优化谱对齐的三维模型簇一致性对应关系计算  

Consistency correspondence calculation of 3D shape collections using optimized spectral alignment

作　　者：吴衍 杨军[1,3] 张思洋 WU Yan;YANG Jun;ZHANG Siyang(School of Electronic and Information Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China;School of Big Data and Artificial Intelligence,Fujian Polytechnic Normal University,Fuqing 350300,Fujian,China;Faculty of Geomatics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学电子与信息工程学院,兰州730070 [2]福建技术师范学院大数据与人工智能学院,福建福清350300 [3]兰州交通大学测绘与地理信息学院,兰州730070

出　　处：《哈尔滨工业大学学报》2024年第5期84-92,共9页Journal of Harbin Institute of Technology

基　　金：国家自然科学基金(42261067,61862039);兰州市人才创新创业项目(2020-RC-22);兰州交通大学天佑创新团队(TY202002);福建省自然科学基金(2022J01972);福建省中青年教师教育科研项目(JAT201378)。

摘　　要：为了解决非刚性三维模型簇对应关系计算准确率低、一致性差,且难以实现双射的问题,提出了一种采用优化谱对齐算法和规范一致潜在基的非刚性三维模型簇对应关系计算新方法。首先,利用函数映射的伴随算子实现模型间谱域信息的对齐,计算模型簇中每个模型对的函数映射矩阵,解决函数映射与逐点映射方向不一致的问题;其次,使用改进的模型映射集合算法为每个模型对的函数映射矩阵赋予相应权重,降低初始化参数的噪声对模型簇对应关系计算结果的影响;最后,在模型簇的对应关系计算过程中加入极限模型的规范一致潜在基,极限模型可以看成模型簇中所有模型的类型结构,是一个具有几何可变性的中间模型,提高算法的一致性和双射性。实验结果表明:与已有算法相比,本算法在FAUST、SCAPE、TOSCA和SHERC’16 Topology数据集上构建的对应关系测地误差最小,能够减少初始化参数的噪声,解决模型自身对称性影响对应关系计算的问题,更加精确地构建出具有一致性和双射性的非刚性三维模型簇对应关系。This paper focuses on the problems of computing correspondences among non-rigid 3D shape collections with a low accuracy rate,poor consistency,and difficult bijectivity.The novel approach proposed in this paper is based on the optimized spectral alignment algorithm and the canonical consistent latent basis.Firstly,we use the adjoint operator derived from the functional map to align the information between shapes in the spectral domain.The functional map matrix of each shape pair in the shape collections is calculated,resolving the problem of inconsistent direction between functional map and pointwise map.Secondly,we adapt the improved collections of shape maps approach to assign corresponding weights to the functional map matrix of each shape pair,reducing the impact of initialization parameter noise on the shape collection matching calculation results.Finally,we add the canonical consistent latent basis of the limit shape to compute the shape collections correspondence.The limit shape can be seen as a type structure of all shapes in the shape collection,which is an intermediate model with geometric variability,improving the consistency and bijectivity of the algorithm.The experimental results show that compared with the existing algorithms,this algorithm has the lowest geodesic error and the highest accuracy of global correspondence on FAUST,SCAPE,TOSCA,and SHERC’16 Topology datasets.Meanwhile,our method can reduce the noise of initialization parameters,solve the symmetric ambiguity problem,and more accurately compute the consistent and bijective correspondence of non-rigid 3D shape collections.

关 键 词：对应关系 非刚性三维模型簇 优化谱对齐 规范一致潜在基 函数映射 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]