分类分布的形态学
Morphology on categorical distributions
摘要：
分类分布是多类分割中不确定性的自然表示。在两类的情况下，分类分布减少到伯努利分布，灰度形态学提供了一系列有用的操作。在一般情况下，对不确定的多类分割应用形态学运算并不简单，因为分类分布的图像不是完整的格。虽然彩色图像的形态学得到了广泛的关注，这是不是这样的颜色编码或分类的图像，甚至更少的分类分布的图像。在这项工作中，我们建立了一套要求的形态学分类分布相结合的经典形态学的概率视图。然后，我们定义运营商尊重这些要求，介绍保护操作的分类分布，并说明这些运营商的效用在两个示例任务：建模注释器偏见脑肿瘤分割和分割囊泡实例从多类U-网的预测。
英文摘要：
The categorical distribution is a natural representation of uncertainty in multi-class segmentations. In the two-class case the categorical distribution reduces to the Bernoulli distribution, for which grayscale morphology provides a range of useful operations. In the general case, applying morphological operations on uncertain multi-class segmentations is not straightforward as an image of categorical distributions is not a complete lattice. Although morphology on color images has received wide attention, this is not so for color-coded or categorical images and even less so for images of categorical distributions. In this work, we establish a set of requirements for morphology on categorical distributions by combining classic morphology with a probabilistic view. We then define operators respecting these requirements, introduce protected operations on categorical distributions and illustrate the utility of these operators on two example tasks: modeling annotator bias in brain tumor segmentations and segmenting vesicle instances from the predictions of a multi-class U-Net.
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