This paper considers the problem associated with the segmentation of trabecular bone image obtained from micro-computed tomography (microCT). The morphometric indices of a 3D bone image, which are associated with the trabecular bone strength, may play an important clinical role in early predictions of osteoporosis onset and in longitudinal studies of different medical treatments for osteoporosis. Correct estimation of morphologic parameters requires accurate segmentation of bone images. In the present approach, a connectivity-preserving threshold algorithm, Connectivity Stable Thresholding (CST), is introduced. The algorithm is based on the coupling of topological parameter Conn.D and geometric parameter structure model index (SMI) to select an optimal threshold. The experimental results indicate that CST gives good results.