Multi-line fitting and straight edge detection using polynomial phase signals

A new signal processing method is developed for solving the multi-line fitting problem in a two dimensional image. We first reformulate the former problem in a special parameter estimation framework such that a first order or a second order polynomial phase signal structure is obtained. Then, the previously developed algorithms in that formalism can be exploited to produce accurate estimates for line parameters. The signal representation employed in this formulation can be generalized to handle both problems of line fitting (in which a set of binary valued discrete pixels is given) and straight edge detection (in which one starts with a grey scale image). A main advantage of the proposed method is its ability to estimate the parameters of parallel lines with different offsets which can not be handled by the sensor array processing technique introduced by Aghajan and Kailath (1993). Simulation results are presented to demonstrate the usefulness of the proposed method.