Using diagonals of orthogonal projection matrices for affine invariant contour matching

An efficient and rigorous algorithm is proposed for contour matching invariant to the full set of affine transformations. The algorithm is based on an invariant theory of orthogonal projection matrices derived from configuration matrices of point sets. Diagonals of the orthogonal projection matrices (DOPM) are used as contour descriptors and affinity measures are deduced to act as criteria for contour matching. Perturbation analysis is performed using the theory of polar decomposition, resulting in quantitative perturbation bounds for the affine-invariant descriptors and the affinity measures. A useful schema of outlier removal based upon the monotonic property of contour correspondence is also embedded in the algorithm. Experiments for synthetic and real-world data are provided to test the algorithm and compare it with the state-of-the-art methods, validating that the algorithm is fast, robust and able to match partial contours with occlusions and outliers under affine or more complex transformations.

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► Contour descriptors are invariant to affine and applicable under other transformations
► Quantitative perturbation bounds are proved for contour descriptors and affinity measures
► Algorithm is robust for the matching of partial contours under occlusions and outliers