The Global–Local transformation for noise resistant shape representation

The use of smoothing kernels in boundary curvature calculations, affects both object shape and the localization of edges. The Global–Local transformation (GLT), addresses this issue by providing a framework for shape representation, such that local and global features are simultaneously represented, even in noisy shapes, without the need for smoothing. By means of two-dimensional manifolds (surfaces), embedded into the unit cube, useful properties of the transform space are explored. The expressive power of the GLT is demonstrated by means of a global descriptor, called View Area Representation (VAR). VAR is an intuitive and physically meaningful shape descriptor which is robust to noise, captures curvature and leads to the introduction of novel and hybrid (global/local) shape features. A series of proofs is presented that link VAR and its derivatives to those shape features, providing the basis for shape representation involving global and local features in the presence of noise. The theoretical results are shown to be effective in matching noisy shapes by improving the recognition capability, of Local Area Integral Invariant (LAII), a relevant state of the art method of low complexity. A combination of GLT with VAR is used to define a new matching method certain advantages of which, in recognition ability and execution time, renders the intuitive properties of VAR significant for complexity reduction.