Autonomous mobile robots must visually recognize their three-dimensional environment so that they can quickly discover and avoid obstacles to their movement or find targets. In order to accomplish this objective, it is a matter of essential importance to match curvilinear segments of a two-dimensional stereo dynamic image sequence. This paper proposes a method in which what is called constant-curvature arc data, which include not only curvatures but also the relationship between spacial positions, are used for representing curves. This paper also suggests a method to match two-dimensional curves and verifies its effectiveness through experiments.