Sensitivity Analysis in Translation Averaging

Area of Science:

• Computer Vision
• Robotics
• Geometric Deep Learning

Background:

• Translation averaging is crucial for determining absolute camera positions from relative directions.
• Existing research primarily addresses outlier robustness and solution uniqueness.
• Input uncertainty poses a significant challenge to the reliability of translation averaging.

Purpose of the Study:

• To analyze and quantify sensitivity in translation averaging due to input uncertainty.
• To develop a metric for assessing the conditioning (reliability) of translation averaging problems.
• To propose an efficient algorithm for improving the conditioning and reducing errors.

Main Methods:

• Sensitivity analysis of camera translation estimation.
• Definition and analysis of the conditioning of the translation averaging problem.
• Development of a criterion for well-conditioned problems and an algorithm for ill-conditioned data removal.

Main Results:

• Established a method to analyze sensitivity in translation averaging.
• Defined a conditioning metric to assess the reliability of estimated translations.
• Presented an efficient algorithm that identifies and removes problematic directional combinations, improving conditioning and reducing absolute translation errors.

Conclusions:

• Input uncertainty significantly impacts translation averaging accuracy.
• The proposed conditioning metric and algorithm effectively improve the reliability of translation estimation.
• This work offers a novel approach to enhance the robustness of camera pose estimation.