Geodesic
Transport Distances and Irrigation Models
Journal of convex analysis, Tome 16 (2009) no. 1, pp. 121-152
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Some variational models have been recently introduced to the aim of modeling ramified structures, such as trees, rivers and so on. We introduce a general scheme in which the notion of "transport distance" is introduced starting from a general transport cost functional, through relaxation arguments. Then we apply this general framework to the irrigation cost, which is a particular cost functional depending on a parameter α between 0 and 1. We discuss the equivalence between this abstract approach and the above models. 
@article{JCA_2009_16_1_JCA_2009_16_1_a5,
     author = {F. Maddalena and S. Solimini},
     title = {Transport {Distances} and {Irrigation} {Models}},
     journal = {Journal of convex analysis},
     pages = {121--152},
     year = {2009},
     volume = {16},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_1_JCA_2009_16_1_a5/}
}
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F. Maddalena; S. Solimini. Transport Distances and Irrigation Models. Journal of convex analysis, Tome 16 (2009) no. 1, pp. 121-152. http://geodesic.mathdoc.fr/item/JCA_2009_16_1_JCA_2009_16_1_a5/