Weighted 3D volume reconstruction from series of slice data using a modified Allen–Cahn equation

In this study, we develop a fast and accurate computational method for a weighted three-dimensional (3D) volume reconstruction from a series of slice data using a phase-field model. The proposed method is based on a modified Allen–Cahn (AC) equation with a fidelity term. The algorithm automatically generates the necessary slices between the given slices by solving the governing equation. To reconstruct a 3D volume, we first set a source slice and target slice. Next, we set the source slice as the initial condition and the target slice as the fidelity function. Finally, we retain the numerical solutions during an evolution as intermediate slices between the source and target slices. There are two criteria for choosing the intermediate slice: One is based on the area of the symmetric difference between the phase-field solution and the target and the other is based on the change of the phase-field solution relative to the area of the target. We use the weighted average of the two criteria. To validate the efficiency and accuracy of the proposed numerical algorithm, several computational experiments are conducted. Computational test results confirm the superior performance of the proposed algorithm.