Precise detection and segmentation of spinal vertebrae are crucial in the study of spinal related disease or disorders such as vertebral fractures. Identifying severity of fractures and understanding its causes will help physicians determine the most effective pharmacological treatments and clinical management strategies for spinal disorders. Although image segmentation has been a widely research area, limited work has been done on detecting and segmenting vertebrae. The complexity of vertebrae shapes, gaps in the cortical bone, internal boundaries, as well as the noisy, incomplete or missing information from the medical images have undoubtedly increased the challenge. In this paper, we introduce a new, mathematically driven spinal vertebrae segmentation framework. We first use the traditional image processing techniques, the mathematical morphology and curve fitting to identify the spinal vertebrae and connect them through their centroid. This process is followed by an advanced shape driven level set segmentation, where the level set evolution is guided by a shape constraint and driven by a shape energy coupled with a Gaussian kernel. Experimental results on CT images of spinal vertebrae demonstrate the feasibility of our proposed framework. Our ultimate goal is to provide a quantitative platform for efficient and accurate diagnosis of spinal disorder related diseases.