Markov random fields (MRF) based on linear filter responses are one of the most popular forms for modeling image priors due to their rigorous probabilistic interpretations and versatility in various applications. In this dissertation, we propose an application-independent method to quantitatively evaluate MRF image priors using model samples. To this end, we developed an efficient auxiliary-variable Gibbs samplers for a general class of MRFs with flexible potentials. We found that the popular pairwise and high-order MRF priors capture image statistics quite roughly and exhibit poor generative properties. We further developed new learning strategies and obtained high-order MRFs that well capture the statistics of the inbuilt features, thus being real maximum-entropy models, and other important statistical properties of natural images, outlining the capabilities of MRFs. We suggest a multi-modal extension of MRF potentials which not only allows to train more expressive priors, but also helps to reveal more insights of MRF variants, based on which we are able to train compact, fully-convolutional restricted Boltzmann machines (RBM) that can model visual repetitive textures even better than more complex and deep models.
The learned high-order MRFs allow us to develop new methods for various real-world image analysis problems. For denoising of natural images and deconvolution of microscopy images, the MRF priors are employed in a pure generative setting. We propose efficient sampling-based methods to infer Bayesian minimum mean squared error (MMSE) estimates, which substantially outperform maximum a-posteriori (MAP) estimates and can compete with state-of-the-art discriminative methods. For non-rigid registration of live cell nuclei in time-lapse microscopy images, we propose a global optical flow-based method. The statistics of noise in fluorescence microscopy images are studied to derive an adaptive weighting scheme for increasing model robustness. High-order MRFs are also employed to train image filters for extracting important features of cell nuclei and the deformation of nuclei are then estimated in the learned feature spaces. The developed method outperforms previous approaches in terms of both registration accuracy and computational efficiency
