The Logistic Random Field — A convenient graphical model for learning parameters for MRF-based labeling

Graphical models are fundamental tools for modeling images and other applications. In this paper, we propose the logistic random field (LRF) model for representing a discrete-valued graphical model. The LRF model is based on an underlying quadratic model and a logistic function. The chief advantages of the LRF are its convenience and flexibility. The quadratic model makes inference easy to implement using standard numerical linear algebra routines. This quadratic model also allows the log-likelihood of the training data to be differentiated with respect to any parameter in the model, enhancing the flexibility of the LRF model. To demonstrate the usefulness of this model we use it to learn how to segment objects, specifically roads, horses, and cows. In addition, we demonstrate the flexibility of the LRF model by incorporating super-pixels. We then show that the LRF segmentation model produces segmentations that are competitive with recently published results.