where E1(si) is the likelihood ener

where E1(si) is the likelihood energy, denoting the costwhen the label of node i is si, and E2(si, sj ) is the prior energy, encoding the cost when the labels of adjacent nodes i and j are si and sj respectively. Our problem becomes a graph-cut energy minimization problem [7] and is very similar to the image segmentation problem using graph cuts [17, 9]. An analogy of our problem to image segmentation is shown in Table 1. The main difference with segmentation is that our graph is dual-layered as shown in Figure 6(b), since the exterior and non-exterior surface(s) can be observed at the same time as the object is transparent.