Edge detection in noisy data using finite mixture distribution analysis

Abstract

An algorithm which identifies discontinuities in noisy data is presented. The signal is modelled as step edges with additive normally distributed noise present. Using finite mixture analysis and information criteria, a variable number of mixtures are identified together with the location of the respective edges separating them. The problem is solved using a dynamic programming approach which ensures globally optimal edge positions according to the signal model of a finite mixture of normal distributions. The computational complexity is of order MN 2 where M is the number of discontinuities in the mixture and N is the number of data points in the signal. The algorithm is tested on a range of real and synthetic signals and yields as accurate edge positions as a corresponding minimum square error method. Among applications for this algorithm is edge detection in medical images, and examples from ultrasound imaging are included.