This paper addresses a special Perspective-n-Point (PnP) problem: estimating the optimal pose to align 3D and 2D shapes in real-time without correspondences, termed as correspondence-free PnP. While several studies have focused on 3D and 2D shape registration, achieving both real-time and accurate performance remains challenging. This study specifically targets the 3D-2D geometric shape registration tasks, applying the recently developed Reproducing Kernel Hilbert Space (RKHS) to address the "big-to-small" issue. An iterative reweighted least squares method is employed to solve the RKHS-based formulation efficiently. Moreover, our work identifies a unique and interesting observability issue in correspondence-free PnP: the numerical ambiguity between rotation and translation. To address this, we proposed DynaWeightPnP, introducing a dynamic weighting sub-problem and an alternative searching algorithm designed to enhance pose estimation and alignment accuracy. Experiments were conducted on a typical case, that is, a 3D-2D vascular centerline registration task within Endovascular Image-Guided Interventions (EIGIs). Results demonstrated that the proposed algorithm achieves registration processing rates of 60 Hz (without post-refinement) and 31 Hz (with post-refinement) on modern single-core CPUs, with competitive accuracy comparable to existing methods. These results underscore the suitability of DynaWeightPnP for future robot navigation tasks like EIGIs.

翻译：本文研究一种特殊的透视n点（PnP）问题：在无需对应关系的情况下实时估计最优位姿以对齐3D与2D形状，称为无对应关系PnP。尽管已有若干研究关注3D与2D形状配准，但实现实时且精确的性能仍具挑战。本研究特别针对3D-2D几何形状配准任务，应用近期发展的再生核希尔伯特空间（RKHS）以解决“大配小”问题。采用迭代重加权最小二乘法高效求解基于RKHS的公式化表达。此外，我们的工作发现了无对应关系PnP中一个独特而有趣的可观测性问题：旋转与平移之间的数值模糊性。为此，我们提出DynaWeightPnP，引入动态加权子问题及交替搜索算法，旨在提升位姿估计与对齐精度。实验在典型场景——即血管内图像引导介入手术（EIGIs）中的3D-2D血管中心线配准任务——上进行。结果表明，所提算法在现代单核CPU上实现了60 Hz（无后优化）与31 Hz（含后优化）的配准处理速率，其精度与现有方法相比具有竞争力。这些结果印证了DynaWeightPnP在未来如EIGIs等机器人导航任务中的适用性。