In this paper, we consider the problem of unsupervised video object\nsegmentation via background subtraction. Specifically, we pose the nonsemantic\nextraction of a video's moving objects as a nonconvex optimization problem via\na sum of sparse and low-rank matrices. The resulting formulation, a nonnegative\nvariant of robust principal component analysis, is more computationally\ntractable than its commonly employed convex relaxation, although not generally\nsolvable to global optimality. In spite of this limitation, we derive intuitive\nand interpretable conditions on the video data under which the uniqueness and\nglobal optimality of the object segmentation are guaranteed using local search\nmethods. We illustrate these novel optimality criteria through example\nsegmentations using real video data.\n