Even years ago, Szeliski et al. published an influential study on energy minimization methods for Markov random fields (MRF). This study provided valuable insights in choosing the best optimization technique for certain classes of problems. While these insights remain generally useful today, the phenominal success of random field models means that the kinds of inference problems we solve have changed significantly. Specifically, the models today often include higher order interactions, flexible connectivity structures, large label-spaces of different cardinalities, or learned energy tables. To reflect these changes, we provide a modernized and enlarged study. We present an empirical comparison of 24 state-of-art techniques on a corpus of 2,300 energy minimization instances from 20 diverse computer vision applications. To ensure reproducibility, we evaluate all methods in the OpenGM2 framework and report extensive results regarding runtime and solution quality. Key insights from our study agree with the results of Szeliski et al. for the types of models they studied. However, on new and challenging types of models our findings disagree and suggest that polyhedral methods and integer programming solvers are competitive in terms of runtime and solution quality over a large range of model types.

The quality of any tracking-by-assignment hinges on the accuracy of the foregoing target detection / segmentation step. In many kinds of images, errors in this first stage are unavoidable. These errors then propagate to, and corrupt, the tracking result. Our main contribution is the first probabilistic graphical model that can explicitly account for over- and under segmentation errors even when the number of tracking targets is unknown and when they may divide, as in cell cultures. The tracking model we present implements global consistency constraints for the number of targets comprised by each detection and is solved to global optimality on reasonably large 2D+t and 3D+t datasets. In addition, we empirically demonstrate the effectiveness of a post processing that allows to establish target identity even across occlusion / under segmentation. The usefulness and efficiency of this new tracking method is demonstrated on three different and challenging 2D+t and 3D+t datasets from developmental biology.