Quantifying the accuracy of segmentation and manual delineation of organs, tissue types and tumors in medical images is a necessary measurement that suffers from multiple problems. One major shortcoming of all accuracy measures is that they neglect the anatomical significance or relevance of different zones within a given segment. Hence, existing accuracy metrics measure the overlap of a given segment with a ground-truth without any anatomical discrimination inside the segment. For instance, if we understand the rectal wall or urethral sphincter as anatomical zones, then current accuracy measures ignore their significance when they are applied to assess the quality of the prostate gland segments. In this paper, we propose an anatomy-aware measurement scheme for segmentation accuracy of medical images. The idea is to create a "master gold" based on a consensus shape containing not just the outline of the segment but also the outlines of the internal zones if existent or relevant. To apply this new approach to accuracy measurement, we introduce the anatomy-aware extensions of both Dice coefficient and Jaccard index and investigate their effect using 500 synthetic prostate ultrasound images with 20 different segments for each image. We show that through anatomy-sensitive calculation of segmentation accuracy, namely by considering relevant anatomical zones, not only the measurement of individual users can change but also the ranking of users' segmentation skills may require reordering.