Accurate surface extraction on CT volume using gradients obtained by differentiating FDK formula

In this paper, we propose an accurate surface extraction algorithm from X-ray CT volumes for industrial applications. Isosurfacing is well known and the most widely used surface extraction, but varying the isovalue may cause deformation of the extracted shape and the resulting surface is not very suitable to some industrial applications. Another type of surface is the gradient maximal surface that is the set of the maxima of the gradient norm of CT value. The gradient maximal surface gives more accurate surface in the sense of being less affected by inhomogeneity of the CT value than the isosurface. For computing the gradient, there are two ways. The discrete gradient first integrates the projection values to obtain the CT value, and then differentiates the CT value. In contrast, the analytical gradient first differentiate the projection value, and then integrates the obtained gradient by the filtered back projection (FDK). In this paper, we investigate the influence of the gradient computation ways on the accuracy of their extracted surfaces. We found that the analytical gradient contributes more than the discrete gradient to the accuracy of the extracted gradient maximal surface, and show this fact with some experimental results and comparisons of them.