Image decompositions and transformations as peaks and wells

10 pages to be submitted to ISMM2011International audienceAn image may be decomposed as a difference between an image of peaks and an image of wells. Applying a morphological operator to these two components before reconstructing a final image produces interesting filters for grey tone or binary images. This decomposition depends upon the point of view from where the image is considered

Scheduling trains with delayed departures

10 pages ; submitted to ISMM 2011 conferenceA 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)