A MODIFIED CAHN–HILLIARD EQUATION FOR 3D VOLUME RECONSTRUCTION FROM TWO PLANAR CROSS SECTIONS

Abstract

In this paper, we present an implicit method for reconstructing a 3D solid modelfrom two 2D cross section images. The proposed method is based on the Cahn–Hilliard modelfor the image inpainting. Image inpainting is the process of reconstructing lost parts of imagesbased on information from neighboring areas. We treat the empty region between thetwo cross sections as inpainting region and use two cross sections as neighboring information. We initialize the empty region by the linear interpolation. We perform numerical experimentsdemonstrating that our proposed method can generate a smooth 3D solid model from two crosssection data. 1