A Minimal Solution to Radial Distortion Autocalibration.

Area of Science:

• Computer Vision
• Geometric Modeling
• Robotics

Background:

• Estimating camera pose and geometry is crucial for 3D reconstruction.
• Minimal solvers for radial distortion and epipolar geometry typically require nine point correspondences.
• Existing methods face challenges with computational efficiency and robustness.

Purpose of the Study:

• To develop novel minimal solvers for simultaneous estimation of radial distortion and epipolar geometry.
• To reduce the number of required point correspondences from nine to eight.
• To provide efficient and robust solutions using algebraic geometry techniques.

Main Methods:

• Formulating the problem as a system of algebraic equations derived from eight point correspondences.
• Enforcing the determinant of the fundamental matrix to be zero.
• Solving the simplified system using Gröbner basis and polynomial eigenvalue computation.

Main Results:

• Two novel algorithms for estimating radial distortion and epipolar geometry from eight points were developed.
• The methods successfully reduce the correspondence requirement compared to prior work.
• Experimental results on synthetic and real data demonstrate efficiency, robustness, and practicality.

Conclusions:

• The proposed methods offer a more efficient and practical approach to estimating radial distortion and epipolar geometry.
• Reducing the number of correspondences enhances the applicability of these techniques in real-world scenarios.
• The Gröbner basis and polynomial eigenvalue methods provide reliable solutions for computer vision tasks.