We address the problem of object detection and segmentation using global holistic properties of object shape. Global shape representations are highly susceptible to clutter inevitably present in realistic images, and can be applied robustly only using a precise segmentation of the object. To this end, we propose a figure/ground segmentation method for extraction of image regions that resemble the global properties of a model boundary structure and are perceptually salient. Our shape representation, called the chordiogram, is based on geometric relationships of object boundary edges, while the perceptual saliency cues we use favor coherent regions distinct from the background. We formulate the segmentation problem as an integer quadratic program and use a semdefinite programming relaxation to solve it. Obtained solutions provide the segmentation of an object as well as a detection score used for object recognition. Our single-step approach achieves state-of-the-art performance on several object detection and segmentation benchmarks.