We present a range image segmentation algorithm based on a robust estimation technique, the M-estimator sample consensus (MSAC). The algorithm is a parallelizable "global-to-local" approach for the extraction of planar surfaces directly from range images. Solutions to some problems faced when extracting planar surfaces globally are also proposed. Experimental results show the algorithm is robust to image noise in the sense that it is able to preserve object shapes so that neither presmoothing, nor postprocessing steps are required. It also does not rely on MSAC and can be easily adapted to use other robust estimators. Thus, it may be used as a framework to compare robust estimators.