We apply the facet model to extract edge and surface information from computed tomography (CT) images for precision inspection and shape extraction. First we explore the application of the facet model in a three-dimensional (3-D) filter design. A 3-D directional-derivative- based surface detector is developed to extract surface points from the CT images. Subpixel accuracy is achieved by locating the zeros of the 3-D second directional derivative along the estimated gradient direction. Then we develop a precision inspection system to take turbine blade wall width measurements from CT images and compare them to the corresponding optical measurements. Least mean squares (LMS) methods are used to enhance prediction accuracy with the adaptive property of increasing accuracy when additional verifiable data are available. The system accuracy is within 3 mil. Unverified measurements are adjusted based on the verified measurements, and experiments show increasing accuracy of the adjusted measurements as additional verified measurements are available. Also, quantitative analysis of a trapezoid-shaped workpiece is performed. The results indicate that the CT system performance is affected by the structure and size of a workpiece. We also present an algorithm to extract 3-D shapes from detected surface points interactively and use them for visual inspection.