论文标题
使用4点一致性约束的广义姿势和规模估算
Generalized Pose-and-Scale Estimation using 4-Point Congruence Constraints
论文作者
论文摘要
我们提出GP4PC，这是一种用于计算具有从四个相应3D刻度和射线对的未知内部尺度的通用相机绝对姿势的新方法。与大多数姿势和尺度方法不同，GP4PC是基于由两组与未知相似性转换相关的四个点所定义的形状一致性产生的约束。通过为问题选择新的参数化，我们在四个标量变量中得出了四个二次方程的系统。变量代表沿摄像头中心沿光线的3D点的距离。通过基于Groebner的自动多项式求解器求解该系统后，我们使用有效的3D点点比对方法来计算相似性转换。我们还针对Coplanar点的求解器提出了一个专门的求解器变体，该变体在计算上非常有效，比现有最快的求解器快3倍。我们对真实和合成数据集的实验表明，在RANSAC框架内使用的总运行时间方面，GP4PC是最快的方法之一，同时实现了竞争性数值稳定性，准确性，准确性和噪声鲁棒性。
We present gP4Pc, a new method for computing the absolute pose of a generalized camera with unknown internal scale from four corresponding 3D point-and-ray pairs. Unlike most pose-and-scale methods, gP4Pc is based on constraints arising from the congruence of shapes defined by two sets of four points related by an unknown similarity transformation. By choosing a novel parametrization for the problem, we derive a system of four quadratic equations in four scalar variables. The variables represent the distances of 3D points along the rays from the camera centers. After solving this system via Groebner basis-based automatic polynomial solvers, we compute the similarity transformation using an efficient 3D point-point alignment method. We also propose a specialized variant of our solver for the case of coplanar points, which is computationally very efficient and about 3x faster than the fastest existing solver. Our experiments on real and synthetic datasets, demonstrate that gP4Pc is among the fastest methods in terms of total running time when used within a RANSAC framework, while achieving competitive numerical stability, accuracy, and robustness to noise.
