We present a novel segmentation algorithm based on a hierarchical representation of images. The main contribution of this work is to explore the capabilities of the a contrario reasoning when applied to the segmentation problem and to overcome the limitations of current algorithms within that framework. This exploratory approach has three main goals. Our first goal is to extend the search space of greedy merging algorithms to the set of all partitions spanned by a certain hierarchy and to cast the segmentation as a selection problem within this space. In this way we increase the number of tested partitions, and thus we potentially improve the segmentation results. In addition, this space is considerably smaller than the space of all possible partitions, and thus we still keep the complexity controlled. Our second goal aims to improve the locality of region merging algorithms, which usually merge pairs of neighboring regions. In this work, we overcome this limitation by introducing a validation procedure for complete partitions rather than for pairs of regions. The third goal is to perform an exhaustive experimental evaluation methodology in order to provide reproducible results. Finally, we embed the selection process on a statistical a contrario framework which allows us to have only one free parameter related to the desired scale.

J. Cardelino and V. Caselles acknowledge partial support by MICINN project, reference MTM2009-08171 and by GRC, reference 2009 SGR 773, funded by the Generalitat de Catalunya. V. Caselles also acknowledges partial support by ”ICREA Acade`mia” prize for excellence in research funded by the Generalitat de Catalunya, and by the ERC Advanced Grant INPAINTING (Grant agreement no.: 319899). M. Bertalm´ıo acknowledges support by European Research Council, Starting Grant ref. 306337, and Spanish grants AACC, ref. TIN2011-15954-E, and Plan Nacional, ref. TIN2012-38112. J. Cardelino also acknowledges partial support by ALFA-CVFA project and Tecnocom scolarship.