Classical morphological filters suffer from well performing in a noisy environment, and intrinsic image structures are not taken into account. The authors propose here an alternative to overcome such weaknesses, by properly using robust shock filters and inhomogeneity. Thus, they obtain multiscale morphological operators by using image edge functions as local weights in inhomogeneous Hamiltonians in classical multiscale dilations/erosions formulated with partial differential equations (PDEs). They provide the equivalent sup–inf-based formulations, and derive sharpening/enhancement methods. In addition, they establish the PDE associated with the asymptotical iterations of the proposed robust and adaptive filters. The good behaviours of the proposed sup–inf and PDE-based methods are illustrated on synthetic, greyscale, and colour images; results are analysed both qualitatively and quantitatively.

中文翻译：

---

用于鲁棒和自适应图像冲击滤波器的非均匀形态PDE

经典的形态过滤器在嘈杂的环境中表现良好，并且没有考虑固有的图像结构。作者在这里提出了一种替代方法，可以通过适当使用健壮的冲击滤波器和非均质性来克服这些缺点。因此，他们通过在偏微分方程（PDE）公式化的经典多尺度膨胀/侵蚀中，使用图像边缘函数作为不均匀哈密顿量中的局部权重，获得多尺度形态算子。他们提供了等效的基于sup-inf的公式，并推导了锐化/增强方法。另外，它们建立与所提出的鲁棒和自适应滤波器的渐近迭代相关的PDE。在合成，灰度和彩色图像上说明了所建议的sup-inf和基于PDE的方法的良好行为。