ハーミルトンベクトル場のリー代数による物体の不変な表現と認識

概要

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It has been proposed in [1] to use linear Lie algebra of the tangential or normal vector fields to derive global representation of smooth objects which can be uniquely determined by completely local information. This approach has been proved successful in the sense that it can express a wide class of shapes which has 1 in 2D cases and 3 in 3D cases more degrees of freedom than the algebraic shapes. Moreover,the complete set of invariants of the object model can be easily calculated by solution of a local system of linear equations. On the other hand, this model often represents non compact shapes,which then can only be used as patches for a composite representation. It is then desirable to have a kind of object models which can both provide even more degrees of freedom and also describe compact shapes. In this paper,we show a method to represent objects as homogeneous spaces of Hamiltonian vector fields on tangent bundles of shapes.
社団法人電子情報通信学会の論文
1995-09-05