基于生成树代价和和几何约束的文物碎片自动重组方法

Reassembly of Fractured Fragments Based on Spanning Tree Cost and Geometric Constraints

在文物碎片自动重组过程中,针对传统基于几何驱动重组的方法容易受噪声影响会产生误匹配等问题,本文提出一种基于生成树代价和和几何约束的文物碎片自动重组方法.首先,采用曲度函数提取碎片断裂面上凹凸性显著的n个特征点;进而,对其进行拓扑重构,以特征点空间位置之间的欧氏距离为权值,构造n阶带权无向完全图及其最小、最大生成树,以生成树的代价和为邻接约束,快速筛选潜在匹配碎片;然后,再以特征点的主曲率构造特征串,引入Hausdorff距离来衡量两个特征串之间的相似程度,可以有效找出配对碎片;最后,采用四元数法估算旋转平移矩阵将碎片粗对齐,再采用迭代最近点算法实现精确对齐.实验结果表明,重组误差小于1 mm,与传统方法相比,该方法特征点数量较少,计算量小,有效提高了碎片重组的效率和准确性.

In the process of automatic reassembly of fractured fragments,the traditional methods based on geometric feature matching are sensitive to noises,which leads to mismatching points/fragments.An automatic reassembly method based on spanning tree cost and geometric constraints is proposed.Firstly,n features with significant concavity or convexity on the fracture surfaces of the fragments are extracted using the curvature function.Then,the topologies of the features are reconstructed,therefore,the n-th order weighted undirected complete graph and its minimum and maximum spanning trees can be constructed by setting the Euclidean distance between the feature points as the weights;thus the cost of spanning trees are utilized as the adjacency constraint in order to quickly screens the potential matching fragments.Furthermore,the feature strings are formed by aggregating the main curvatures of the feature points,and the Hausdorff distance is used to measure the similarities between the two feature strings.Consequently,the matching pieces of fragments can be effectively detected.Finally,the quaternion method is performed to complete the coarse alignment of adjacent fragments,and then the iterative closest point algorithm(ICP)is used to achieve precise alignment.The experimental results demonstrate that the reassembly error is less than 1 mm,and compared to the traditional method,the number of feature points used in the proposed method is relatively small,and the computational complexity is reduced,which effectively improves the efficiency and accuracy of fragments reassembly.