We present a family of scale-invariant local shape features formed by chains of k connected roughly straight contour segments (kAS), and their use for object class detection. kAS are able to cleanly encode pure fragments of an object boundary without including nearby clutter. Moreover, they offer an attractive compromise between information content and repeatability and encompass a wide variety of local shape structures. We also define a translation and scale invariant descriptor encoding the geometric configuration of the segments within a kAS, making kAS easy to reuse in other frameworks, for example, as a replacement or addition to interest points (IPs). Software for detecting and describing kAS is released at http://lear.inrialpes.fr/software. We demonstrate the high performance of kAS within a simple but powerful sliding-window object detection scheme. Through extensive evaluations, involving eight diverse object classes and more than 1,400 images, we (1) study the evolution of performance as the degree of feature complexity k varies and determine the best degree, (2) show that kAS substantially outperform IPs for detecting shape-based classes, and (3) compare our object detector to the recent state-of-the-art system by Dalal and Triggs (2005).