多视图自标定的最小约束松弛
Minimal Constraint Relaxation for Multiview Autocalibration
为多视图自标定中的过约束多项式系统提供了一套可复用的约束松弛枚举与分类流程，结合符号计算与数值同伦延拓筛选出良态、有限解的约束子集，可直接用于改进三视图自标定的数值稳定性。
原文依据 we introduce a minimal relaxation framework for identifying subsets of constraints leading to geometrically valid solutions
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论多视图几何中的多项式系统往往是过约束的，而朴素地删除方程可能导致不稳定或不一致的解。我们通过约束松弛重新审视这一问题——有选择地删除方程，以获得有限个孤立的（理想情况下良态的）解。聚焦于用于自标定的三视图 Kruppa 方程，我们引入一个最小松弛框架，用于识别能导出几何上有效解的约束子集。借助符号计算与数值同伦延拓方法，我们枚举并分类了由我们所构造的 Kruppa 方程形式所产生的全部可能松弛模式，并分离出所有能给出有限多个解的模式。在合成图像与真实图像的实验中，我们经验性地证明特定的松弛具有良好条件数，并稳定优于多个基线，包括更经典的一种 Kruppa 表述。总体而言，我们的发现确立了最小松弛框架作为多视图几何计算中一种实用工具的地位。
英文原文摘要 1084 字符
Polynomial systems in multiview geometry are often over-constrained, and naively removing equations can lead to unstable or inconsistent solutions. We revisit this issue through constraint relaxation---selectively removing equations to obtain a finite set of isolated (and, ideally, well-conditioned) solutions. Focusing on the three-view Kruppa equations for autocalibration, we introduce a minimal relaxation framework for identifying subsets of constraints leading to geometrically valid solutions. Using both symbolic computation and numerical homotopy continuation methods, we enumerate and classify all possible relaxation patterns arising from our formulation of Kruppa's equations, isolating all patterns that yield finitely-many solutions. In experiments with synthetic and real images, we demonstrate empirically that specific relaxations are well-conditioned and consistently outperform multiple baselines, including a more classical Kruppa formulation. Overall, our findings establish the minimal relaxation framework as a practical tool in multiview geometry computation.