A new type of motion-induced illusory figure determined by local kinematic information is investigated. The new figure is induced by radial line patterns subjected to either figure motion (the lines change as if they were stationary and a triangle was rotating in front of them) or background motion (the lines change as if they were being rotated behind a stationary triangle). Although the two kinds of motion are equivalent from the viewpoint of relative displacements, perceptually they yield very different results. With background motion, observers tend to perceive rigid figures that have a triangular shape. With figure motion, observers report seeing deforming figures with shapes that vary depending on the number of lines in the display. We consider two alternative accounts for this asymmetry which we term the background superiority effect (BSE). The first account proposes that the effect is due to retinal persistence and to figure stability. Against this line of explanation, we demonstrate that observers also see rigid triangular shapes in displays where both the figure and the radial lines rotate (double motion displays). The second account proposes that the effect depends on the availability of local kinematic information constraining contour orientation. This second line of explanation is consistent with observers' reports of bowed edges in double motion displays rotating in phase or in counterphase. Candidate mechanisms for extracting local kinematic information are discussed.