在谁的坐标系中退化？激光雷达配准的退化检测的等变性条件
Degenerate in Whose Frame? An Equivariance Condition for Degeneracy Detection in LiDAR Registration
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中文总结 AI 辅助
该研究针对激光雷达配准退化检测中坐标系依赖问题，提出等变度量规则，构建等变点位移度量，经实验验证其特征值与阈值的不变性，为退化检测提供坐标系无关的准则。
中文摘要 AI 辅助
激光雷达配准的退化检测器通常返回六个沿各轴的二元标签。我们询问这些标签是否是场景的属性。在坐标系变换下，点到平面信息矩阵通过同余变换：H' = Ad(T)^T H Ad(T)，而非相似变换。同余变换保持零空间，并通过伴随重参数化识别相同的物理 Twist 子空间；各轴的特征范围和阈值化谱不必是不变的。在无噪声的圆形隧道中，将原点平移一米会改变被标记的自由度。广义准则 Hv = λ Mv 在正定信息形式上是通用坐标系无关的，当且仅当其度量规则是等变的。没有固定度量符合要求，而仅在十九次调查校准中的一次零螺距时，才存在适配 rig 的度量。等变点位移度量 M = Σ_i J_i^T J_i 产生无量纲、场景尺度不变的广义特征值，它们对坐标系、长度单位的一致变化和场景尺度均不变；阈值在不同序列间经验上可转移。在四个公开序列的 365 帧对中，标签在实际外部量下很少变化，但重映射估计器的校正量在坐标系选择间有 44.5%-69.5% 的对存在差异，中位数为 0.7-4.0 mm，最大值为 0.87 m。即使在等变度量下，各轴的特征范围仍会变化，这使得根本问题在于所报告的量。
英文摘要
Degeneracy detectors for LiDAR registration commonly return six per-axis binary labels. We ask whether these labels are properties of the scene. Under a body-frame change, the point-to-plane information matrix transforms by congruence, H' = Ad(T)^T H Ad(T), not similarity. Congruence preserves nullity and, through the adjoint reparameterization, identifies the same physical twist subspace; the per-axis footprint and a thresholded spectrum need not be invariant. In a noise-free circular tunnel, shifting the origin by one metre changes which degrees of freedom are flagged. A generalized criterion Hv = lambda Mv is universally frame-independent over positive-semidefinite information forms if and only if its metric rule is equivariant. No fixed metric qualifies, while a rig-adapted one exists only at zero screw pitch, met in one of nineteen surveyed calibrations. The equivariant point-displacement metric M = sum_i J_i^T J_i yields dimensionless, scene-scale-invariant generalized eigenvalues. They are invariant to body frame, consistent changes of length unit and scene scales; the threshold also transfers empirically across sequences. Across 365 frame pairs from four public sequences, labels rarely change at practical extrinsic magnitudes, yet a remapping estimator's correction differs between body-frame choices on 44.5-69.5% of pairs, with a median of 0.7-4.0 mm and a maximum of 0.87 m. The per-axis footprint changes even under the equivariant metric, placing the fundamental issue in the reported quantity.
发表机构
- School of Mechanical Engineering, Hebei University of Technology（河北工业大学机械工程学院）
机构由 AI 辅助整理，请以论文原文为准。
