As local correspondence methods alone often do not achieve a sufficient robustness and accuracy, a subsequent refinement stage is commonly employed to improve upon the initial disparity estimates. In recent years, cross bilateral filters have already been successfully applied for this purpose. They do not only smooth the disparity maps but also help to better align the disparity values with the object edges resulting in an improved object segmentation. In this paper, a refinement step based on an extension of a cross bilateral filter is proposed that utilizes explicit reliability information in order to create robust and reliable disparity maps.