This paper conducts an in-depth study on a classical perceptual-organization problem: finding salient closed boundaries from a set of boundary fragments detected in a noisy image. In this problem, a saliency boundary is formed by identifying and connecting a subset of fragments according to the simple Gestalt laws of closure, continuity, and proximity. Our specific interest is focused on the methods that aim to achieve boundary closure, an important global property of perceptual salient boundaries. In this paper, we analyze and compare three such methods that are developed in recent years: (a) Elder and Zucker?s method based on the shortest-path algorithm, (b) Williams and Thornber?s method combining the spectral-analysis and the strongly-connected- component algorithms, and (c) Wang, Kubota, and Siskind?s method based on ratio-contour algorithm. Both theoretic analysis and experimental study show that, with a unified setting of fragment saliency, Wang, Kubota, and Siskind?s method more appropriately constrains the search space for the closed boundaries, and usually produces better performance than or at least comparable performance as the other two methods. Particularly, Wang, Kubota, and Siksind?s method can always guarantee the boundary closure and simplicity, which may not be always hold in the other two methods. We construct and collect a variety of synthesized and real images for this comparison.