High-accuracy Surface Extraction Using the High-order differentiation of X-ray CT Values

In manufacturing, accurate shape acquisition of products (such as dimensional evaluation and defect detection) provides assurance of product quality. One prominent geometry-acquisition method is X-ray computed tomography (CT), which non-destructively obtains the three-dimensional data (i.e., a CT volume) of the internal geometry of an object. Within a CT volume, the CT values of the voxels are proportional to the local densities of the object. Because a CT volume is a discrete dataset, an X-ray CT scan can not potentially meet the accuracy requirement due to discretization error. In this paper, we extract the surface of an object with high accuracy of about one-tenth of the voxel size by defining a surface point as a point at which the differentiation of the gradient norm of the CT value in the gradient direction is zero. This method uses analytical differentiations of the CT values that are directly computed from the X-ray projection values, which are less affected by CT-reconstruction artifacts than the discrete differentiations computed the CT volume. In an experimental analysis, we show that this algorithm can extract the surface more accurately than conventional methods.