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