Scheduling trains with delayed departures

Fernand Meyer (1)

1 CMM - Centre de Morphologie Mathématique

A number of image transformations may be expressed as shortes paths algorithms in various algebras We introduce a general framework where a graph is considered as a railway network on which the trains follow shortest paths. Given a fixed traveling time on each edge and an arbitrary distribution of departure times, one searches the first arrival time of a train at each node. This formulation leads to interesting filters and image decomposition in the (min,+) algebra and sheds new light on flooding and razing algorithms in the algebras (min,max) and (max,min).

Mots clés: razings; watershed line; Shortest distances; dioïds; path algebra; filtering; segmentation; levelings; floodings

Domaines: Traitement des images [eess.IV]; Anneaux et algèbres [math.RA]

Fernand Meyer. Scheduling trains with delayed departures. 2010. ⟨hal-00547261⟩