🤖 AI Summary
This paper addresses the Perspective-Three-Point (P3P) problem—estimating camera pose from three 3D world points and their 2D image projections. We propose a novel geometric solution based on conic transformations, centered on a canonical parabola mapping framework: a coordinate transformation converts the original intersecting conic pair into a standard parabola and another conic, thereby explicitly decoupling variables, eliminating complex arithmetic, and yielding a real-coefficient quartic equation. Analytic elimination and normalized polynomial root-finding ensure efficient and robust real-root computation. Experiments demonstrate that our method achieves superior computational speed over state-of-the-art algorithms while maintaining numerical stability and pose estimation accuracy, making it suitable for real-time visual pose estimation.
📝 Abstract
We propose a conic transformation method to solve the Perspective-Three-Point (P3P) problem. In contrast to the current state-of-the-art solvers, which formulate the P3P problem by intersecting two conics and constructing a degenerate conic to find the intersection, our approach builds upon a new formulation based on a transformation that maps the two conics to a new coordinate system, where one of the conics becomes a standard parabola in a canonical form. This enables expressing one variable in terms of the other variable, and as a consequence, substantially simplifies the problem of finding the conic intersection. Moreover, the polynomial coefficients are fast to compute, and we only need to determine the real-valued intersection points, which avoids the requirement of using computationally expensive complex arithmetic. While the current state-of-the-art methods reduce the conic intersection problem to solving a univariate cubic equation, our approach, despite resulting in a quartic equation, is still faster thanks to this new simplified formulation. Extensive evaluations demonstrate that our method achieves higher speed while maintaining robustness and stability comparable to state-of-the-art methods.