A non parametric theory for histogram segmentation

Histograms are a widely used tool for data analysis. In this paper, we propose a theory to segment a 1D-histogram without a priori assumptions about the undelying density function. Our approach considers a rigorous definition of an admissible segmentation, which provides a criterion allowing to avoid over and undersegmentation problems. A simple, parameter-free and fast algorithm leading to such a segmentation is proposed. As a product of the method, all multimodal densities can be estimated by a parameterless algorithm. Applications to document image analysis are presented. Indeed, this application requires the accurate detection of very small histogram modes, which cannot be found by Gaussian mixtures.