This paper proposes a fully automatic approach for computing Nuchal Translucency (NT) measurement in an ultrasound scans of the mid-sagittal plane of a fetal head. This is an improvement upon current NT measurement methods which require manual placement of NT measurement points or user-guidance in semi-automatic segmentation of the NT region. The algorithm starts by finding the pose of the fetal head using discriminative learning-based detectors. The fetal head serves as a robust anchoring structure and the NT region is estimated from the statistical relationship between the fetal head and the NT region. Next, the pose of the NT region is locally refined and its inner and outer edge approximately determined via Dijkstra's shortest path applied on the edge-enhanced image. Finally, these two region edges are used to define foreground and background seeds for accurate graph cut segmentation. The NT measurement is computed from the segmented region. Experiments show that the algorithm efficiently and effectively detects the NT region and provides accurate NT measurement which suggests suitability for clinical use.