基于断裂面匹配的破碎刚体复原研究
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摘要
破碎刚体复原问题,是计算机图形学、计算机视觉和模式识别中一个有待解决的问题,在文物保护、工业设计和临床医学等方面有着重要的应用价值。目前,国内外研究较多的是基于轮廓曲线的不带厚度碎片的拼接,对于带厚度碎块的拼接研究的较少,而国内还很少有这方面的研究。因此,我们针对带厚度的碎块,研究了基于断裂面匹配问题中的关键技术,包括断裂面分割、断裂面匹配和整体拼合,并应用在兵马俑等碎块上,主要工作如下：
(1)给出了一种基于法矢的断裂面分割算法。根据相邻三角片法矢的夹角,采用区域生长算法,将碎块以棱边为界限分割成多张曲面,然后,根据曲面法矢扰动区分原始面和断裂面。对于具有尖锐棱边的碎块,算法能正确地识别出断裂面。
(2)给出了一种基于多尺度曲率的断裂面分割和轮廓曲线提取算法。提出了将基于面和基于边两种分割策略相结合的方法,先根据多尺度曲率采用基于面的方法进行曲面分割,然后对得到的初始边界点扩展后进行边界跟踪,提取出最终的边界点,并优化处理。当碎块边界处过渡缓慢时,算法也能正确地分割。
(3)给出了一种基于轮廓曲线的断裂面匹配算法。以断裂面轮廓曲线为特征进行匹配,之后根据断裂面的整体信息,依次通过跨界切矢连续约束和曲面匹配误差排除误匹配。当两断裂面有相似边界时,算法能正确实现碎块的部分和完全匹配。
(4)给出了一种基于曲率和三维直方图的断裂面匹配算法。提出以显著特征点为中心将断裂面划分为多个面片,并使用三维直方图比较面片问的相似性,之后使用三角形约束的穷举搜索方法进行断裂面匹配。算法能正确实现碎块间的部分和完全匹配。
(5)给出了一种基于积分不变量和特征区域进行断裂面匹配的算法。根据积分不变量将断裂面划分为多个特征区域,然后使用主成分分析法计算相似区域对,并根据距离主方向约束排除伪区域对,最后使用ICP算法判断两断裂面是否匹配,同时将它们对齐校准。算法能正确实现碎块间的部分和完全匹配。
(6)给出了一种带回溯的子图融合方法进行碎块整体拼合。先建立碎块间的匹配关系图,将每一碎块看成一个子图,然后将满足条件的子图进行融合,直至所有子图融合为一个整体,如果存在无法融合的子图,则需要进行回溯。
Reassembling3D broken solids is a prominent and difficult problem in the fields of computer graphics, computer vision and pattern recognition. It can be applied in many fields such as archaeology, industrial design, clinic medicine and so on. More researches address fragments that have no thickness based on contour curve matching than fragments with thickness. We focuse on the reassembling broken solids based on surface matching, including fracture surfaces segmention, matching and fragments reassembly, all algorithms are verified in Terra Cotta Warriors and other fragments. Mainly works are as following:
(1)We present a fracture surfaces segmentation algorithms based on normal vectors. First we segment the fragments into a set of surfaces bounded by sharp curves according to the angle of normal vectors of adjacent triangles.Then use perturbation value to distinguish the original surfaces and fractures. The algorithm is suited for fragments with sharp boundary.
(2) We present a surface segmentation and contour curve extraction algorithm based on multi-scale curvature. We give a new method which first segments surface then spreads their initial boundary point and uses boundary tracking to get the final boundary. The algorithm is effective for fragments with sharp and complex boundary.
(3) A fracture surfaces matching algorithm based on contour curve matching is presented. First we find pairs of matching surfaces based on their contour curve similarity and then we delete outliers according to normal vector continuous constraint and surface matching error. The algorithm is suited for surfaces matching when they have similar boundary.
(4) A fracture surfaces matching algorithm based on multi-scale curvedness and3D histogram is presented. We give a new method which first divides fracture surfaces into several small regions whose centres are significant feature point and then uses3D histogram to compare region similarity. After that an exhaustive search method constrained by triangle similarity and voting scheme is used to match fracture surfaces.
(5) A fracture surfaces matching algorithm based on integral invariants and feature region is presented. First fracture surfaces are divided into several featured region according to the concave or convex. Then we use principal component analysis (PCA) to obtain similar region pairs and eliminate outliers according to the distance and principal direction constraints. Finally we use ICP algorithm to verify the reliability of matching result.
