Abstract: Most MAP inference algorithms for CRFs optimize an energy function knowing all the potentials. In this paper, we focus on CRFs where the computational cost of instantiating the potentials is orders of magnitude higher than MAP inference. This is often the case in semantic image segmentation, where most potentials are instantiated by slow classifiers fed with costly features. We introduce Active MAP inference 1) to on-the-fly select a subset of potentials to be instantiated in the energy function, leaving the rest of the parameters of the potentials unknown, and 2) to estimate the MAP labeling from such incomplete energy function. Results for semantic segmentation benchmarks, namely PASCAL VOC 2010 [5] and MSRC-21 [19], show that Active MAP inference achieves similar levels of accuracy but with major efficiency gains.