The insideness problem is an aspect of image segmentation that consists of determining which pixels are inside and outside a region. Deep neural networks (DNNs) excel in segmentation benchmarks, but it is unclear if they have the ability to solve the insideness problem as it requires evaluating long-range spatial dependencies. In this letter, we analyze the insideness problem in isolation, without texture or semantic cues, such that other aspects of segmentation do not interfere in the analysis. We demonstrate that DNNs for segmentation with few units have sufficient complexity to solve the insideness for any curve. Yet such DNNs have severe problems with learning general solutions. Only recurrent networks trained with small images learn solutions that generalize well to almost any curve. Recurrent networks can decompose the evaluation of long-range dependencies into a sequence of local operations, and learning with small images alleviates the common difficulties of training recurrent networks with a large number of unrolling steps.

内部问题是图像分割的一个方面，包括确定哪些像素在区域内部和外部。深度神经网络 (DNN) 在分割基准方面表现出色，但尚不清楚它们是否有能力解决内部问题，因为它需要评估远程空间依赖性。在这封信中，我们孤立地分析内部问题，没有纹理或语义线索，这样分割的其他方面就不会干扰分析。我们证明了用于具有少量单元的分割的 DNN 具有足够的复杂性来解决任何曲线的内部性。然而，此类 DNN 在学习通用解决方案方面存在严重问题。只有用小图像训练的循环网络才能学习几乎可以很好地泛化到任何曲线的解决方案。