Analysis And Recognition Of Three-Dimensional Closed Boundaries

Abstract

An autoregressive model is introduced for modelling, invariant feature extraction, and recognition of arbitrary three-dimensional (3D) dosed boundary curves. An orthogonal estimation algorithm is derived for the estimation of the coefficient matrix associated with the model and an error reduction ratio is used to detect the order of the model. It is shown that the eigenvalues and the determinant of the coefficient matrix are invariant to rotation around the origin, to the choice of starting point in tracing the boundary, and to scale and translation which can therefore be extracted for the recognition of the 3D closed boundary curves.