In orthodontics, a patient is collected a lot of 3D oral cavity data, including oral cavity gypsum and scan data sets. To accurately measure the patient's tooth movement, this paper proposes a robust and precise isotropic scaling registration algorithm using bi-directional distance and correntropy. Firstly, because the oral cavity gypsum data sets have a lot of gypsum tumors and bubbles, which can cause the accuracy of registration results to decrease. Then, we introduce the correntropy into the traditional scaling registration model. Secondly, since unconstrained scaling registration is an ill-posed problem, bi-directional distance is used to enhance the robustness. In this way, a registration model using bi-directional distance and correntropy is established. In order to solve this problem, this paper proposes a new registration algorithm with iterative closest point. Moreover, the convergence of the algorithm is proved theoretically. Finally, the proposed algorithm is tested on the orthodontic database, and our experimental results demonstrate that our algorithm performs robust and high accuracy.

在正畸学中，患者会收集很多3D口腔数据，包括口腔石膏和扫描数据集。为了准确地测量患者的牙齿运动，本文提出了一种使用双向距离和熵的鲁棒且精确的各向同性缩放配准算法。首先，由于口腔石膏数据集具有大量的石膏肿瘤和气泡，这可能导致配准结果的准确性降低。然后，将熵引入到传统的缩放配准模型中。其次，由于不受约束的缩放配准是不适的问题，因此双向距离用于增强鲁棒性。以这种方式，建立了使用双向距离和熵的配准模型。为了解决这个问题，提出了一种新的具有迭代最近点的配准算法。此外，从理论上证明了该算法的收敛性。最后，在正畸数据库上对该算法进行了测试，实验结果表明该算法具有鲁棒性和较高的准确性。