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Analysis of algebraic and geometric distances for projective transformation estimation

Estimation of projective transformations is an essential process in modern vision-based applications. Usually, the provided experimental point correspondences required to estimate the projective transformations are corrupted with random noise. Thus, for an accurate estimation of the actual projective transformation, a robust optimization criterion must be employed. In this work, we analyze a two-step estimation approach for robust projective transformation estimation. First, the algebraic distance is employed to obtain an initial guess. Then, the geometric distance is used to refine this initial guess. Three geometric-based refining methods are evaluated, namely, the one-image error, the symmetric-transfer error, and reprojection. The obtained results confirm a high accuracy and robustness of the analyzed approach.