Cancellous bone consists of a network of bony struts and plates that provide mechanical strength to much of the skeleton at minimum weight. It has been shown that loss in bone mass is accompanied by architectural changes that relate to both scale and topology of the network. In this paper, the concept of three-dimensional (3D) digital topology is presented for characterizing the local topology of each bone voxel after skeletonization of the binary bone images. This method allows us to identify each voxel as belonging to a surface, curve, or junction structure in the trabecular bone network. The method has been quantitatively validated on synthetic images demonstrating its relative immunity to partial volume blurring and noise. Parameters introduced to characterize network topology include surface-to-curve ratio and erosion index. Finally, the technique is shown to quantify the architecture of human trabecular bone in magnetic resonance micro-images acquired from cadavers and in vivo