A concave optimization algorithm for matching partially overlapping point sets

Highlights：

• Our CVPR paper imposes regularization on transformation which causes the transformation solution close to the predefined value. To address this issue, we propose a new formulation targeted at 2D/3D similarity registration problems, where regularization on transformation is abandoned in favor of constraints on transformation. This results in an algorithm capable of handling unknown arbitrary similarity transformations.

• We conducted extensive experiments on 2D/3D synthetic and real data to test the performance ofthe proposed method. The experimental results demonstrate much better robustness of the proposed method over state-of-the-art methods.

摘要

•All the transformation parameters including those of translation are regularized in our CVPR paper, causing the method not able to handle un- known arbitrary translations. To address this issue, we show that under a mild condition, the objective function of RPM is strictly convex quadratic w.r.t. translation. Thus, translation can first be eliminated via minimization. Then, we only need to enforce regularization on the non-translational part of the transformation. This enables our algorithm to handle unknown arbitrary translations and more applicable to practical problems.•Our CVPR paper imposes regularization on transformation which causes the transformation solution close to the predefined value. To address this issue, we propose a new formulation targeted at 2D/3D similarity registration problems, where regularization on transformation is abandoned in favor of constraints on transformation. This results in an algorithm capable of handling unknown arbitrary similarity transformations.•We conducted extensive experiments on 2D/3D synthetic and real data to test the performance ofthe proposed method. The experimental results demonstrate much better robustness of the proposed method over state-of-the-art methods.