The automatic extraction of the vertebra's shape from dynamic magnetic resonance imaging (MRI) could improve understanding of clinical conditions and their diagnosis. It is hypothesized that the shape of the sacral curve is related to the development of some gynecological conditions such as pelvic organ prolapse (POP). POP is a critical health condition for women and consists of pelvic organs dropping from their normal position. Dynamic MRI is used for assessing POP and to complement clinical examination. Studies have shown some evidence on the association between the shape of the sacral curve and the development of POP. However, the sacral curve is currently extracted manually limiting studies to small datasets and inconclusive evidence. A method composed of an adaptive shortest path algorithm that enhances edge detection and linking, and an improved curve fitting procedure is proposed to automate the identification and segmentation of the sacral curve on MRI. The proposed method uses predetermined pixels surrounding the sacral curve that are found through edge detection to decrease computation time compared to other model-based segmentation algorithms. Moreover, the proposed method is fully automatic and does not require user input or training. Experimental results show that the proposed method can accurately identify sacral curves for nearly 91% of dynamic MRI cases tested in this study. The proposed model is robust and can be used to effectively identify bone structures on MRI.