Fageot Julien, Uhlmann Virginie, Puspoki Zsuzsanna, Beck Benjamin, Unser Michael, Depeursinge Adrien
IEEE Trans Image Process. 2021;30:4465-4478. doi: 10.1109/TIP.2021.3072499. Epub 2021 Apr 21.
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.
我们提供了一个完整的流程，用于检测图像中感兴趣的模式。在我们的方法中，假设这些模式可以由已知模板进行充分建模，并且位于我们旨在检索的未知位置和方向上。我们提出了一种连续域加法图像模型，其中被分析的图像是要定位的模式与具有自相似各向同性功率谱的背景之和。然后，我们能够基于单个模板和背景对计算满足信噪比标准的最优滤波器：它对模板有强烈响应，同时与背景模型实现最优解耦。此外，我们将滤波器约束为可转向的，这使得能够快速进行模板检测并同时估计方向。在实际应用中，实现需要在极坐标网格上对连续域公式进行离散化，这通过二次径向B样条来完成。我们在各种模板近似和模式检测实验中展示了我们方法的实际有效性。我们表明，当我们通过背景的功率谱衰减利用其统计信息时，检测性能会大幅提高，我们将其称为频谱整形。所提出的方案在绝对检测性能上比现有最先进的可转向方法高出多达50%。
