## 2 Materials and Methods
### Second Part: Comparative Analysis for the Automated System Validation  
This second part of the study focused on validating the automated FHC/DAE system through a comparative analysis with expert examiners. A total of 70 VDHE radiographs from dogs (140 hip joints) were selected from the Veterinary Hospital of UTAD and the Danish Kennel Club databases. These radiographs were acquired for CHD screening between 2010 and 2024, and each dog's age, breed, and sex were recorded. To ensure a diverse and representative sample covering all degrees of CHD, images for the second part of the study were selected based on the NA values of the hip joints. From a previously annotated dataset of 1150 VDHE radiographs, approximately equal numbers of images were chosen for five predefined NA categories: values of 105\({}^{\circ}\) or more, around 105\({}^{\circ}\), around 100\({}^{\circ}\), around or greater than 90\({}^{\circ}\), and below 90\({}^{\circ}\). This approach yielded a balanced dataset reflecting a broad spectrum of hip joint conformations. In this part of the study, FHC/DAE measurements were performed on the selected 140 hip joints using DICOM format images. The analyses were conducted independently by two experienced examiners, P.F.-G. (Examiner 1, E1) and M.G. (Examiner 2, E2). Following the training phase, the system was used to generate FHC/DAE measurements for the same 140 hip joints. Measurements obtained from the two examiners and the system were then compared to assess reproducibility, both between examiners and between examiners and the system. Figure 6: Illustration of the application of the algorithm for calculating the horizontal distance between the femoral head center (FHC) and the nearest intersection point on the acetabular contour on a VDHE radiographic image. Each plot demonstrates the identified contour points (blue), the calculated center point (red), and the horizontal distance (\(-\)3.18 mm) to the intersection (green dashed line). The FHC/DAE metric reflects the positional relationship (in millimeters) between the FHC and the DAE. According to [PERSON]'s CHD point-system protocol, positive FHC/DAE values indicate that the FHC is positioned medially relative to the DAE, while negative values denote a lateral position. In clinical terms, negative values correspond to reduced acetabular coverage, whereas positive values suggest improved coverage and joint congruity. A value of 0 signifies perfect superimposition between the FHC and DAE. For the purposes of this study, and to ensure clinical relevance and comparability, FHC/DAE measurements in this study were categorized according to [PERSON]'s protocol into six relationship-based groups: medial+ (\(>\)2 mm), medial (\(\leq\)2 to 1 mm), superimposed (\(<\)1 to \(-\)1 mm), lateral (\(<\)\(-\)1 to \(-\)5 mm), lateral+ (\(-\)6 to \(-\)10 mm), and luxation (\(<\)\(-\)10 mm) [3]. Values between the lateral and lateral+ categories were rounded to the nearest integer. As performed by the examiners, the FHC/DAE metric was manually determined through a two-step process using the Dys4 Vet image analysis software. First, the FHC was determined by drawing a circle encompassing the femoral head to locate its center. Then, a horizontal line, roughly parallel to the image width, was drawn to measure the distance between the FCH and the DAE (Figure 7). Statistical Analysis was performed using the SPSS software (SPSS Statistics for Windows 128 Version 27.0: IBM Corp., Armonk, NY, USA). A \(p\)-value of \(<\)0.05 was considered statistically significant. The Central Limit Theorem was adopted, which stipulates that for sufficiently large sample sizes (\(n>30\)), the distribution tends to be normally distributed, regardless of the original distribution of the variable in the population; therefore, parametric tests for data analysis were used [26]. In this study, weighted kappa was used to assess the agreement between FHC/DAE classifications made by the two examiners and between the examiners and the automated FHC/DAE system.