| Curves are important features in computer vision and pattern recognition, and their classification under a variety of transformations, such as Euclidean, affine or projective, poses a great challenge. Invariant features of these curves turn out to be crutial to simplifying any classification procedure. This, as a result, has recently led to a renewed research interest in transformation invariants.;In this thesis, new explicit formulae for integral invariants for curves in 3D with respect to the special and the full affine groups are presented. The development of the 3D integral invariant are based on an inductive approach in terms of Euclidean invariants. For the first time, a clear geometric interpretation of both 2D and 3D integral invariants is presented. Since integration attenuates the effects of noise, integral invariants have advantages in computer vision applications. We use integral invariants to construct global and local signatures that characterize curves up to the special affine transformations, subsequently extended to the full affine group. Global Signatures are independent of parameterization, and Local Signatures are independent of both parameterization and initial point selection. We analyze the robustness of these invariants in their application to the problem of classification of noisy spatial curves extracted as characteristics from a 3D object.;Our investigation of 2D and 3D integral invariants and signatures, originally motivated by Biometrics applications, are successfully implemented and applied to face recognition to eliminate the effects of pose and facial expression. A high recognition performance rate of 95% is achieved in the test with a large face data set. |
