  This technical report is devoted to the continuous estimation of an
epsilon-assignment. Roughly speaking, an epsilon assignment between two sets V1
and V2 may be understood as a bijective mapping between a sub part of V1 and a
sub part of V2 . The remaining elements of V1 (not included in this mapping)
are mapped onto an epsilon pseudo element of V2 . We say that such elements are
deleted. Conversely, the remaining elements of V2 correspond to the image of
the epsilon pseudo element of V1. We say that these elements are inserted. As a
result our method provides a result similar to the one of the Sinkhorn
algorithm with the additional ability to reject some elements which are either
inserted or deleted. It thus naturally handles sets V1 and V2 of different
sizes and decides mappings/insertions/deletions in a unified way. Our
algorithms are iterative and differentiable and may thus be easily inserted
within a backpropagation based learning framework such as artificial neural
networks.
