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摘要: 针对计算机辅助文物虚拟复原中由于破损文物断裂部位边缘受损而引起的轮廓线不能充分表示断裂面几何特征的问题，提出了一种基于断裂面拓扑特征的破碎文物自动拼接算法.首先，定义碎片模型顶点显著度指标函数，提取断裂面特征点，依据Morse-Smale复形理论构建并简化断裂面的几何拓扑图；然后，通过定义基准点与0值面，从而计算目标点的对应高度差值，将拓扑图中四边形曲面构造成为能完整表示断裂面几何特征的特征描述符，并根据凹凸互补性计算初始特征四边形匹配集的误差，筛选出最优匹配集；最后，采用四元组方法计算旋转、平移矩阵，利用穷举搜索法实现碎片的精确拼接.实验结果表明，该方法针对断裂部位边缘受损的破碎文物模型可获得较满意的拼接效果.
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关键词:
- Morse-Smale复形 /
- 刚体变换 /
- 特征描述符 /
- 四元数 /
- 穷举搜索
Abstract: In order to address the problem that the traditional break-curves methods fail to reassemble fractured fragments with incompleteness in contours, a novel automatic reassembly method is proposed using topological feature of fracture surfaces in this paper. First, the Morse-Smale complex on the fractured surfaces of fragments is constructed with curvedness as the indicator function. Then, the tangent plane is calculated through height comparison among key points and the quadrilateral descriptor is obtained by computing height difference. After that, according to the correlation between adjacent regions, optimal quadrilateral descriptors are selected. The rigid transformation matrices that maximize the contact area between surfaces are obtained by quaternion method, such that two fragments can be precisely aligned based on optimal rigid motion through exhaustive search. Experimental results show that satisfactory performance can be achieved by several uses of the algorithm on the fragments of the terracotta warriors.1) 本文责任编委 刘成林 -
图 9 G10-26号俑部分邻接碎片拼接结果
Fig. 9 Reassembly results of some adjacent fragments of Warriors G10-26
图 10 G10-19号俑部分邻接碎片拼接结果
Fig. 10 Reassembly results of some adjacent fragments of Warriors G10-19
图 11 G10-23号俑部分邻接碎片拼接结果
Fig. 11 Reassembly results of some adjacent fragments of Warriors G10-23
图 12 G10-18号俑部分邻接碎片拼接结果
Fig. 12 Reassembly results of some adjacent fragments of Warriors G10-18
图 13 G10-36号俑部分邻接碎片拼接结果
Fig. 13 Reassembly results of some adjacent fragments of Warriors G10-36
图 14 G10-22号俑部分邻接碎片拼接结果
Fig. 14 Reassembly results of some adjacent fragments of Warriors G10-22
表 1 兵马俑碎片实验数据
Table 1 Experimental datas of the Terracotta Army fragments
编号 碎片数量 网格总数 特征四边形总数 匹配精度 G10-18 7 674 477 253 0.924 G10-26 2 38 602 32 0.929 G10-36 6 591 641 191 0.961 G10-22 5 451 750 103 0.975 G10-19 3 94 276 93 0.924 G10-23 3 12 147 84 0.896 
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表 2 本文算法运行时间
Table 2 Execute times of the proposed algorithm
编号 T1 (s) T2 (s) T3 (s) 总时间(s) G10-18 68.461 17.436 7.246 93.143 G10-36 53.534 16.990 6.128 76.652 G10-22 30.157 12.631 4.021 46.809 G10-26 7.065 3.518 0.981 11.564 G10-19 17.913 6.349 2.065 26.327 G10-23 19.254 7.521 2.731 29.506
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