Three-dimensional volume reconstruction from multi-slice data using a shape transformation

We present a computational method for the 3D volume reconstruction from cross-sectional data. The proposed method is based on the Allen-Cahn (AC) equation with a source term. The source term is related to shape transformation from a source object to a target object. Using the operator splitting method, the governing equation is solved by splitting it into three steps. The numerical solution is obtained explicitly using the Euler's methods and the separation of variables. To reconstruct the 3D object from two slice data, we set one slice as the target data and the other data as the initial data. We solve the governing equation and stack intermediate solutions based on the relative fraction of the symmetric difference of two regions occupied by the target and source data. To demonstrate that the proposed method can reconstruct a 3D model through extracted intermediate slice data during shape transformation, we perform several computational tests. Furthermore, the proposed method is applied to a 3D volume reconstruction from multi-slice data of human vertebra.