We introduce a new causal hierarchical belief network for image segmentation. Contrary to classical tree structured (or pyramidal) models, the factor graph of the network contains cycles. Each level of the hierarchical structure features the same number of sites as the base level and each site on a given level has several neighbors on the parent level. Compared to tree structured models, the (spatial) random process on the base level of the model is stationary which avoids known drawbacks, namely visual artifacts in the segmented image. We propose different parameterizations of the conditional probability distributions governing the transitions between the image levels. A parametric distribution depending on a single parameter allows the design of a fast inference algorithm on graph cuts, whereas for arbitrary distributions, we propose inference with loopy belief propagation. The method is evaluated on scanned document images from the 18th century, showing an improvement of character recognition results compared to other methods.