Automated detection of stable fracture points in a sequence of Computed Tomography (CT) images is a challenging task. In this paper, an innovative scheme for automatic fracture detection in CT images is presented. The input to the system is a sequence of CT image slices of a fractured human mandible. Techniques based on curvature scale-space theory and graph-based filtering (using prior anatomical knowledge) are used to first detect candidate fracture points in the individual CT slices. Subsequently, a Kalman filter incorporating a Bayesian perspective is employed for testing the consistency of the candidate fracture points across all the CT slices in a given sequence. For the purpose of checking statistical consistency, both 95% and 99% high posterior density (HPD) prediction intervals are constructed. A spatial consistency term is formulated for each candidate fracture point in terms of the number of slices in the CT image sequence, the number of times a fracture point detected in that sequence and the number of times it is found to be statistically consistent. Fracture points with spatial consistency terms close to unity are deemed to be stable fracture points for the CT image sequence under consideration.