Improvement on Dynamic Elastic Interpolation Technique for Reconstructing 3-D Objects from Serial Cross Sections

An improved method for automatically reconstructing a three-dimensional object from serial cross sections is presented in this paper. The method improves the dynamic elastic contour interpolation technique [21]. There are two major improvements: 1) in the case of branching that involves concave contours, instead of pairwise interpolation between the start contour and each goal contour, the goal image is considered globally and local constraints are imposed on the forces exerting upon the vertices; 2) it takes the continuity of high-order derivatives into consideration and incorporates the schemes of spline theory, quadratic-variation-based surface interpolation, and finite-element-based multilevel surface interpolation to create smoother surfaces of the reconstructed object. In the proposed method, the initial description of the object is formed by applying the elastic interpolation algorithm to generate a series of intermediate contours between each input pair of consecutive cross sections. After this, a preliminary processing for surface computation is carried out by mapping the contours onto the domain of surface function and then using spline functions to calculate the initial surface values. Based on the output from the preliminary processing, two alternatives, viz. quadratic-variation-based surface interpolation algorithm and finite-element-based multilevel surface interpolation algorithm, can be adopted to obtain the final surface representation.