In many applications of Computed Tomography (CT), we may know that the object under the test is composed of a finite number of materials meaning that the images to be reconstructed are composed of a finite number of homogeneous area. To account for this prior knowledge, we propose a family of Gauss-Markov fields with hidden Potts label fields. Then, using these models in a Bayesian inference framework, we are able to jointly reconstruct the images and segment them in an optimal way. In this paper, we first present these prior models, then propose appropriate MCMC or variational methods to compute the mean posterior estimators. We finally show a few results showing the efficiency of the proposed methods for CT with limited angle and number of projections. Keywords: Computed Tomography; Gauss-Markov-Potts Priors; Bayesian computation; MCMC; Joint Segmentation and Reconstruction 1 This discretized presentation of CT, gives the possibility to analyse the most classical methods of image reconstruction [3, 4]. For example, it is very easy to see that the solution ̂f = H t g = ∑ l H t l gl (5) corresponds to the classical Backprojection (BP) and the minimum norm solution of Hf = g: ̂f = H t (HH t) −1 g = ∑ l H t l (HlH t l) −1 gl (6) can be identified to the classical Filtered Backprojection (FBP) and the least squares (LS) solution ̂f = (H t H) −1 H t g (7) can be identified to the Backprojection and Filtering (BPF). Also, defining the LS criterion