Fig. 1 Measuring system and coordinate systems defined for the measurement process: ( a ) coordinate measuring system using AprilTag and ( b ) probe More

Fig. 2 Projection of the AprilTag coordinate system into the pixel coordinate system of the image plane using homography matrix H More

Fig. 3 Automated generation of 3D model (SG) with a fixed cross section: ( a ) given 2D contour (CPL), ( b ) measured points (VL) of extrusion, ( c ) frame list for extrusion generated based on VL, and ( d ) extruded 3D structure More

Fig. 4 Automated digitization of a 3D structure based on aluminum profiles. Reference frames are defined using an AprilTag. The reference frame in ( a ) is defined such that the x -axis aligns with the long edge. The 3D aluminum profile structure in ( c ) is rotated in the positive direction of t... More

Fig. 5 Automated digitization of a triangular prism: ( a ) data points of sample and measurement, ( b ) comparison of sample and measured CPL, ( c ) 3D-printed sample structure, and ( d ) digitized 3D model More

Fig. 6 Automated digitization of a cylinder: ( a ) design parameters of sample cylinder and measurement, ( b ) comparison of sample and measured CPL, ( c ) 3D-printed sample structure, and ( d ) digitized 3D model More

Fig. 7 Automated digitization of a half sphere: ( a ) design parameters of sample sphere and measurement, ( b ) comparison of sample and measured sphere, ( c ) 3D-printed structure, and ( d ) digitized 3D model More

Fig. 1 X-ray powder diffraction More

Fig. 2 XRPD images with circular, elliptical, and parabolic Debye–Scherrer rings [ 2 ] More

Fig. 3 Types of clustering algorithms illustrated for data having two clusters. ( a ) Hierarchical clustering for the same data. Each data point is an individual cluster, and most similar clusters are iteratively merged to form bigger groups. ( b ) Spectral clustering using graph min-cut approach.... More

Fig. 4 Mapping D -dimensional data matrix ( X ) to c -dimensional matrix ( U ) of eigenvectors More

Fig. 5 2D XRPD image data from different detectors, and with varying degrees of noise: ( a ) Max1: noiseless with some rings occurring very close to each other, ( b ) Si12: moderately noisy, ( c ) LaB6: highly noisy with a lot of spots around the rings, and ( d ) Tilted: noiseless and well-separat... More

Fig. 6 Results of hierarchical clustering algorithms for XRPD images from both orthogonal (cols 1–3) and nonorthogonal (col 4) detectors. The results show that among all agglomerative hierarchical algorithms, only HC-Sng is able to detect some rings in noiseless images (cols 1 and 4). Also, divisi... More

Fig. 7 Results of various spectral clustering algorithms for XRPD images from both orthogonal (cols 1–3) and nonorthogonal (col 4) detectors. Most spectral algorithms correctly identify some or all rings in noiseless images (cols 1 and 4); however, their performance decreases as the spottiness of ... More