基于核密度估计的三维非等距模型簇的对应关系计算方法

Correspondence calculation method of three-dimensional non-isometric model cluster based on kernel density estimation

针对三维非等距模型簇的一致对应关系计算问题,提出了一种基于核密度估计的三维非等距模型簇对应关系计算方法。首先引入离散时间演化过程描述符(DEP)提取三维模型表面的特征描述符,得到不同区域的不同分布特征;其次通过核密度估计建立非等距模型间的映射关系;最后利用弹性网罚函数对非等距模型簇映射关系进行凸优化,从而得到更准确的三维非等距模型簇点到点对应关系。实验结果表明,利用时变描述符与核密度估计相结合的方法计算非等距模型簇的对应关系,在一定程度上减小了模型簇一致对应的测地错误,与Aubry的算法比较,测地错误平均下降至0.054。该基于核密度估计的匹配算法与使用函数映射或随机森林函数的方法相比,能构建出更为准确的非等距模型簇一致对应关系。

Aiming at the correspondence calculation problem of 3 D non-isometric model cluster,a new method for the correspondence calculation of 3 D non-isometric model cluster based on kernel density estimation was proposed. Firstly,the feature descriptors on the surface of the three-dimensional model were obtained by Discrete-time Evolution Process(DEP)descriptor. Secondly,the correspondence between non-isometric models was established by kernel density estimation.Finally,the penalty function of the elastic net was used to conduct convex optimization for the mapping correspondence between non-isometric models and obtain a more accurate point-to-point correspondence of the 3 D non-isometric model cluster. The experimental results show that the correspondence of the non-isometric model cluster is calculated by combining DEP descriptor with kernel density estimation,which can reduce the geodetic error of correspondence to a certain extent.Compared with Aubry’s algorithm,the geodetic error dropped to 0. 054 on average. Compared with the functional maps and random forests,the matching algorithm based on kernel density estimation in this paper can obtain more accurate correspondence between non-isometric model cluster.