An intraoperative Image Guidance System (IGS), facilitating the localisation of pathological tissue or vasculature, could greatly support medical decisions during minimally invasive interventions. In our IGS for laparoscopic surgery, the 3D reconstruction of abdominal organs requires fast and accurate depth information from stereo images. To this end, we employ a state-of-the-art algorithm for dense disparity estimation. To cope with low processing performance, previous solutions used only downscaled images, and hence produced disparities of low quality. In this work, we present methods and implementations which improve and accelerate disparity estimation such that it runs with FullHD resolution images at full camera framerate.