A new surface interpolation technique for reconstructing 3-D objects from serial cross sections

Abstract

A method for automatically reconstructing a three-dimensional object from serial cross sections is presented. The method combines the techniques of dynamic elastic contour interpolation, spline theory, and quadratic-variation-based surface interpolation. 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 pair of consecutive cross sections. After this, preliminary processing for surface computation is carried out by mapping the contours into the domain of the surface function and then using spline functions to calculate the initial surface values. Based on the output from preliminary processing, the quadratic-variation-based surface interpolation algorithm is applied to calculate the final surface representation. Since the presented methods take the continuity of high-order derivatives into consideration, smooth and complete surface of a 3-D object can be reconstructed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>