(6) We employ a sub-graph merging algorithm based on backtracking to merge all matched fragments until the object is reassembled.When there is a fragment which is not fusion, then backtracking.
(1)给出了一种基于法矢的断裂面分割算法。根据相邻三角片法矢的夹角,采用区域生长算法,将碎块以棱边为界限分割成多张曲面,然后,根据曲面法矢扰动区分原始面和断裂面。对于具有尖锐棱边的碎块,算法能正确地识别出断裂面。
(2)给出了一种基于多尺度曲率的断裂面分割和轮廓曲线提取算法。提出了将基于面和基于边两种分割策略相结合的方法,先根据多尺度曲率采用基于面的方法进行曲面分割,然后对得到的初始边界点扩展后进行边界跟踪,提取出最终的边界点,并优化处理。当碎块边界处过渡缓慢时,算法也能正确地分割。
(3)给出了一种基于轮廓曲线的断裂面匹配算法。以断裂面轮廓曲线为特征进行匹配,之后根据断裂面的整体信息,依次通过跨界切矢连续约束和曲面匹配误差排除误匹配。当两断裂面有相似边界时,算法能正确实现碎块的部分和完全匹配。
(4)给出了一种基于曲率和三维直方图的断裂面匹配算法。提出以显著特征点为中心将断裂面划分为多个面片,并使用三维直方图比较面片问的相似性,之后使用三角形约束的穷举搜索方法进行断裂面匹配。算法能正确实现碎块间的部分和完全匹配。
(5)给出了一种基于积分不变量和特征区域进行断裂面匹配的算法。根据积分不变量将断裂面划分为多个特征区域,然后使用主成分分析法计算相似区域对,并根据距离主方向约束排除伪区域对,最后使用ICP算法判断两断裂面是否匹配,同时将它们对齐校准。算法能正确实现碎块间的部分和完全匹配。
(6)给出了一种带回溯的子图融合方法进行碎块整体拼合。先建立碎块间的匹配关系图,将每一碎块看成一个子图,然后将满足条件的子图进行融合,直至所有子图融合为一个整体,如果存在无法融合的子图,则需要进行回溯。
Reassembling3D broken solids is a prominent and difficult problem in the fields of computer graphics, computer vision and pattern recognition. It can be applied in many fields such as archaeology, industrial design, clinic medicine and so on. More researches address fragments that have no thickness based on contour curve matching than fragments with thickness. We focuse on the reassembling broken solids based on surface matching, including fracture surfaces segmention, matching and fragments reassembly, all algorithms are verified in Terra Cotta Warriors and other fragments. Mainly works are as following:
(1)We present a fracture surfaces segmentation algorithms based on normal vectors. First we segment the fragments into a set of surfaces bounded by sharp curves according to the angle of normal vectors of adjacent triangles.Then use perturbation value to distinguish the original surfaces and fractures. The algorithm is suited for fragments with sharp boundary.
(2) We present a surface segmentation and contour curve extraction algorithm based on multi-scale curvature. We give a new method which first segments surface then spreads their initial boundary point and uses boundary tracking to get the final boundary. The algorithm is effective for fragments with sharp and complex boundary.
(3) A fracture surfaces matching algorithm based on contour curve matching is presented. First we find pairs of matching surfaces based on their contour curve similarity and then we delete outliers according to normal vector continuous constraint and surface matching error. The algorithm is suited for surfaces matching when they have similar boundary.
(4) A fracture surfaces matching algorithm based on multi-scale curvedness and3D histogram is presented. We give a new method which first divides fracture surfaces into several small regions whose centres are significant feature point and then uses3D histogram to compare region similarity. After that an exhaustive search method constrained by triangle similarity and voting scheme is used to match fracture surfaces.
(5) A fracture surfaces matching algorithm based on integral invariants and feature region is presented. First fracture surfaces are divided into several featured region according to the concave or convex. Then we use principal component analysis (PCA) to obtain similar region pairs and eliminate outliers according to the distance and principal direction constraints. Finally we use ICP algorithm to verify the reliability of matching result.
(6) We employ a sub-graph merging algorithm based on backtracking to merge all matched fragments until the object is reassembled.When there is a fragment which is not fusion, then backtracking.
引文
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