Persistent Homologies have been successfully used to increase the performance of deep networks trained to detect curvilinear structures and to improve the topological quality of the results. However, existing methods are very global and ignore the location of topological features. In this paper, we introduce an approach that relies on a new filtration function to account for location during network training. We demonstrate experimentally on 2D images of roads and 3D image stacks of neuronal processes that networks trained in this manner are better at recovering the topology of the curvilinear structures they extract.

翻译：已经成功地利用持久性人类学来提高深层网络的性能,这些深层网络受过训练,可以探测曲线结构,提高结果的表层质量;然而,现有的方法非常全球化,忽视了地形特征的位置;在本文件中,我们采用了一种方法,在网络培训期间,依靠新的过滤功能来说明位置;我们实验性地展示了2D的公路图象和3D的神经过程图层,以这种方式培训的网络在恢复它们提取的曲线结构的地形方面做得更好。