Fibre Bundle Models and 3 D Object Recognition 18

Surface modeling is a fundamental issue in 3D images, shape synthesis and recognition. Recently, a surface model called the fibre bundle model is proposed (Chao et al., 2000; Chao & Kim, 2004; Chao et al., 2004; Chao & Li, 2005; Suzuki & Chao, 2002). The fibre bundle model becomes powerful in its full generality however still needs much information, the information of these two curves at all points, which are roughly equivalent to the information of pointwise representation itself. On the other hand, to apply such a surface model efficiently in shape generation and representation, one needs to know the geometrical quantities of the model. Object recognition techniques using 3D image data are expected to play an important role in recognition-synthesis image coding of 3D moving pictures or animations in virtual environments and image communications. Currently used 3D free object representations seem insufficient in the sense that, for models such as generalized cylinders or super-quadratics, it is usually difficult to find the invariant features, especially to find the complete set of invariants, which is defined as the smallest number of invariants in order to uniquely determine and reproduce the shapes (Chao & Ishii, 1999; Chao & Suzuki, 2002; Chao et al., 1999; Kawano et al., 2002; Sano et al., 2001). From the view of differential geometry and Riemannian geometry, the authors obtained the geometric structures about fibre bundle models (Li et al., 2008, 1; 2). Meanwhile, an algorithm of 3D object recognition using the linear Lie algebra models is presented, including a convenient recognition method for the objects which are symmetrical about some axis (Li et al., 2009).