## 2 Materials and Methods  
The panoramic radiographs we analyzed were retrospectively selected from a private radiological center (Centro de Radiologia Principe, Vigo, Spain). Patients with fully erupted mandibular dentition (18 teeth) or without wisdom teeth (16 teeth) were included. The participants were patients who regularly visited the dental clinic for treatment and previously had panoramic radiographs taken, and they consented to the use of their image data in the study. All image data were anonymized prior to analysis. In total, 383 panoramic radiographs were included: 94 for training and technical validation and 289 for posterior clinical validation. All radiographs were taken using a standard technique (70 Kvp, 15 mA, patient in analog position, and 10 seg). The study was approved by the Santiago-LugoResearch Ethics Committee with registration code 2017/121. Radiographs were acquired using a CS 8100 device (SN EBXG197; Carestream Health Inc., Noisy-le-Grand, France). Panoramic Dental Application (PDApp) is a desktop tool that runs on a general-purpose computer under the Linux and Windows operating systems. It was written in the C++ programming language using the GIMP Tool Kit (GTK+) library ([[https://www.gtk.org/](https://www.gtk.org/)]([https://www.gtk.org/](https://www.gtk.org/)) (accessed on 16 February 2023)) to develop the GUI. Figure 1 shows the GUI of PDApp with a typical radiological image loaded, processed, and reviewed by a dental expert and with the lateral panel displayed. PDApp is a modular and extensible application composed of three layers:  
1. The GUI layer, which facilitates user interaction through editing tools, including modules to draw and manage objects, set preferences, or interact with the software. 2. The logic application layer, which contains modules to measure distances and angles, predict the third molar potential, train the classifier, and calculate the statistical results. 3. The persistence layer, which stores all the data needed and calculated by the software, including modules to save the image overlays and the statistical results. The image overlays, which contain analyses supervised by experts, are stored in the popular Extensible Markup Language (XML) text format. The statistical results, calculated from the overlays, are stored in the comma-separated values (CSV) text format, which is portable and allows import from other spreadsheet software for further use. Figure 2 shows a flowchart with the main functionality of PDApp, which is accessible from its GUI. A typical working session for a user should include the following actions:  
Figure 1: Screenshot of PDApp v.1 software with analysis of typical panoramic radiograph and lateral panel open. In the right molar, the pink line represents third molar diameter, the yellow line represents retromolar space, and blue lines represent the angle. Measurement of the left molar (violet objects) are shown in the lateral panel. 1. Open a radiological image. 2. Manually draw the retromolar space, the third molar diameter, and the angle for each third molar. 3. Automatically measure the distances and angles. 4. Automatically classify the third molars. 5. Refer to expert's supervision, as described below. 6. Save the overlays drawn on the image into an XML file. 7. Export the statistical measurements to a CSV file. 8. At any time, the user can select an optional functionality: set preferences, save joined results of a set of patients, or train the classifier. Once the image is loaded, the user must manually draw the retromolar space, the third molar diameter, and the angle using the editing tools. Next, the classifier can be run in order to label each third molar as erupted or non-erupted/retained. As mentioned in Section 1, our previous studies [20; 21], and other published research [22], the retromolar space, third molar diameter, and third molar angulation are the key parameters in predicting third molar eruption/retention.