We propose a novel abstraction of the image segmentation task in the form of a combinatorial optimization problem that we call the multi-separator problem. Feasible solutions indicate for every pixel whether it belongs to a segment or a segment separator, and indicate for pairs of pixels whether or not the pixels belong to the same segment. This is in contrast to the closely related lifted multicut problem where every pixel is associated to a segment and no pixel explicitly represents a separating structure. While the multi-separator problem is NP-hard, we identify two special cases for which it can be solved efficiently. Moreover, we define two local search algorithms for the general case and demonstrate their effectiveness in segmenting simulated volume images of foam cells and filaments.

翻译：我们提出了一种新颖的图像分割任务抽象形式，即一个称为多分隔符问题的组合优化问题。可行解指示每个像素属于一个分割区域还是分割区域分隔符，并指示像素对是否属于同一分割区域。这与密切相关的提升多割问题形成对比，后者中每个像素关联到一个分割区域，且没有像素明确表示分隔结构。尽管多分隔符问题是NP难的，我们识别出其两种可高效求解的特例情况。此外，我们针对一般情况定义了两种局部搜索算法，并通过在泡沫细胞与丝状物的模拟体素图像分割中展示了其有效性。