Showing papers by "Andrew Zisserman published in 1990"

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.

Invariance-a new framework for vision

Abstract: It is shown that curved planar objects have shape descriptors that are unaffected by the position, orientation and intrinsic parameters of the camera. These shape descriptors can be used to index quickly and efficiently into a large model base of curved planar objects, because their value is independent of pose and unaffected by perspective. Thus, recognition can proceed independent of calculating pose. Object curves are represented using conics, attached with a fitting technique that commutes with projection. This means that the pose of an object can be determined by backprojecting known conics. The authors show examples of recognition and pose determination using real image data. >

Transformational invariance - a primer.

Abstract: The shape of objects seen in images depends on the viewpoint. This effect confounds recognition. We demonstrate a theoretical framework within which it is possible to construct descriptors for curves which do not vary with viewpoint. These descriptors are known as invariants. We use this framework to construct invariant shape descriptors for plane curves. These invariant shape descriptors make it possible to recognise plane curves, without explicitly determining the relationship between the curve reference frame and the camera coordinate system, and can be used to index quickly and efficiently into a large model base of curves. Many of these ideas are demonstrated by experiments on real image data.

Relative motion and pose from invariants.

Abstract: Projectively invariant shape descriptors efficiently identify instances of object models in images without reference to object pose. These descriptions rely on frame independent representations of planar curves, using plane conies. We show that object pose can be determined from coplanar curves, given such a frame independent representation. This result is demonstrated for real image data. The shape of objects in images changes as the camera is moved around. This extremely simple observation represents the dominant problem in model based vision. Nielsen [4, 5] first suggested using projectively invariant labels as landmarks for navigation. Recent papers [1, 2] have shown that it is possible to compute shape descriptors of arbitrary plane objects that are unaffected by camera position. These descriptors are known as transformational invariants. At no stage in this process, however, is the pose of the model determined. In this paper, we show that the available information does in fact determine the pose of the model. In particular, for complex planar objects, pose determination can be reduced to the simpler problem of pose determination for a pair of known planar conies.

Towards qualitative vision: motion parallax.

Abstract: A robot vehicle moving under visual guidance needs to compute approximate geometry of obstacles in its environment It is unreasonable to assume that egomotion is known to the sort of precision that is available for a camera mounted on a high quality robot arm Generally a nominal estimate for egomotion is available One possibility is to refine this estimate using optic flow data (Harris, 1987) Alternatively, the problem can be turned on its head: what geometric information remains stable under perturbation of assumed egomotion? This question has been addressed by Koenderink and van Doom (1977), Nelson and Aloimonos (1988) and Verri et al (1989), in the case of continuous motion fields and, in the domain of stereoscopic vision, by Weinshall (1990) Part of the answer, we claim, lies in the use of motion parallax as a geometric cue Motion parallax, which is a relative measure of the positions of two points, can be very much more robust as a cue than the absolute position of a single point This is true for computation of relative depth, curvature on specular surfaces and curvature on extremal boundaries