Differentiable Collision-Supervised Tooth Arrangement Network with a Decoupling Perspective

TL;DR

A differentiable collision-supervised tooth arrangement network, decoupling predicting tasks and feature modeling, and a novel differentiable collision loss function for point cloud data to constrain the related gestures between teeth, which can be easily extended to other 3D point cloud tasks.

Abstract

Tooth arrangement is an essential step in the digital orthodontic planning process. Existing learning-based methods use hidden teeth features to directly regress teeth motions, which couples target pose perception and motion regression. It could lead to poor perceptions of three-dimensional transformation. They also ignore the possible overlaps or gaps between teeth of predicted dentition, which is generally unacceptable. Therefore, we propose DTAN, a differentiable collision-supervised tooth arrangement network, decoupling predicting tasks and feature modeling. DTAN decouples the tooth arrangement task by first predicting the hidden features of the final teeth poses and then using them to assist in regressing the motions between the beginning and target teeth. To learn the hidden features better, DTAN also decouples the teeth-hidden features into geometric and positional features, which are further supervised by feature consistency constraints. Furthermore, we propose a novel differentiable collision loss function for point cloud data to constrain the related gestures between teeth, which can be easily extended to other 3D point cloud tasks. We propose an arch-width guided tooth arrangement network, named C-DTAN, to make the results controllable. We construct three different tooth arrangement datasets and achieve drastically improved performance on accuracy and speed compared with existing methods.

Figures (13)

• Figure 1: Comparisons on different paradigms of previous arrangement methods and ours.
• Figure 2: Comparison of the errors between our method and others. The abscissa represents the threshold of the mean pointwise distance (mm), and the lines depict the accuracy of each method under this threshold. "Reg" indicates that we use the location features extracted from the ground truth as $\bm F^*$ to assist the network in transform parameter regression, resulting in almost no error.
• Figure 3: Input teeth meshes and corresponding teeth labels. The first digit indicates the quadrant where the teeth are located. The second digit indicates the classes of teeth: 1-2 for incisors, 3 for cuspids, 4-5 for bicuspids, and 6-7 for molars.
• Figure 4: Overview of DTAN. We use a three-phase network to generate the transformation parameters of our arrangement. The first phase contains one global encoder and two local encoders to extract global features, local geometric features, and local positional features. The second phase propagates teeth features and then projects them to hidden features of target dentition. Then, the third phase integrates features and generates transformation parameters. At last, the parameters are applied to the original input for the final dentition result.
• Figure 5: Overview of the Feature consistency supervision. $\bm{P^*}$ represents the point cloud of neat teeth from ground truth, and $\hat{\bm{P^*}}$ represents rearranged $\bm{P^*}$ with different categories.