This letter argues that many visual scenes are based on a “Manhattan” three-dimensional grid that imposes regularities on the image statistics. We construct a Bayesian model that implements this assumption and estimates the viewer orientation relative to the Manhattan grid. For many images, these estimates are good approximations to the viewer orientation (as estimated manually by the authors). These estimates also make it easy to detect outlier structures that are unaligned to the grid. To determine the applicability of the Manhattan world model, we implement a null hypothesis model that assumes that the image statistics are independent of any three-dimensional scene structure. We then use the log-likelihood ratio test to determine whether an image satisfies the Manhattan world assumption. Our results show that if an image is estimated to be Manhattan, then the Bayesian model's estimates of viewer direction are almost always accurate (according to our manual estimates), and vice versa.

Many perception, reasoning, and learning problems can be expressed as Bayesian inference. We point out that formulating a problem as Bayesian inference implies specifying a probability distribution on the ensemble of problem instances. This ensemble can be used for analyzing the expected complexity of algorithms and also the algorithm-independent limits of inference. We illustrate this problem by analyzing the complexity of tree search. In particular, we study the problem of road detection, as formulated by Geman and Jedynak (1996). We prove that the expected convergence is linear in the size of the road (the depth of the tree) even though the worst-case performance is exponential. We also put a bound on the constant of the convergence and place a bound on the error rates.