基于轮廓形变的复杂表面重构

本文提出了一种基于自由形变（Free-Form Deformation, FFD）及外轴投影（External Axes Projection, EAP）的复杂表面重构算法.该算法以目标形状的切片轮廓作为输入数据，此后轮廓被嵌入到高维空间有向距离场中，在此隐式空间中，算法主要分为以下三步：生成计算序列，计算序列由计算单元组成，每一个计算单元包含上下相邻的两个轮廓；根据相邻轮廓间的拓扑关系，进行外轴投影（EAP），以解决潜在的分支问题；在每个计算单元中，根据轮廓长度决定自由形变方向，并进行自由形变，根据自由形变结果，建立轮廓间顶点的一一对应关系，并以此进行表面重构.该方法具有以下特点：输入轮廓可具有任意拓扑结构；所生成表面与输入轮廓完全贴合，生成表面准确，无自我重叠，拓扑关系不发生改变；算法高度并行，执行效率高.实验结果证明，该算法可以解决复杂表面的重构问题.

Surface Reconstruction of Complex Shapes Based on Contour Deformation

In this paper, we present a novel reconstruction method based on free-form deformation (FFD) and External Axes Projection (EAP) to improve the surface smoothness effect of 3D reconstruction. The contours of the slices are implicitly embedded in a higher dimensional space of distance transforms. In this implicit embedding space, reconstruction is formulated in a manner:An arrangement of the planar slices is computed to support the approach, the arrangement is consisted of cells, each cell consists of two adjacent contours; the branching problem is converted into one-to-one case by the external axes projection; computing direction for each cell of the arrangement is decided by the length energy. Then in each cell a B-spline based free-form deformation is used to establish the correspondence between the adjacent contours. Finally, the contours are stitched together based on the correspondence. The key advantage of such framework:(1) it naturally deals with contours of arbitrary topology, and it preserves shape topology, and (2)the established one-to-one correspondences between two adjacent contours can guarantee the surface is continuous and no intersection, (3)this framework is highly parallel. Experimental results show that our approach performs well and can handle complicated situations.