X-ray CT scanners, due to the transmissive nature of X-rays, have enabled the non-destructive evaluation of industrial products, even inside their bodies. In light of its effectiveness, this study intro-duces a new approach to accelerate the inspection of many mechanical parts with the same shape in a bin. The input to this problem is a volumetric image (i.e., CT volume) of many parts obtained by a single CT scan. We need to segment the parts in the volume to inspect each of them; however, random postures and dense contacts of the parts prohibit part segmentation using traditional template matching. To address this problem, we convert both the scanned volumetric images of the template and the binned parts to simpler graph structures and solve a subgraph matching problem to segment the parts. We perform a distance transform to convert the CT volume into a distance field. Then, we construct a graph based on Morse theory, in which graph nodes are located at the extremum points of the distance field. The experimental evaluation demonstrates that our fully automatic approach can detect target parts appropriately, even for a heap of 50 parts. Moreover, the overall com-putation can be performed in approximately 30 min for a large CT volume of approximately $2000\times 2000\times 1000$ voxels.

This paper proposes a lightweight bi-directional scattering distribution function (BSDF) model for layered materials with anisotropic reflection and refraction properties. In our method, each layer of the materials can be described by a microfacet BSDF using an anisotropic normal distribution function (NDF). Furthermore, the NDFs of layers can be defined on tangent vector fields, which differ from layer to layer. Our method is based on a previous study in which isotropic BSDFs are approximated by projecting them onto base planes. However, the adequateness of this previous work has not been well investigated for anisotropic BSDFs. In this paper, we demonstrate that the projection is also applicable to anisotropic BSDFs and that the BSDFs are approximated by elliptical distributions using covariance matrices.