Logistic regression of point matches for accurate transformation estimation

Feature extraction and matching (FEM) has been widely used for the registration of partially overlapping 3D shapes. Due to various factors such as imaging noise, simple geometry, or clutter, it usually introduces false positive ones. To reliably estimate the underlying transformation that brings one partial shape into the best possible alignment with another, it is critical to estimate the extent to which the established point matches are correct. To this end, we propose to use the logit function for the regression of the errors of these point matches. The novel method includes three steps: (i) normalization of the errors of the point matches, (ii) logistic regression of the point matches for the estimation of their reliabilities/weights, and (iii) estimation of the underlying transformation in the weighted least squares sense. These steps are repeated until either the maximum number of iterations has been reached or the weighted average of the errors of the point matches has been below the scanning resolution. A comparative study using real data captured by different range sensors shows that the proposed method outperforms two state-of-the-art ones for more accurate estimation of the underlying transformation.