A surface model based on a fibre bundle of 1-parameter groups of Hamiltonian Lie algebra

This paper extends a successful fibre-bundle surface model using l-parameter groups of a linear Lie algebra as fibres. The new model uses a fibre-bundle of l-parameter groups of a Hamilton Lie algebra, therefore is rich in descriptive power to represent bounded shapes as closed surfaces. A surface represented by this model is uniquely determined by a finite number of invariants. The complete invariant set of the model under action of Euclidean motions is obtained. Conditions for the surfaces to be bounded or closed are also given. Another feature is that the surfaces can be synthesized by elementary functions therefore free of numerical integration errors. This model can be used in recognition-synthesis-based coding of 3D images, image retrieving and copyright protection as well.