first, 2 of 2)

- [Fast Normalized Cross-Correlation for Template Matching with Rotations](https://mlsanity.com/paper/2311.07561/) (2023)
- [Tensorial template matching for fast cross-correlation with rotations and its application for tomography](https://mlsanity.com/paper/2408.02398/) (2024)

## Abstract (arXiv)

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.