Minimal Solvers for Rectifying From Radially-Distorted Conjugate Translations

Area of Science:

• Computer Vision
• Geometric Computer Vision
• Robotics

Background:

• Lens distortion and scene rectification are crucial in computer vision.
• Existing methods often require complex computations or multiple feature correspondences.
• Man-made environments frequently exhibit coplanar translated and reflected scene textures.

Purpose of the Study:

• To develop minimal solvers for joint radial lens undistortion and affine rectification.
• To utilize local features from coplanar textures for efficient geometric correction.
• To improve robustness and speed compared to state-of-the-art methods.

Main Methods:

• Employing algebraic geometry techniques for solver formulation.
• Developing solvers that accommodate various local features and sampling strategies.
• Proposing variants requiring only a single feature correspondence.

Main Results:

• Solvers are computationally efficient, stable, and small.
• Demonstrated superior robustness to noise in synthetic and real-world experiments.
• Achieved accurate rectification of imaged scene planes from challenging imagery.

Conclusions:

• The proposed minimal solvers offer a significant advancement in lens undistortion and affine rectification.
• The solvers are effective for rectifying textured planes, even with challenging wide-field-of-view lenses.
• Integration into an automated system highlights practical applicability in computer vision tasks.