The detection of contours in noise has been extensively studied, but the detection of closed contours, such as the boundaries of whole objects, has received relatively little attention. Closed contours pose substantial challenges not present in the simple (open) case, because they form the outlines of whole shapes and thus take on a range of potentially important configural properties. In this paper we consider the detection of closed contours in noise as a probabilistic decision problem. Previous work on open contours suggests that contour complexity, quantified as the negative log probability (Description Length, DL) of the contour under a suitably chosen statistical model, impairs contour detectability; more complex (statistically surprising) contours are harder to detect. In this study we extended this result to closed contours, developing a suitable probabilistic model of whole shapes that gives rise to several distinct though interrelated measures of shape complexity. We asked subjects to detect either natural shapes (Exp. 1) or experimentally manipulated shapes (Exp. 2) embedded in noise fields. We found systematic effects of global shape complexity on detection performance, demonstrating how aspects of global shape and form influence the basic process of object detection.