In this paper, we present a new method for non-linear pairwise registration of 3D point sets. In this method, we consider the points of the first set as the draws of a Gaussian mixture model whose centres are the displaced points of the second set. Next we perform a maximum a posteriori estimation of the parameters (which include the unknown transformation) of this model using the expectation–maximisation (EM) algorithm. Compared to other methods using the same “EM-ICP” framework, we propose four key modifications leading to an efficient algorithm allowing for fast registration of large 3D point sets: (1) truncation of the cost function; (2) symmetrisation of the point-to-point correspondences; (3) specification of priors on these correspondences using differential geometry; (4) efficient encoding of deformations using the RKHS theory and the Fourier analysis. We evaluate the added value of these modifications and compare our method to the state-of-the-art CPD algorithm on real and simulated data.

在本文中，我们提出了一种用于3D点集的非线性成对配准的新方法。在这种方法中，我们将第一组的点视为高斯混合模型的绘图，该模型的中心是第二组的位移点。接下来，我们使用期望最大化（EM）算法对该模型的参数（包括未知变换）进行最大后验估计。与使用相同“ EM-ICP”框架的其他方法相比，我们提出了四个关键修改，从而产生了一种有效的算法，可以快速注册大型3D点集：（1）截断成本函数；（2）点对点对应关系的对称性；（3）使用微分几何来指定这些对应关系的先验；（4）使用RKHS理论和傅立叶分析对变形进行有效编码。我们评估了这些修改的附加价值，并将我们的方法与针对真实和模拟数据的最新CPD算法进行了比较。