3D Object Recognition Based on Linear Lie Algebra Model

A surface model called the fibre bundle model and a 3D object model based on linear Lie algebra model are proposed.Then an algorithm of 3D object recognition using the linear Lie algebra models is presented.It is a convenient recognition method for the objects which are symmetric about some axis.By using the presented algorithm,the representation matrices of the fibre or the base curve from only finite points of the linear Lie algebra model can be obtained.At last some recognition results of practicalities are given.     

On Fibre Bundle Surfaces and Their Curvatures

A surface model called the fibre bundle model is proposed. This model represents a surface locally as a direct product of two curves:a base curve and a fibre curve. We introduce the fibre bundle model and then obtain the Gaussian curvatures and the mean curvatures of a certain kind of fibre bundle surface models using 1-parameter groups of a linear Lie algebra as fibres. Some examples are given to verify our results.