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Medical imaging has produced a large number of volumetric images capturing biological structures in 3D. Computer-based understanding of these structures can often benefit from the knowledge of shape components, particularly rod-like and plate-like parts, in such volumes. Previously, skeletons have been a common tool for identifying these shape components in a solid object. However, obtaining skeletons of a grayscale volume poses new challenges due to the lack of a clear boundary between object and background. In this paper, we present a new skeletonization algorithm on grayscale volumes typical to medical imaging (e.g., MRI, CT and EM scans), for the purpose of identifying shape components. Our algorithm does not require an explicit segmentation of the volume into object and background, and is capable of producing skeletal curves and surfaces that lie centered at rod-shaped and plate-shaped parts in the grayscale volume. Our method is demonstrated on both synthetic and medical data.