A Grassmannian Graph Approach to Affine Invariant Feature Matching

TL;DR

This paper introduces GrassGraph, a novel affine invariant feature matching method that uses Grassmannian representations and Laplace-Beltrami operator approximation to robustly match 2D and 3D features even in noisy and occluded scenarios.

Contribution

The paper presents a new Grassmannian graph framework that achieves affine invariance and robust feature matching through a two-stage process involving Grassmannian mapping and Laplace-Beltrami operator approximation.

Findings

Achieves state-of-the-art performance on extensive 2D and 3D datasets.

Robustly handles noise, outliers, and occlusions in feature matching.

Validated with over 440,000 experimental trials.

Abstract

In this work, we present a novel and practical approach to address one of the longstanding problems in computer vision: 2D and 3D affine invariant feature matching. Our Grassmannian Graph (GrassGraph) framework employs a two stage procedure that is capable of robustly recovering correspondences between two unorganized, affinely related feature (point) sets. The first stage maps the feature sets to an affine invariant Grassmannian representation, where the features are mapped into the same subspace. It turns out that coordinate representations extracted from the Grassmannian differ by an arbitrary orthonormal matrix. In the second stage, by approximating the Laplace-Beltrami operator (LBO) on these coordinates, this extra orthonormal factor is nullified, providing true affine-invariant coordinates which we then utilize to recover correspondences via simple nearest neighbor relations. The resulting GrassGraph algorithm is empirically shown to work well in non-ideal scenarios with noise, outliers, and occlusions. Our validation benchmarks use an unprecedented 440,000+ experimental trials performed on 2D and 3D datasets, with a variety of parameter settings and competing methods. State-of-the-art performance in the majority of these extensive evaluations confirm the utility of our method.