These invariants are local - that is, the invariants are found for each point on the curve, which may be quite general. Unfortunately, these invariants are extremely large and complex polynomials, requiring up to seventh derivatives of the curve, which makes them practically unusable due to image noise and acquisition errors, although noise-resistant local invariants are beginning to appear. However, if additional information is available, higher derivatives may be avoided. Stability of invariants is another crucial property which affects their applicability. The robustness of invariants to image noise and errors introduced by image sensors is of prime importance, although not much is known about this.
Different invariants have different stability and distinguishing powers.
An example of recognition of man-made objects using invariant description of four coplanar lines, a conic and two lines, and a pair of coplanar conics is given. The recognition system is based on a model library containing over thirty object models - significantly more than that reported for other recognition systems. Further, there is no need for camera calibration.