Hierarchical Shape Description Via the Multiresolution Symmetric Axis Transform

A method is proposed that produces a shape description in the form of a hierarchy by scale of simple symmetric axis sequences. An axis segment that is a child of another has smaller scale and is seen as a branch of its parent. The scale value and parent-child relationship are induced by following the symmetric axis under successive reduction of resolution. The result, in two or three dimensions, is a figure-rather than boundary-oriented shape description that has natural segments and is insensitive to noise in the object description. The general approach of hierarchy production by following a feature through successive resolution reduction will be presented, as will methods of resolution reduction and computer implementation. Also, the relation of this figure-based shape description to those based on boundary curvature will be briefly discussed.