We introduce a linearly weighted variant of the total
variation for vector fields in order to formulate regularizers
for multi-class labeling problems with non-trivial interclass
distances. We characterize the possible distances,
show that Euclidean distances can be exactly represented,
and review some methods to approximate non-Euclidean
distances in order to define novel total variation based regularizers.
We show that the convex relaxed problem can
be efficiently optimized to a prescribed accuracy with optimality
certificates using Nesterov’s method, and evaluate
and compare our approach on several synthetical and realworld
examples.
J. Lellmann, F. Becker, C. Schn¨orr