Image segmentation based on statistically principled clustering

A statistically principled approach to 1-dimensional clustering was introduced by Pauwels abd Frederix (2000). In this approach clustering is achieved by finding the smoothest density that is statistically compatible with the observed data. In the current contribution we propose two solutions for the optimisation problem that is at the heart of this algorithm. The first solution is based on spline-functions, while the second hinges on an expansion of the density in terms of Gaussians. The latter is reminiscent of mixture-models but fundamentally different in its interpretation. Finally, we argue that 1-dimensional histogram segmentation yields a powerful local nonparametric cluster-validity criterion that can be used to check the quality of proposed clusterings in higher dimensions.