A new graph algorithm for the multiscale segmentation of large three-dimensional medical data sets is presented. It is a region-merging segmentation algorithm based on minimizing the Mumford-Shah energy. The Mumford-Shah functional formulation leads to improved segmentation results compared with alternative approaches; and the graph theoretic approach yields improved performance and simplified data structures. Also, the graph algorithm acts on only a subset of the full data set at a given time, allowing its application to large data sets such as whole-body scans. Results on a head MRI data set are presented and compared with a manual segmentation of this data set.