An efficient volume repairing method by using a modified Allen-Cahn equation

Abstract

Classifying and rendering volumes of the structure are two essential goals of the visualization process. However, loss of some voxels can cause poor visualization results, such as small holes or non-smooth patches in visualized volumes. Beginning with the classified volumes, we propose a modified Allen-Cahn equation, which has the motion of mean curvature, to recover lost voxels and to fill holes. Consequently, a probability function can be obtained, which indicates the probability of each voxel being a volume voxel. Usually, the obtained probability function is smooth due to the motion of the mean curvature flow. Therefore visualization quality of volumes can be significantly improved. The equation is numerically computed by the unconditional stable operator splitting method with a large time step size. Thus the numerical scheme is fast and can be straightforwardly applied to GPU-accelerated DCT implementation that performs up to many times faster than CPU-only alternatives. Many experimental results have been performed to demonstrate the efficiency of the proposed method.