A Fast and Reliable Solution to PnP, Using Polynomial Homogeneity and a Theorem of Hilbert.

Area of Science:

• Computer Vision
• Robotics
• Geometric Computer Vision

Background:

• The Perspective-n-Point (PnP) problem is fundamental in 3D computer vision for determining camera pose.
• Existing accurate solutions involve minimizing a fourth-degree polynomial, but lack speed.
• Convex relaxation using Sum of Squares (SOS) is a common but computationally intensive approach.

Purpose of the Study:

• To develop a significantly faster algorithm for solving the PnP problem.
• To introduce a novel, efficient, and parallelizable approximation method for PnP.

Main Methods:

• Leveraging the homogeneity of the PnP polynomial for a speedup.
• Utilizing Hilbert's theorem for a guaranteed, parallelizable approximation.

Main Results:

• Achieved a speed improvement of approximately 10x over state-of-the-art methods.
• Developed a fast, guaranteed, and easily parallelizable approximation algorithm for PnP.

Conclusions:

• The proposed methods offer substantial performance gains for PnP problem solving.
• These advancements have implications for real-time applications in robotics and augmented reality.