Detection of Convexity and Concavity in Context Marco Bertamini University of Liverpool Sensitivity to shape changes was measured, in particular detection of convexity and concavity changes. The available data are contradictory. The author used a change detection task and simple polygons to systematically manipulate convexity/concavity. Performance was high for detecting a change of sign (a new concave vertex along a convex contour or a new convex vertex along a concave contour). Other things being equal, there was no evidence of an advantage for detecting a new concavity compared with a new convexity, for detecting a change of angle to a concave vertex compared with a convex vertex, for detecting a change within a concave region compared with a change within a convex region, or for an interaction between convexity and concavity and changes affecting or not affecting a vertex. The author concludes that change detection is affected by changes of sign of curvature (leading to changes in part structure). However, contrary to previous proposals, there is no special role for negative curvature or minima of curvature in guiding attention. Keywords: visual perception, shape, signal detection, object representation Convexity and concavity information has been long recognized as important for how humans perceive shape (e.g., in Alhazen’s Optics, around 1030, and in modern times by Attneave, 1954). It is also generally accepted that observers may gain information about Gaussian curvature from curvature along a contour (Koen- derink, 1984; Richards, Koenderink, & Hoffman, 1987) and that concavities play a central role in perceived part structure (Hoffman & Richards, 1984; Singh & Hoffman, 2001). Recently, using a detection task, researchers have found that changes in contours are more easily detected if they involve a concavity rather than a convexity (Barenholtz, Cohen, Feldman, & Singh, 2003; Cohen, Barenholtz, Singh, & Feldman, 2005). This concavity advantage seems to be consistent with an advantage in detection of concavities using the visual search paradigm (Hulle- man, te Winkel, & Boselie, 2000; Humphreys & Mu ¨ller, 2000; Wolfe & Bennett, 1997). The speculation is that, because concav- ities have a central role in describing shape, “fast selection of concave edges, perhaps via the activation of specialized detectors, may thus serve a useful computational purpose” (Humphreys & Mu ¨ller, 2000, p. 197). In their review of attributes that guide the deployment of attention, Wolfe and Horowitz (2004) cite curvature as a likely attribute with a possible preference for concavity and make reference to the work by Barenholtz et al. (2003). A few different hypotheses can be formulated about when attention is guided towards concavity. The critical factor may be whether a contour has concave curvature. Alternatively, attention may be directed towards concave regions once a change of cur- vature takes place, for instance because a new minima is intro- duced. Another possibility is that attention is directed not towards concavities in general but only towards minima (peaks of negative curvature). All these possibilities are tested in this article. There is, however, another difficulty with the idea that attention is guided towards concavities. Some tasks, discussed in more details below, point to an advantage in processing convex infor- mation or information located at convexities. In this article, I argue that the changes always need to be seen in their context; for instance, a new concavity may be salient only when it is introduced in an object that was mainly convex before the change. On this basis, I reanalyze the critical factors for change detection and conclude that (a) changes in sign of curvature along the contour are always easier to detect compared with changes that do not involve a change of sign; and (b) other things being equal, there is no evidence that changes involving concavities are more salient than changes involving convexities. This second conclusion is more problematic given that it is based on null findings, but two things need to be considered. First, I argue that the existing evidence for the saliency of concavities only supports the saliency of changes of sign. Second, in this article I present data from five experiments, and I propose different criteria to test for a concavity advantage. For instance, it may be reasonable to argue that only concave changes involving vertices should be salient (relative to convex vertices) because such points are critical for part parsing (Exper- iment 5). None of these multiple tests confirmed that changes involving concavities are more salient than changes involving convexities. Detection of Shape Changes The paradigm introduced by Barenholtz et al. (2003) used a two-intervals forced choice task (cf. Phillips, 1974). A polygon is presented and in the second interval its shape may change slightly. A similar design and similar stimuli have subsequently been used by Bertamini and Farrant (2005); Cohen et al. (2005); and Vandekerckhove, Panis, and Wagemans (2005, 2007). The original study used closed polygons and introduced shape changes by adding (or removing) a new vertex in the middle of a straight edge (Barenholtz et al., 2003), as illustrated in Figure 1. Correspondence concerning this article should be addressed to Marco Bertamini, School of Psychology, University of Liverpool, Eleanor Rath- bone Building, Bedford Street South, Liverpool L69 7ZA, United King- dom. E-mail: M.Bertamini@liv.ac.uk Journal of Experimental Psychology: Copyright 2008 by the American Psychological Association Human Perception and Performance 2008, Vol. 34, No. 4, 775–789 0096-1523/08/$12.00 DOI: 10.1037/0096-1523.34.4.775 775