为了有效提取散乱点云上的特征点,针对现有点云特征提取算法采用全局统一的特征度量阈值易造成特征误判、漏判及需要多次人工调参的问题,基于离散Morse理论,提出一种自适应的特征提取算法。首先,采用基于局部邻域的协方差分析计算每个数据点的特征度量,标定潜在特征点。然后将潜在特征点与其邻域点在主方向上所形成的夹角平均值作为局部特征检测算子,利用该算子计算该点的离散梯度;最后,构建每个潜在特征点局部邻域内的Voronoi图,利用线性插值法计算离散点所在泰森多边形所有顶点的梯度构建离散梯度向量域,将离散梯度向量域中的梯度极值点判定为特征点。为提高算法的稳健性和抗噪能力,将离散梯度计算扩展到多尺度上,将邻域大小作为离散的尺度参数,多尺度地对一点进行判定。实验结果表明,该方法简单、稳健性好,不依赖于特征的尖锐程度,能在有效提取较尖锐特征的同时,尽可能多地保留较平滑特征。当噪声为0.03 dB时,可以有效地提取点云特征,而当噪声为0.05 dB时,尽管存在个别特征点消失的情况,但整体上显著特征点能够得到较好地提取,效果令人满意。

For the erroneous detection of feature points and multi-adjustment of the thresholds caused by global thresholds in the extraction of feature points from scattered point clouds, an adaptive feature extraction method based on Morse theory is proposed. Firstly, the potential feature points are marked by assigning weights that are computed by covariance analysis. Secondly, the mean angle along the principle direction between the point and its neighboring points is defined as the local feature descriptor, in order to compute the discrete gradient of the potential feature points. Finally, the Voronoi diagram of each local feature neighborhood is established,the linear interpolation method is utilized to compute the discrete gradient of the vertices of the Thiessen polygonal, and the gradient extreme points are marked as feature points according to the local discrete gradient vector domain. In order to improve the robustness and the anti-noise performance, the discrete gradient computation is performed using multi-scale where the neighborhood scale is used as the scale parameter, and then the features are extracted with multi-scale analysis. The experimental results demonstrate that the proposed method is simple, robust and does not depend on the sharpness of the features; furthermore, it extracts both sharp and blunt features. The results are satisfactory at different levels of noises from 0.03 dB to 0.05 dB, even though some of the features may be missing under 0.05 dB noise level.