Accurately segmenting a series of 2D serial-sectioned images for multiple, contiguous 3D structures has important applications in medical image processing, video sequence analysis, and materials science image segmentation. While 2D structure topology is largely consistent across consecutive serial sections, it may vary locally because a 3D structure of interest may not span the entire 2D sequence. In this paper, we develop a new approach to address this challenging problem by considering both the global consistency and possible local inconsistency of the 2D structural topology. In this approach, we repeatedly propagate a 2D segmentation from one slice to another, and we formulate each step of this propagation as an optimal labeling problem that can be efficiently solved using the graph-cut algorithm. Specifically, we divide the optimal labeling into two steps: a global labeling that enforces topology consistency, and a local labeling that identifies possible topology inconsistency. We justify the effectiveness of the proposed approach by using it to segment a sequence of serial-section microscopic images of an alloy widely used in material sciences and compare its performance against several existing image segmentation methods.