GMM-IKRS: Gaussian Mixture Models for Interpretable Keypoint Refinement and Scoring (2408.17149v1)

Abstract: The extraction of keypoints in images is at the basis of many computer vision applications, from localization to 3D reconstruction. Keypoints come with a score permitting to rank them according to their quality. While learned keypoints often exhibit better properties than handcrafted ones, their scores are not easily interpretable, making it virtually impossible to compare the quality of individual keypoints across methods. We propose a framework that can refine, and at the same time characterize with an interpretable score, the keypoints extracted by any method. Our approach leverages a modified robust Gaussian Mixture Model fit designed to both reject non-robust keypoints and refine the remaining ones. Our score comprises two components: one relates to the probability of extracting the same keypoint in an image captured from another viewpoint, the other relates to the localization accuracy of the keypoint. These two interpretable components permit a comparison of individual keypoints extracted across different methods. Through extensive experiments we demonstrate that, when applied to popular keypoint detectors, our framework consistently improves the repeatability of keypoints as well as their performance in homography and two/multiple-view pose recovery tasks.

• The paper introduces a framework that refines keypoints using Gaussian Mixture Models to enhance robustness and precision.
• It assigns two interpretable scores per keypoint: one for robustness against viewpoint changes and one for localization accuracy.
• The approach consistently improves keypoint repeatability and matching metrics across diverse datasets and detectors.

GMM-IKRS: Gaussian Mixture Models for Interpretable Keypoint Refinement and Scoring

The paper "GMM-IKRS: Gaussian Mixture Models for Interpretable Keypoint Refinement and Scoring" addresses a long-standing concern in computer vision: the quality and interpretability of image keypoints generated by various detectors. The authors propose GMM-IKRS, a novel framework that refines keypoints from any detection method while assigning them interpretable scores for robustness and localization accuracy.

Core Contributions

The contributions of the paper can be encapsulated as follows:

1. A novel framework for keypoint refinement:
   • The GMM-IKRS refines the positions of input keypoints by evaluating their quality through a robust Gaussian Mixture Model (GMM).
   • The framework is designed to work with any keypoint detector, making it broadly applicable in diverse computer vision applications.
2. Interpretable scoring mechanism:
   • The framework provides two scores for each refined keypoint: robustness, which represents the probability of rediscovering the same keypoint under varied viewpoints, and deviation, which quantifies the localization accuracy.
3. Robust GMM fitting:
   • A modification of the Expectation-Maximization (EM) algorithm ensures the GMM fitting process is robust to outliers, which are common in keypoint detections.

Methodology

The proposed method exploits affine transformations to account for potential viewpoint changes, generating multiple warped versions of the original image. The keypoints detected in these warped images are projected back to the original image, and a KDE is used for an initial density estimation, guiding the GMM fitting process.

The novelty of the approach lies in the robust GMM fit, which refines keypoints and assigns the two critical scores. The scores enable an objective comparison of keypoints across different detection methods, addressing the often opaque scoring mechanisms provided by various keypoint detectors.

Results

HPatches v-set Evaluation

The evaluation on the HPatches v-set, focused on scenes with viewpoint changes, demonstrates that GMM-IKRS consistently improves repeatability, mutual-nearest-neighbor repeatability, mean matching accuracy, matching score, and homography accuracy across different pixel thresholds. Notably:

• Harris keypoints saw improved repeatabilities when evaluated with the more robust Repeatability-MNN metric.
• For methods like DISK and SuperPoint, the refined keypoints provided substantial improvements in mean matching accuracy and homography accuracy auc.

Image Matching Benchmark

The framework's generalization capabilities were validated on the Image Matching Challenge (IMC) phototourism dataset. Here, GMM-IKRS showed improvements across metrics:

• Enhanced average accuracy (mAA) in stereo and multi-view 3D reconstruction tasks, suggesting that refined keypoints result in better pose estimations.
• The average number of inliers and the number of reconstructed 3D points also increased, showing the practical benefits of the refinement process.

Statistical Insights

One of the strengths of GMM-IKRS is its capability to provide deeper insights into the performance of various keypoint detectors. For instance, the robust and deviation distributions reveal nuanced behaviors of different methods.

• DoG, while obtaining high repeatability, showed a propensity for accurately localized but less robust keypoints.
• SuperPoint demonstrated its capacity to detect many robust keypoints, accounting for its significant performance gains in practical tasks.

Implications and Future Directions

The practical implications of GMM-IKRS are substantial for applications requiring robust and well-localized keypoints, such as SLAM, SfM, and 3D reconstruction. The framework's compatibility with any keypoint detector and its interpretable scoring system make it an excellent tool for analyzing and improving keypoint quality across diverse scenarios.

Future developments could explore leveraging GMM-IKRS for generating high-quality, sub-pixel accurate keypoints as ground truth in deep learning frameworks. This could open avenues for improving training pipelines in a teacher-student fashion, enhancing the performance of deep keypoint detectors.

In conclusion, GMM-IKRS represents a significant step towards refining and interpreting keypoints in a manner that enhances their utility across a broad range of computer vision tasks. The robust and interpretable nature of the framework provides a valuable tool for both academic research and practical applications in the field.