  We present a variational multi-label segmentation algorithm based on a robust
Huber loss for both the data and the regularizer, minimized within a convex
optimization framework. We introduce a novel constraint on the common areas, to
bias the solution towards mutually exclusive regions. We also propose a
regularization scheme that is adapted to the spatial statistics of the residual
at each iteration, resulting in a varying degree of regularization being
applied as the algorithm proceeds: the effect of the regularizer is strongest
at initialization, and wanes as the solution increasingly fits the data. This
minimizes the bias induced by the regularizer at convergence. We design an
efficient convex optimization algorithm based on the alternating direction
method of multipliers using the equivalent relation between the Huber function
and the proximal operator of the one-norm. We empirically validate our proposed
algorithm on synthetic and real images and offer an information-theoretic
derivation of the cost-function that highlights the modeling choices made.
