A novel region-based approach is proposed to find a thin plate spline map between a pair of deformable 3D objects represented by triangular surface meshes. The proposed method works without landmark extraction and feature correspondences. The aligning transformation is simply found by solving a system of integral equations. Each equation is generated by integrating a non-linear function over the object domains. We derive recursive formulas for the efficient computation of these integrals for open and closed surface meshes. Based on a series of comparative tests on a large synthetic dataset, our triangular mesh-based algorithm outperforms state of the art methods both in terms of computing time and accuracy. The applicability of the proposed approach has been demonstrated on the registration of 3D lung CT volumes, brain surfaces and 3D human faces.

中文翻译：

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三角形曲面网格的弹性对齐

提出了一种新的基于区域的方法，以在由三角形表面网格表示的一对可变形 3D 对象之间找到薄板样条图。所提出的方法无需地标提取和特征对应即可工作。通过求解积分方程组可以简单地找到对齐变换。每个方程都是通过对对象域上的非线性函数进行积分来生成的。我们推导出递归公式，用于有效计算开放和封闭表面网格的这些积分。基于对大型合成数据集的一系列比较测试，我们基于三角形网格的算法在计算时间和准确性方面均优于最先进的方法。所提出的方法的适用性已在 3D 肺 CT 体积、大脑表面和 3D 人脸的配准上得到证明。