通过无假阴性与无假阳性的完备连续等距不变量识别未标记点云的刚性模式
计算机视觉与模式识别
2023-03-28 v1 计算几何
度量几何
摘要
汽车或任何其他固体对象等刚性结构常由有限的未标记点云表示。这些点云上最自然的等价关系是保持所有点间距离的刚体运动或等距。点云的刚性模式仅能由完备等距不变量可靠比较，其亦可称为无假阴性（等距点云具不同描述）且无假阳性（非等距点云具相同描述）的等变描述子。数据中的噪声与运动促使人们寻找在合适度量下于点扰动下连续的不变量的需求。我们提出任意欧几里得空间中未标记点云的首个连续且完备的不变量。对固定维度，该不变量所用新度量可在点数的多项式时间内计算。
引用
@article{arxiv.2303.15385,
title = {Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positives},
author = {Daniel Widdowson and Vitaliy Kurlin},
journal= {arXiv preprint arXiv:2303.15385},
year = {2023}
}
备注
This conference version is for CVPR (Computer Vision and Pattern Recognition), https://cvpr2023.thecvf.com. The latest file is http://kurlin.org/projects/cloud-isometry-spaces/distance-based-invariants.pdf. The extended versions of sections 3-4 with all proofs and big examples are at arXiv:2303.14161 for metric spaces, arXiv:2303.13486 for Euclidean spaces. arXiv admin note: substantial text overlap with arXiv:2303.13486, arXiv:2303.14161