基于加权PCA分析的三维点云模型对称性检测算法

Symmetry detection of point-based 3D models algorithm based on weighted PCA

对普通PCA(principal component analysis)算法进行了改进,使之能用来检测点云模型中存在的平面反射对称性。算法的执行过程如下:首先,使用每个点元的面积作为权重,执行一次加权PCA确定一个近似的对称平面作为初始平面;然后,采用迭代的方法逐步调整上述的对称平面,使之趋向于真正的对称平面(主对称平面)。在每次迭代过程中,算法根据一个距离度量来更新每个点元的权重,通过新的权重执行加权PCA计算来确定一个新的对称平面。如果当前的对称平面与上一次迭代中的对称平面足够接近或者迭代次数超过了给定的阈值,迭代就会终止,从而计算获得整体点云的主对称平面。实验结果表明即使对于非完美对称的模型,该算法也能精确地找出模型的主对称平面。

The common PCA （principal component analysis）algorithm was improved,which can be used to detect the presence of plane reflection symmetry of point-based 3 D model.The iteratively re-weighted PCA process works as fol-lows：Firstly,an initial approximate symmetry plane is computed through a weighted PCA process.Then,the area of each surfel is calculated as its weight.Thereafter,the approximate symmetry plane is refined iteratively.In each itera-tion,we firstly update each surfel’s weight based on a distance metric at that surfel,and secondly conduct the weighted PCA to refine the approximate symmetry plane.The iteration will stop to give the final approximate symmetry plane un-til the new symmetry plane and the previous one are closely enough or the number of iterations goes beyond a threshold. According to the experiment results,the primary symmetry plane of the models that are not perfectly symmetric can also be found by the proposed algorithm.