We define morphological operators and filters for directional images whose pixel values are unit vectors. This requires an ordering relation for unit vectors which is obtained by using depth functions. They provide a centre-outward ordering with respect to a specified centre vector. We apply our operators on synthetic directional images and compare them with classical morphological operators for grey-scale images. As application examples, we enhance the fault region in a compressed glass foam and segment misaligned fibre regions of glass fibre reinforced polymers.

翻译：本文针对像素值为单位向量的方向图像，定义了形态学算子和滤波器。这需要利用深度函数建立单位向量的排序关系，该排序以指定中心向量为基准，实现从中心到外部的有序化。我们将所提出的算子应用于合成方向图像，并与经典灰度图像形态学算子进行对比。在应用实例中，我们对压缩玻璃泡沫的断层区域进行增强，并对玻璃纤维增强聚合物中未对齐纤维区域进行分割。