We compute precise estimates for dimensions of 3D-encryption techniques of 3D-point clouds which use permutations and rigid body motion, in which geometric stability is to be guaranteed. Few attempts are made in this direction. An attempt is established using the notions of dimensional and spatial stability by Jolfaei et al. (2015), who also proposed a 3D object encryption algorithm, claiming that it preserves dimensional and spatial stability. However, as we mathematically prove neither the algorithm, nor the associated estimates are correct. We introduce more rigorous definitions of the geometric stability of such 3D data encryption algorithms, followed by dimensionality measures
翻译:我们通过排列和刚体运动计算三维点云加密技术的维度精确估计,从而确保其几何稳定性。此前已有少数研究尝试过相关尝试,其中Jolfaei等人曾于2015年提出3D对象加密算法,宣称其保持了维度和空间稳定性。但我们在数学上证明算法本身以及相关估计均存在问题。我们引入更为严格的几何稳定性定义,随后给出维度度量。