基于凹凸区域的断裂面匹配算法

Fractured surfaces matching based on concave-convex regions

针对破碎刚体复原给出一种断裂面匹配算法。根据平均曲率判断顶点的凹凸性,对凹凸顶点进行聚类将断裂面划分为多个凹凸特征区域;定义特征区域的协方差矩阵,根据其主成分和主方向定义特征区域的尺寸特征和各向异性特征,面积相近、类型相同和特征相近的区域为相似区域对,之后再根据距离主方向约束排除伪区域对;采用穷举法对每3对质心不共线的相似区域对,计算三维变换,将断裂面粗略对齐,再根据最近点迭代算法的收敛程度得到最优匹配,同时将两断裂面精细校准。实验结果表明,该算法能够实现较复杂断裂面的部分和完全匹配。

The paper presents a new fractured surfaces matching algorithm for reassembling 3D broken solids. Firstly, everyfractured surface is divided into several feature regions based on its all vertex’s convexity which is estimated according tomean curvature. Then it defines size characteristics and anisotropic characteristics based on the main ingredient and themain direction of feature regions’covariance matrix, similar regions are obtained through principal component analysisand discard outliers according to geometric constraints. Finally, using exhaustive method for every 3 similar area, theircenter is non-collinear to calculate 3D transform to coarsely align the two surfaces, and then according to the IterativeClosest Point（ICP）algorithm that is convergent or not it gets the optimal matching and achieves fine alignment. Experimentalresults show that the algorithm can deal with full and partial surfaces matching problem.