Good Keypoints for the Two-View Geometry Estimation Problem (2503.18767v2)

Abstract: Local features are essential to many modern downstream applications. Therefore, it is of interest to determine the properties of local features that contribute to the downstream performance for a better design of feature detectors and descriptors. In our work, we propose a new theoretical model for scoring feature points (keypoints) in the context of the two-view geometry estimation problem. The model determines two properties that a good keypoint for solving the homography estimation problem should have: be repeatable and have a small expected measurement error. This result provides key insights into why maximizing the number of correspondences doesn't always lead to better homography estimation accuracy. We use the developed model to design a method that detects keypoints that benefit the homography estimation and introduce the Bounded NeSS-ST (BoNeSS-ST) keypoint detector. The novelty of BoNeSS-ST comes from strong theoretical foundations, a more accurate keypoint scoring due to subpixel refinement and a cost designed for superior robustness to low saliency keypoints. As a result, BoNeSS-ST outperforms prior self-supervised local feature detectors on the planar homography estimation task and is on par with them on the epipolar geometry estimation task.

Analysis of Keypoints for Two-View Geometry Estimation

The study presented in "Good Keypoints for the Two-View Geometry Estimation Problem" reveals critical insights into the properties of keypoints that are beneficial for solving the two-view geometry estimation problem, particularly homography estimation. The investigation revolves around identifying key characteristics of local features which significantly impact downstream applications such as Structure-from-Motion (SfM) and visual SLAM (vSLAM) systems.

Theoretical Contributions

The authors introduce a theoretical model to score feature points (keypoints) in the context of homography estimation. The model emphasizes two primary characteristics for effective keypoints: repeatability and minimization of the expected measurement error (EME). These criteria define the reliability and precision of the correspondences formed between feature points across images, thereby influencing the accuracy of homography estimation. The study challenges conventional metrics, demonstrating why maximizing the number of correspondences does not necessarily lead to improved estimation precision.

Methodology: BoNeSS-ST Keypoint Detector

The study presents the BoNeSS-ST keypoint detector, improving upon prior detectors through several novel features:

1. Strong Theoretical Foundation: The detector leverages substantial theoretical underpinnings, grounded in the study's model for scoring keypoints based on repeatability and EME, facilitating enhanced selection of feature points for geometry estimation.
2. Subpixel Refinement: This refinement technique allows for more precise scoring of keypoints, optimizing their positional accuracy and reducing the measurement error.
3. High Robustness to Low Saliency Keypoints: The detector employs a cost mechanism designed to mitigate the impact of low salience feature points, thereby improving robustness and keypoint selection quality.

Numerical Results and Experimental Validation

BoNeSS-ST is experimentally validated across several benchmarks, including planar homography and epipolar geometry estimation tasks on datasets such as HEB, IMC-PT, MegaDepth, and ScanNet. The detector demonstrates superior performance over prior self-supervised detectors, establishing new standards in self-supervised keypoint detection. Notably, BoNeSS-ST maintains higher relative pose accuracy, robust performance across various environments, and greater downstream task applicability than competitive methods.

Implications and Future Directions

The research emphasizes that maximizing the number of keypoint correspondences does not inherently correlate with improved estimation accuracy. Instead, the focus should be on optimizing for properties like repeatability and EME. This rethinking of conventional metrics holds substantial potential for enhancing visual SLAM systems and SfM. Future explorations could extend this analysis to different types of geometry estimation challenges, potentially integrating more advanced learning mechanisms to further refine detector accuracy.

Conclusion

This paper contributes significantly to understanding the intrinsic properties of keypoints that facilitate effective two-view geometry estimations. The advancements instilled by BoNeSS-ST illustrate a crucial aspect of feature detection technology—balancing the quantity and quality of keypoints. Such insights could catalyze notable progress in fields relying on image-based correspondences, from robotics to augmented reality systems.