Stochastic Models for Closed Boundary Analysis: Part I. Representation and Reconstruction.
MARYLAND UNIV COLLEGE PARK COMPUTER SCIENCE CENTER
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This paper deals with the analysis of closed boundaries of arbitrary shape in a plane. Specifically, it is concerned with the problems of representation and reconstruction. We first set up a one to one correspondence between the given closed boundary and a univariate or multivariate sequence of real numbers. Univariate or multivariate circular autoregressive models are suggested for the representation of the sequence of numbers derived from the closed boundary. The stochastic model representing the closed boundary is invariant to transformations of the boundary such as scaling, rotation and choice of the starting point. Methods for estimating the unknown parameters of the model are given and a decision rule for choosing the appropriate order of the model is included. Constraints on the estimates are derived so that the estimates are invariant to transformations of the boundaries. The specific stochastic model used enables us to reconstruct a closed boundary with less computational effort using FFT algorithms. Results of simulations are included and applications to contour coding are discussed. In a subsequent paper we will consider the classification problem. Author
- Statistics and Probability