Calibration by correlation using metric embedding from nonmetric similarities.

Area of Science:

• Computer Vision
• Geometric Methods
• Machine Learning

Background:

• Traditional camera calibration requires specific patterns or known scene geometry.
• Existing methods for intrinsic calibration from motion are limited in scope and robustness.
• Analyzing pixel correlations during random camera motion offers a new avenue for calibration.

Purpose of the Study:

• To develop a new intrinsic calibration method for generic single-view cameras using only random motion.
• To formalize camera calibration as a metric embedding problem from non-metric measurements.
• To analyze the observability and provide a generic solution for reconstructing camera geometry from pixel correlations.

Main Methods:

• Computing pairwise time correlation of luminance signals for pixels from video sequences.
• Formulating calibration as a generalization of multidimensional scaling (MDS).
• Analyzing observability based on local geometric (curvature) and global topological (connectedness) properties of the manifold.

Main Results:

• Demonstrated that on a sphere, scale can be recovered, enabling metrically accurate solutions from non-metric data.
• Developed a robust algorithm that recovers metrically accurate solutions when metric information is observable.
• Achieved calibration results comparable to classical methods for pin-hole, fish-eye, and omnidirectional cameras.

Conclusions:

• The proposed method provides a robust and generic intrinsic camera calibration technique.
• The approach successfully addresses the challenges of observability and generic solutions in metric embedding for camera calibration.
• This method offers a practical alternative for calibrating various camera types with simple random motion.