| Invariant features play a key role in object and pattern recognition studies. Features that are invariant to geometrical transformations offer succinct representations of underlying objects so that they can be reliably identified.; In this dissertation, we introduce a family of novel invariant features based on Cartan's theory of moving frames. We call these new features summation invariants. Compared to existing invariant features, summation invariants are inherently numerically stable, and do not require computationally complex numerical integrations or analytical representations of underlying data. We develop robust methods for extracting summation invariants from sampled 2D contours and 3D surfaces. We further apply these new invariant features to 2D and 3D object recognition problems.; In an application to a 2D shape recognition problem, we compare the performance of the proposed 2D contour summation invariant features with that of integral invariant features as well as wavelet invariant features. We observe marked performance enhancement achieved by the new summation invariant features.; The summation invariant features are also successfully applied to 3D face recognition applications. We propose robust methods to extract summation invariant features based on 2D contours and 3D shapes of given facial range images. We further work out an optimal feature selection and decision fusion method to select the most discriminating invariant features. The same method also facilitates the development of a multi-region face recognition method that achieves higher performance than using a monolithic facial image. To validate the proposed novel 3D face recognition algorithms, we test them on the Face Recognition Grand Challenge (FRGC) version 2 dataset with a data corpus of more than 50,000 facial images. The multi-region summation-invariant algorithm outperforms the best results in the recent FRGC report.; To conclude, we introduce a systematic approach for constructing robust geometrically invariant features. The proposed features provide improved accuracy and are applicable to a wide range of pattern recognition applications. These are versatile features that can be adapted to an engineer's choice of transformation group, such as rigid, affine, or similarity transformation group, to mention a few. |
