Segmenting material images into underlying objects is an important but challenging problem given object complexity and image noise. Consistency of shape, appearance, and topology among the underlying objects are critical properties of materials images and can be considered as criteria to improve segmentation. For example, some materials may have objects with a specific shape or appearance in each serial section slice, which only changes minimally from slice to slice; and some materials may

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... it specific interobject topology which constrains their neighboring relations. In this paper, we develop new graph-cut based approaches for materials science image segmentation. Specifically, these approaches segment image volumes by repeatedly propagating a 2D segmentation from one slice to another. We introduce different terms into the graph-cut cost function to enforce desirable shape, appearance, and topology consistency. We justify the effectiveness of the proposed approaches by using them to segment sequences of serial-section images of different materials. Segmentation via Labeling In this paper we use the multi-labeling framework outlined in [1, 2, 3, 4] to propagate a 2D segmentation from one segmented slice S i to another S i+1 . A labeling algorithm simply assigns an integer (label) to each pixel in S i+1 , in which we use labels to represent the phases in a material (e.g. specific crystal structures, or different material states). A label function in this framework f is formulated as