The course takes an in-depth look at various Bayesian methods in computer and medical vision. Through the language of Bayesian inference, the course will present a coherent view of the approaches to various key problems such as detecting objects in images, segmenting object boundaries, and recognizing objects. The course is roughly partitioned into two halves: modeling and inference. In the first half, it will cover both classical models such as weak membrane models and Markov random fields as well as more recent models such as conditional random fields, latent Dirichlet allocation, and topic models. In the second half, it will focus on inference algorithms. Methods include PDE boundary evolution algorithms such as region competition, discrete optimization methods such as graph-cuts and graph-shifts, and stochastic optimization methods such as data-driven Markov chain Monte Carlo. An emphasis will be placed on both the theoretical aspects of this field as well as the practical application of the models and inference algorithms.