There are known tendencies to interpret as figure against background those regions that are lighter, or smaller or, especially, regions that are more convex. Wherever convex, opaque objects abut or partially occlude one another in an image, the points of contact between the silhouettes form concave cusps, each indicating the local assignment of figure versus ground across the contour segments. We propose that this local geometric feature is a preattentive determiner of figure-ground, and that it contributes to the previously-observed tendency to prefer convexity in general. Evidence is given that (1) figure-ground can be determined solely on the basis of the concave cusp feature, and (2) the salience of the cusp derives from the local geometry and not from the adjacent contour convexity.