Revised spectral matching algorithm for scenes with mutually inconsistent local transformations

Spectral matching (SM) is an efficient and effective greedy algorithm for solving the graph matching problem in feature correspondence in computer vision and graphics. However, the classic SM algorithm cannot extract correspondences well when the affinity matrix is sparse and reducible (i.e. its corresponding graph is not connected). This case often happens when the geometric deformations consist of transformations with local inconsistency. The authors analyse this problem and show how the original SM could fail in this scenario. Then, the authors propose a revised two-step pipeline to tackle this issue: (1) decompose the mutually inconsistent local deformations into several consistent transformations which can be solved by individual SM; (2) filter out incorrect correspondences through an automatic thresholding. The authors perform experiments to demonstrate that this modification can effectively handle the coarse correspondence computation in shape or image registration where the global transformation consists of multiple inconsistent local transformations.