For workpiece inspection applications such as internal edge measurement verifications, 3D data processing for detecting the internal and external surface of the object is required. Rather than detecting edge points on each slice of CT image and stacking them up, we detect the 3D surface points directly from a sequence of CT images. Using this strategy, surfaces whose normals are vertical to the slices can be detected. We present a set of 3D edge detection methods, facet-model-based, morphology-based, and wavelet-based for evaluation. The facet-model-based surface detection method uses facet model to estimate the local 3D directional derivatives and location of the zeros of the second 3D directional derivatives along the direction of gradient. Subvoxel accuracy can be achieved using this method. The morphology-based method performs a 3D dilation-erosion residue operation first. Then the zero crossings of the residue result images are detected, and the surface points are extracted. The wavelet-based method performs a 3D wavelet transform on the CT images, and the local maxima of the gradient are detected and marked as surface points. The performance of these surface detectors are compared. Finally, as an illustration, we apply the facet-model-based method on a set of engine blade CT images with resolution of 5 mil by 5 mil and the measurements of thickness of wall are taken. A linear regression model is used to correct the systematic error. The results are very close to the direct optical measurements of cut-up sections of the blade with a maximum error of 3 mil.