Abstract: In the presence of outliers, noise, or missing points, it is difficult to distinguish abnormal points and normal points in a damaged point set, and the matching relationship between point sets is also affected by these abnormal points. Based on the prior knowledge of the connections between normal points and the differences between normal points and abnormal points, it was proposed to model the estimation problem of matching relationship between point sets to the process of machine learning. Firstly, considering the error characteristics between two normal point sets, a learning method based on Deep Belief Network (DBN) was proposed to train the network with normal point sets. Then, the damaged point set was tested by using the trained DBN, and the outliers and mismatched points could be identified at the output of network according to the set error threshold. In the matching experiments of 2D and 3D point sets with noise and missing points, the matching performance between point sets was quantitatively evaluated by the model prediction results of samples. The precision of matching can reach more than 94%. The experimental results show that, the proposed algorithm can successfully detect the noise in the point set, and it can identify almost all matching points even in the case of data loss.

Key words: machine learning, Deep Belief Network (DBN), abnormal point set, point set registration

摘要： 在存在异常值、噪声或缺失点的情况下，损坏的点集中很难区分异常点与正常点，并且点集之间的匹配关系也会受到这些异常点的影响。基于正常点之间存在某种联系以及正常点与异常点之间存在差异的先验知识，提出将点集间匹配关系的估计问题模型化为机器学习的过程。首先，考虑到两个正常点集之间的误差特征，提出了一种基于深度信念网络（DBN）的学习方法来训练具有正常点集的网络；然后，使用训练好的DBN测试损坏的点集，根据设置的误差阈值在网络输出端就可以识别异常值和不匹配的点。对存在噪声和缺失点的2D、3D点集所做的匹配实验中，利用模型预测样本的结果定量评估了点集间的匹配性能，其中匹配的精确率可以达到94%以上。实验结果表明，所提算法可以很好地检测点集中的噪声，即使在数据缺失的情况下，该算法也可以识别几乎所有的匹配点。

关键词: 机器学习, 深度信念网络, 异常点集, 点集配准