Topology-Preserving Multi-label Image Segmentation

Enforcing a specific topology in image segmentation is a very important but challenging problem, which has attracted much attention in the computer vision community. Most recent works on topology-constrained image segmentation focus on binary segmentation, where the topology is often described by the connectivity of both foreground and background. In this paper, we develop a new multi-labeling method to enforce topology in multi-label image segmentation. In this case, we not only require each segment to be a connected region (intra-segment topology), but also require specific adjacency relations between each pair of segments (inter-segment topology). We develop our method in the context of segmentation propagation, where a segmented template image defines the topology, and our goal is to propagate the segmentation to a target image while preserving the topology. Our method requires good spatial structure continuity between the template and the target such that the template segmentation can be used as a good initialization for segmenting the target. In addition, we focus on multi-label segmentation where a segment and its adjacent segments form a ring structure, which is among the most complex type of inter-segment topology for 2D structures. We apply the proposed method to segment 3D metallic image volumes for the underlying grain structures and achieve better results than several comparison methods. Finally, we also apply the proposed method to interactive segmentation and stereo matching applications.