Learning to Solve Hard Minimal Problems.

Area of Science:

• Computer Vision
• Geometric Optimization
• Robotics

Background:

• Geometric optimization problems are fundamental in computer vision and robotics.
• The Random Sample Consensus (RANSAC) framework is widely used but can be computationally intensive for complex problems.
• Minimal problem relaxations in RANSAC can generate numerous spurious solutions, hindering efficiency.

Purpose of the Study:

• To develop an efficient approach for solving hard geometric optimization problems within the RANSAC framework.
• To avoid the computation of a large number of spurious solutions.
• To create a learning strategy for selecting effective initial problem-solution pairs for numerical continuation.

Main Methods:

• Developed a learning strategy to select a starting problem-solution pair.
• Employed numerical continuation to reach the desired problem and solution.
• Implemented a RANSAC solver for relative pose estimation of three calibrated cameras using a minimal four-point relaxation.
• Benchmarked performance on the relative pose estimation of two calibrated cameras using a minimal five-point case.

Main Results:

• The proposed approach effectively avoids computing large numbers of spurious solutions.
• The RANSAC solver for three calibrated cameras achieves an average solution time of under 70 microseconds.
• The method demonstrates efficiency and provides insights into engineering choices for geometric optimization.

Conclusions:

• The novel learning strategy significantly enhances the efficiency of solving hard geometric optimization problems in RANSAC.
• The approach offers a practical and fast solution for relative pose estimation tasks.
• This method has the potential to improve real-time performance in various computer vision and robotics applications.