Morphological neural networks, or layers, can be a powerful tool to boost the
progress in mathematical morphology, either on theoretical aspects such as the
representation of complete lattice operators, or in the development of image
processing pipelines. However, these architectures turn out to be difficult to
train when they count more than a few morphological layers, at least within
popular machine learning frameworks which use gradient descent based
optimization algorithms. In this paper we investigate the potential and
limitations of differentiation based approaches and back-propagation applied to
morphological networks, in light of the non-smooth optimization concept of
Bouligand derivative. We provide insights and first theoretical guidelines, in
particular regarding initialization and learning rates.

研究了基于差分和反向传播的形态学网络的潜力和限制，尤其是在初始化和学习速率方面的理论指导，以解决当形态学网络层数增加时的训练困难。

使用梯度下降训练形态神经网络：一些理论洞见

Training morphological neural networks with gradient descent: some  theoretical insights

We summarise the properties of the Sloan Digital Sky Survey (SDSS) project,
discuss our software infrastructure, and outline the architecture of the SDSS
image processing pipelines.
We then discuss two of the algorithms used in the SDSS image processing; the
KL-transform based modelling of the spatial variation of the PSF, and the use
of galaxy models in star/galaxy separation.
We conclude with the first author's personal opinions on the challenges that
the astronomical community faces with major software projects.

本文总结了 Sloan Digital Sky Survey（SDSS）项目的特性，讨论了软件基础设施，并概述了 SDSS 图像处理管道的架构。然后，我们讨论了 SDSS 图像处理中使用的两种算法：基于 KL 变换的 PSF 空间变化建模以及在星 / 星系分离中使用星系模型。最后，第一作者对天文学界在大型软件项目方面面临的挑战提出了个人观点。