Projectively invariant representations using implicit algebraic curves

Abstract We demonstrate that it is possible to compute polynomial representations of image curves which are unaffected by the projective frame in which the representation is computed. This means that: ‘The curve chosen to represent a projected set of points is the projection of the curve chosen to represent the original set.’ We achieve this by using algebraic invariants of the polynomial in the fitting process. We demonstrate that the procedure works for plane conic curves. For higher order plane curves, or for aggregates of plane conies, algebraic invariants can yield powerful representations of shape that are unaffected by projection, and hence make good cues for model-based vision. Tests on synthetic and real data have yielded excellent results.