Multicomponent volume reconstruction from slice data using a modified multicomponent Cahn–Hilliard system

We propose an efficient and robust algorithm to reconstruct the volumes of multi-labeled objects from sets of cross sections without overlapping regions, artificial gaps, or mismatched interfaces. The algorithm can handle cross sections wherein different regions have different labels. The present study represents a multicomponent extension of our previous work (Li et al. (2015), [1]), wherein we modified the original Cahn–Hilliard (CH) equation by adding a fidelity term to keep the solution close to the single-labeled slice data. The classical CH equation possesses desirable properties, such as smoothing and conservation. The key idea of the present work is to employ a multicomponent CH system to reconstruct multicomponent volumes without self-intersections. We utilize the linearly stabilized convex splitting scheme introduced by Eyre with the Fourier-spectral method so that we can use a large time step and solve the discrete equation quickly. The proposed algorithm is simple and produces smooth volumes that closely preserve the original volume data and do not self-intersect. Numerical results demonstrate the effectiveness and robustness of the proposed method.