  Segmentation algorithms based on an energy minimisation framework often
depend on a scale parameter which balances a fit to data and a regularising
term. Irregular pyramids are defined as a stack of graphs successively reduced.
Within this framework, the scale is often defined implicitly as the height in
the pyramid. However, each level of an irregular pyramid can not usually be
readily associated to the global optimum of an energy or a global criterion on
the base level graph. This last drawback is addressed by the scale set
framework designed by Guigues. The methods designed by this author allow to
build a hierarchy and to design cuts within this hierarchy which globally
minimise an energy. This paper studies the influence of the construction scheme
of the initial hierarchy on the resulting optimal cuts. We propose one
sequential and one parallel method with two variations within both. Our
sequential methods provide partitions near the global optima while parallel
methods require less execution times than the sequential method of Guigues even
on sequential machines.
