Utilizing Variational Optimization to Learn Markov Random Fields

Markov random field, or MRF, models are a powerful tool for modeling images. While much progress has been made in algorithms for inference in MRFs, learning the parameters of an MRF is still a challenging problem. In this paper, we show how variational optimization can be used to learn the parameters of an MRF. This method for learning, which we refer to as variational mode learning, finds the MRF parameters by minimizing a loss function that penalizes the difference between ground-truth images and an approximate, variational solution to the MRF. In particular, we focus on learning parameters for the field of experts model of Roth and Black. In addition to demonstrating the effectiveness of this method, we show that a model based on derivative filters performs quite similarly to the field of experts model. This suggests that the field of experts model, which is difficult to interpret, can be understood as imposing piecewise continuity on the image.