Proof Sketch: Let ( R ) be a rotation of image A by ( \phi ). Then ( \theta_A,i \rightarrow \theta_A,i + \phi ). Similarly, if the same rotation is applied to image B, ( \theta_B,i \rightarrow \theta_B,i + \phi ). The difference ( \theta_B,i - \theta_B,j ) remains unchanged, and ( |\theta_A,i - \theta_A,j - (\theta_B,i - \theta_B,j)| ) is invariant. Radial distances are unchanged.
Intuition: If two matches are geometrically consistent under a similarity transform, their relative polar angles should be preserved up to a global rotation. For match ( m_i ), compute its support as: [ \textvote(i) = \sum_j \neq i S(i,j) \cdot w_ij ] where ( w_ij = \exp(-\lambda \cdot |d_i - d_j|) ) is a descriptor confidence weight. This gives higher influence to neighboring matches with similar descriptor distances. 3.5 Final Classification A match is classified as an inlier if: [ \textvote(i) > \alpha \cdot \textmedian(\textvote) ] where ( \alpha ) is a hyperparameter (default 1.5). Optionally, we apply a non-maximum suppression in polar-angle space to avoid duplicate voting from dense keypoints. 4. Theoretical Analysis Proposition 1 (Rotation Invariance). The CDV score ( S(i,j) ) is invariant to global rotation applied to both images simultaneously. Proof Sketch: Let ( R ) be a rotation of image A by ( \phi )
*GPU time reported, not directly comparable. The difference ( \theta_B,i - \theta_B,j ) remains
Abstract Feature matching is a cornerstone of many computer vision tasks, including Structure from Motion (SfM), visual SLAM, and image stitching. Traditional approaches relying on nearest-neighbor descriptor matching often fail in wide-baseline scenarios, repetitive textures, or under significant viewpoint changes due to ambiguous correspondences. This paper introduces PACDV (Polar-Angular Complementary Directional Voting) , a novel geometric verification and correspondence filtering framework that integrates polar coordinate encoding with angular directional consensus. Unlike existing methods such as GMS (Grid-based Motion Statistics) or RANSAC-based filters, PACDV operates in a joint polar-angular space, capturing both radial and rotational constraints simultaneously. We demonstrate that PACDV achieves superior recall and precision on the HPatches and YFCC100M datasets, especially under large rotation and scale changes. The proposed method is lightweight, parallelizable, and can be integrated as a plug-in module into existing feature matching pipelines. 1. Introduction Local feature matching is typically performed in three stages: (i) keypoint detection and description (e.g., SIFT, SuperPoint), (ii) brute-force or approximate nearest-neighbor matching based on descriptor distance, and (iii) geometric verification using RANSAC with an underlying transformation model (e.g., homography, fundamental matrix). The third stage is critical but often computationally expensive and unstable when inlier ratios are low. For match ( m_i ), compute its support