author = {Braure de Calignon, M. and Luc Brun and Lachaud, Jacques Olivier}, title = {Combinatorial Pyramids and discrete geometry for energy minimizing segmentation}, booktitle = {Proc. Int. Symposium on visual Computing}, year = 2006, number = 4292, series = {LNCS}, address = {Lake Tahoe, Nevada}, month = {November}, publisher = {springer}, theme= {nonhierarchique}, url = {pdf:=https://brunl01.users.greyc.fr/ARTICLES/isvc2006.pdf, arXiv:=https://arxiv.org/abs/0906.2770}, abstract = "The scale set theory allows to define a hierarchy of segmentations according to a scale parameter. This theory closely related to the Bayesian and the Minimum description Length(MDL) frameworks describes the energy of a partition as the sum of two terms : a goodness to fit and a regularisation term. This last term may be interpreted as the encoding cost of the model associated to the partition. It usually includes the total length of the partition's boundaries and is simply computed as the number of lignels between the regions of the partition. We propose to use a better estimation of the total length of the boundaries by using discrete length estimators. We state the basic properties which must be fulfilled by these estimators and show their influence on the partitition's energy."