Cone-beam CT breast imaging provides a digital volume representation of a breast. With a digital breast volume, the immediate task is to extract the breast tissue information, especially for suspicious tumors, preferably in an automatic manner or with minimal user interaction. This paper reports a program for three-dimensional breast tissue analysis. It consists of volumetric segmentation (by globally thresholding), subsegmentation (connection-based separation), and volumetric component measurement (volume, surface, shape, and other geometrical specifications). A combination scheme of multi-thresholding and binary volume morphology is proposed to fast determine the surface gradients, which may be interpreted as the surface evolution (outward growth or inward shrinkage) for a tumor volume. This scheme is also used to optimize the volumetric segmentation. With a binary volume, we decompose the foreground into components according to spatial connectedness. Since this decomposition procedure is performed after volumetric segmentation, it is called subsegmentation. The subsegmentation brings the convenience for component visualization and measurement, in the whole support space, without interference from others. Upon the tumor component identification, we measure the following specifications: volume, surface area, roundness, elongation, aspect, star-shapedness, and location (centroid). A 3D morphological operation is used to extract the cluster shell and, by delineating the corresponding volume from the grayscale volume, to measure the shell stiffness. This 3D tissue measurement is demonstrated with a tumor-borne breast specimen (a surgical part).