Review of Geometric Optimization Paper

write to review this paper

Summary:

The paper "Learning to Solve Hard Minimal Problems" by Petr Hruby and colleagues presents a novel approach for solving geometric optimization problems within the RANSAC framework. The primary focus is on hard minimal problems, which have many spurious solutions when relaxed from the original geometric optimization problem. The authors propose a strategy that combines optimized homotopy continuation (HC) with machine learning to avoid computing a large number of these spurious solutions. They demonstrate the effectiveness of their approach on two problems: the relative pose of three calibrated cameras (the “Scranton” problem) and the classic two-camera five-point problem. The paper showcases significant speed improvements and efficiency in solving these problems compared to existing methods.

Strengths:

1. Innovative Approach: The combination of HC with machine learning for selecting starting problem-solution pairs is novel and addresses the inefficiency of existing methods in handling spurious solutions.
2. Practical Efficiency: The method demonstrates significant speed improvements, solving problems like the Scranton case much faster than previously known methods.
3. General Applicability: The approach is not limited to specific problems but can be adapted to other hard minimal problems, indicating its potential for wide application in geometric optimization.

Weaknesses:

1. Dependence on Training Data: The machine learning model's effectiveness relies heavily on the training data. This could limit the model's generalizability to different types of problems or datasets.
2. Complexity in Implementation: The method appears to be complex in terms of implementation, involving multiple stages and dependencies on precise problem formulations and anchor selections.
3. Potential for Increased Failure Rates: While faster, the method might have higher failure rates compared to traditional complex HC methods, as indicated by the authors' acknowledgment of sacrificing success rate for speed.

Questions:

1. How does the method perform under varying noise levels in the data, and what is its robustness to outliers?
2. Can the approach be extended to problems beyond geometric optimization, such as in other fields where minimal problem formulations are prevalent?
3. What are the computational requirements for training the machine learning model, and how scalable is it for larger or more complex problems?

Recommendation:

Weak Reject. The paper introduces an innovative and potentially impactful approach to solving hard minimal problems. However, concerns about the model's dependence on specific training data, potential limitations in generalizability, and the trade-off between speed and success rate need to be addressed more comprehensively. Further research and refinement could strengthen the paper’s contribution to the field.