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A multilevel quality-guided phase unwrapping algorithm for real-time 3D shape measurement is presented. The quality map is generated from the gradient of the phase map. Multilevel thresholds are used to unwrap the phase level by level. Within the data points in each level, a fast scan-line algorithm is employed. The processing time of this algorithm is approximately 18.3 ms for an image size of 640480 pixels in an ordinary computer. We demonstrate that this algorithm can be implemented into our real-time 3D shape measurement system for real-time 3D reconstruction. Experiments show that this algorithm improves the previous scan-line phase unwrapping algorithm significantly although it reduces its processing speed slightly.

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We provide characterizations of $p\mspace {1mu}$ -nilpotency for fusion systems and $p\mspace {1mu}$ -local finite groups that are inspired by known result for finite groups. In particular, we generalize criteria by Atiyah, Brunetti, Frobenius, Quillen, Stammbach and Tate.