Current approaches to generic segmentation start by creating a hierarchy of nested image partitions and then specifying a segmentation from it. Our first contribution is to describe several ways, most of them new, for specifying segmentations using the hierarchy elements. Then, we consider the best hierarchy-induced segmentation specified by a limited number of hierarchy elements. We focus on a common quality measure for binary segmentations, the Jaccard index (also known as IoU). Optimizing the Jaccard index is highly non-trivial, and yet we propose an efficient approach for doing exactly that. This way we get algorithm-independent upper bounds on the quality of any segmentation created from the hierarchy. We found that the obtainable segmentation quality varies significantly depending on the way that the segments are specified by the hierarchy elements, and that representing a segmentation with only a few hierarchy elements is often possible. (Code is available).

翻译：当前通用分割方法通常先构建嵌套图像分区的层级结构，再从中指定分割结果。本文的首要贡献是描述若干种利用层级元素指定分割的方法（其中多数为全新方案）。随后，我们研究了通过有限层级元素指定的最优层级诱导分割，聚焦于二值分割的常用质量指标——杰卡德指数（亦称IoU）。优化该指数具有极高难度，但我们提出了一种高效方法实现精确优化。由此可获得基于该层级生成的任意分割质量与算法无关的上界。研究发现：根据层级元素指定分割方式的不同，可获取的分割质量存在显著差异，且通常仅需少量层级元素即可表征分割结果。（代码已开源）