In this paper we carry out cooperatively both disparity and object boundary estimation by setting the two tasks in a unified Markovian framework. We introduce a new joint probabilistic model that allows to estimate disparities through a Markov random field model. Boundary estimation then cooperates with disparity estimation to gradually and jointly improve accuracy. The feedback from boundary estimation to disparity estimation is made through the use of an auxiliary field referred to as a displacement field. This field suggests the corrections that need to be applied at disparity discontinuities in order that they align with object boundaries. The joint model reduces to a Markov random field model when considering disparities while it reduces to a Markov chain when focusing on the displacement field. The performance of our approach is illustrated on real stereo images sets, demonstrating the power of this cooperative framework.