This paper introduces an efficient 3D segmentation concept, which is based on extending the well-known Maximally Stable Extremal Region (MSER) detector to the third dimension. The extension allows the detection of stable 3D regions, which we call the Maximally Stable Volumes (MSVs). We present a very efficient way to detect the MSVs in quasi-linear time by analysis of the component tree. Two applications - 3D segmentation within simulated MR brain images and analysis of the 3D fiber network within digitized paper samples - show that reasonably good segmentation results are achieved with low computational effort.