A novel approach

curve tree

is proposed for curve representation and encoding.Binary trees composed of directed relative height are adopted to describe curves.Any curve corresponds to a curve tree.We may take the first n levels of the curve tree

which compose a binary tree roughly describing the curve.The more levels we get

the finer it describes the curve.The representation is invariant to rotation

scaling

and translation.Based on this descriptor

curve distance is defined to weigh the similarity between curves.