Vol.฀63฀No.฀7฀•฀JOM 49 www.tms.org/jom.html Research Summary Large Datasets in Materials Science, Part II Graph-Cut Methods for Grain Boundary Segmentation Song Wang, Jarrell Waggoner, and Jeff Simmons How would you… …describe the overall significance of this paper? This paper introduces new methods for accurately and automatically segmenting the grain boundaries from various material images, which can substantially facilitate the modeling and analysis of the material microstructure, and shorten the period of design and development of new materials. …describe this work to a materials science and engineering professional with no experience in your technical specialty? In this paper, we suggest the use of graph-cut methods for material image segmentation. In these methods, an image is modeled by a graph which considers both intensity and spatial relations of the pixels. New approaches are also introduced to enforce the segmentation continuity between neighboring slices in a sequence of 2-D serial sections. …describe this work to a layperson? Of great importance in studying materials is to extract the boundaries of the microstructures that make up a material. This process, called segmentation, is often done by hand, or with various rudimentary software tools on various material images. In this paper, we describe more advanced graph-cut methods recently investigated in the computer vision community for automatic microstructure segmentation. This paper reviews the recent prog- ress on using graph-cut methods for image segmentation, and discusses their applications to segmenting grain boundaries from materials science im- ages. INTRODUCTION The size and shape of crystals (i.e., grains) in polycrystalline materi- als (e.g., metals and metal alloys) are among the strongest determinants of many material properties, such as me- chanical strength or fracture resistance. In materials science research, the emerging practice involves construct- ing three-dimensional (3-D) models of the grain structure and then apply- ing inite element modeling to infer the mechanical properties from that struc- ture. 1,2 Accurately and automatically segmenting the grain boundaries from various material images can substan- tially facilitate the modeling and analy- sis of the material microstructure, and shorten the period of design and devel- opment of new materials. Image segmentation is a fundamen- tal problem in computer vision and im- age processing. In past decades, many image segmentation algorithms and tools have been developed and are used to process images in different domains, such as pictures taken indoors and out- doors, aerial images, medical images, and videos. Particularly, graph-cut methods for image segmentation have attracted tremendous interest in the computer vision community in recent years. Compared to classical image- segmentation methods, such as edge detection, region splitting/merging, and pixel clustering, graph-cut meth- ods are more “global” by considering well-deined, comprehensive segmen- tation cost functions and seeking their globally optimal solutions using ad- vanced graph theory. GRAPH AND MINIMUM CUT In graph-cut methods, a graph G =(V, E) with vertices V and edges E is irst constructed to represent an image. Considering a two-dimensional (2-D) image, we can construct a vertex for each pixel and an edge between two vertices corresponding to two neigh- boring pixels, as shown in Figure 1. A graph cut divides the graph into two subgraphs G 1 and G 2 by removing all the edges connecting G 1 and G 2 . Two examples are shown in Figure 1b and d, where the removal of the edges inter- sected by the dashed curve constitutes a graph cut. A graph cut corresponds to a segmentation boundary (either open or closed) in the image. Multiple-region image segmentation can be obtained by repeated graph cuts on the subgraphs G 1 and G 2 . Image-intensity information is typi- cally encoded into an edge-weight function w(u, v), where (u, v) ∈ E. For example, we can define w(u, v) as a decreasing function of the intensity dif- ference between vertices (pixels) u and v. This way, a graph cut that removes low-weight edges is more preferred for image segmentation. In graph-cut methods, the two central problems are: 1) defining a cost function for each pos- sible graph cut to reflect the aforemen- tioned preference, and 2) developing a graph algorithm to find the optimal graph cut that minimizes this cost func- tion. In Reference 3, the cost function is defined to be the total weight of the removed edges, i.e. This is the well-known minimum cut problem, and its global optima can be efficiently found by the min-cut max- flow algorithm. However, image seg- mentation using minimum cut has a bias toward producing shorter bound- aries. 3 GRAPH CUTS WITH NORMALIZED COSTS Various kinds of normalization have been incorporated in graph-cut cost