This paper presents two variational multiphase segmentation methods for recovery of segments in weakly structured images, presenting local and global intensity bias fields, as often is the case in micro-tomography. The proposed methods assume a fixed number of classes. They use local image averages as discriminative features and binary labelling for class membership and their relaxation to per pixel/voxel posterior probabilities, Hidden Markov Measure Field Models (HMMFM). The first model uses a Total Variation weighted semi-norm (wTV) for label field regularization, similar to Geodesic Active Contours, but with a different and possibly richer representation. The second model uses a weighted Dirichlet (squared gradient) regularization. Both problems are solved by alternating minimization on computation of local class averages and label fields. The quadratic problem is essentially smooth, except for HMMFM constraints. The wTV problem uses a Chambolle-Pock scheme for label field updates. We demonstrate on synthetic examples the capabilities of the approaches, and illustrate it on a real examples.