# Robust Segmentation of Partial and Imperfect Dental Arches
## 1 Introduction  
In North America, dental clinics handle millions of dental reconstructions annually. The intricacies and irregularities in teeth alignment pose a daunting challenge for manually segmenting optical scans, typically consuming an average of 45 min to complete [1]. Moreover, due to occlusion, digital scans often contain partially missing data. Types of imperfections may entail partial arches, missing teeth, presence of preparations, and noise. According to the statistics of an in-house clinical dataset acquired with the help of a collaborating dental laboratory, the percentage of full arches was less than 17% among upper arches and less than 20% among lower arches. The presence of imperfections hinders the correct segmentation of dental arches. The use of machine learning algorithms in digital dentistry has significantly increased during the past few years [2; 3; 4]. A recent review on tooth segmentation from CBCT images reported issues related to the low amount of available dental data and non-uniformity of evaluation metrics [5]. The same challenges exist in segmentation of teeth from 3D surface scans. Moreover, to the best of the authors' knowledge, published research on dental arch segmentation from 3D surface scans focused on full or perfect arch segmentation such as MeshSegNet [6; 7], Dental Arch Prior-assisted 3D Tooth Instance Segmentation (DArch) [8], dynamic graph convolutional neural network (DGCNN) [3], and tooth segmentation using generative adversarial networks [9]. Therefore, it is important to develop an automatic, generic, and accurate framework capable of efficiently segmenting dental arches with imperfections. In this work, we mainly focus on four main types of imperfections in dental arches, which are classified as follows according to increasing level of difficulty:  
1. Partial arch with less than eight teeth without preparation. This scenario is challenging from a registration point of view because the scan is short and does not always form a curved arch. 2. Partial arch with a preparation. The preparation needs to be segmented accurately because it is required for the dental crown design. 3. Partial arch with only missing tooth with or without space. The most difficult situation is an arch with a missing tooth without space. 4. Partial arch with a preparation and a missing tooth. This is the most challenging situation because it combines Scenarios 2 and 3. Segmentation of 3D dental arches is a fundamental task for various computer-aided dental treatments, in particular dental crowns [3]. In the context of dental crown restoration, we distinguish between master and antagonist arches. The master arch usually contains a prepared tooth, centered between two adjacent teeth, to receive a crown treatment. The antagonist arch opposes the master arch and provides occlusal constraints for the designed crown. Because the antagonist arch does not usually possess a preparation, its segmentation framework could be different than the master arch. In this work, we aim to propose an end-to-end framework for tooth segmentation that could be utilized for a variety of dental treatments including dental crown design. Our main contributions are as follows:  
* A dental arch segmentation framework is designed and implemented to integrate customized trained models which demonstrate robust, scalable, and efficient performance on new data. The model is deployed at [[https://app.intellidentia.com](https://app.intellidentia.com)]([https://app.intellidentia.com](https://app.intellidentia.com)). Different published deep learning models could be integrated in the segmentation framework based on the selection of the user. * A new registration method is applied to bring perfect and imperfect arches in a unified and consistent coordinate system. Most of partial arches do not have an arch shape but rather a rectangular one. This misguides the registration during the lingual/buccal identification. Inspired by this observation, we add a set of three-class models for gingiva cleaning to enhance the registration.