Learning Probabilistic Coordinate Fields for Robust Correspondences.

Area of Science:

• Computer Vision
• Geometric Deep Learning
• Machine Learning

Background:

• Traditional coordinate systems lack geometric invariance for image correspondence.
• Existing methods struggle with affine transformations and quantifying coordinate reliability.

Purpose of the Study:

• Introduce Probabilistic Coordinate Fields (PCFs) for geometrically invariant image coordinate representation.
• Develop PCF-Net, a probabilistic network to learn coordinate confidence for robust image correspondence.
• Demonstrate PCF-Net's versatility as a plug-in for various computer vision tasks.

Main Methods:

• PCFs encode coordinates using correspondence-specific barycentric coordinate systems (BCS) with affine invariance.
• PCF-Net parameterizes coordinate fields as Gaussian mixture models, jointly optimizing fields and confidence.
• Confidence maps quantify the reliability of PCFs, leveraging dense flow information.

Main Results:

• Learned confidence maps exhibit geometric coherence and semantic consistency, enabling robust coordinate representation.
• PCF-Net achieves state-of-the-art performance in sparse feature matching, dense image registration, and camera pose estimation.
• The confidence map facilitates novel applications like texture transfer and multi-homography classification.

Conclusions:

• Probabilistic Coordinate Fields provide a powerful, geometrically invariant representation for image correspondence.
• PCF-Net effectively quantifies coordinate reliability, improving performance across diverse computer vision challenges.
• The interpretable confidence maps offer new avenues for advanced image analysis and manipulation.