## 2 Materials and Methods
### Radiograph Processing  
In the CDA method, for each acquired radiograph, the density standard was positioned perpendicular to the surface of a radiographic cassette. The aluminum-produced density standard (92.71-98.92 Atom% of aluminum) is detailed in [PERSON] et al. (2018). The density standard was shaped like an irregular cuboid with 10 steps (S1-S10) decreasing in height. The height, volume, metal density, and radiological relative density measured in Hounsfield units (HUs) are known and are described in detail in [PERSON] et al. (2018). Each radiograph included the imaged area of the tarsal joint and the density standard. The radiographs were acquired using DxWorks software ([[https://advanced-inst.com/dxworks-2/](https://advanced-inst.com/dxworks-2/)]([https://advanced-inst.com/dxworks-2/](https://advanced-inst.com/dxworks-2/))) (Viewworks Co., Ltd., Seoul, Republic of Korea) as DICOM files.  
Materialise's Interactive Medical Image Control System (MIMICS) software version 14.0 (Materialise HQ, Leuven, Belgium) was used to analyze the attenuation of the X-ray beam passing through the density standard and tarsal joint. The mean relative density of each step (S1-S10) was identified and expressed in HUs (Table 3). Subsequently, each dorsopalmar radiograph was decomposed by masking each relative density range with an assigned color, resulting in ten sub-images, as illustrated in Figure 2. Additionally, the pixels representing the relative density of all steps were masked in white (HEX #FFFFF) in a separate sub-image to calculate the total number of pixels for a particular radiograph, while the next sub-image displayed all the annotated color pixels. In each sub-image, the corresponding relative density was masked with the appropriate color.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Grade** & **Severity** & **Radiographic Signs** \\ \hline
0 & Normal & Normal width and shape of the joint space; smooth cortical bone surface; normal subchondral bone pattern; no periosteal proliferation; no intra-articular mineralization \\ \hline
1 & Mild & Narrow and irregular joint space with osteophytes; irregular cortical bone surface with well-defined protuberance; smooth subchondral bone pattern; flat periosteal proliferation; mild intra-articular mineralization \\ \hline
2 & Moderate & Narrow and irregular joint space with multiple osteophytes, enthesiophytes, and marked asymmetry; irregular cortical bone surface with well-defined bone proliferation; subchondral bone cyst; flat periosteal proliferation; moderate intra-articular mineralization \\ \hline
3 & Severe & Completely narrow joint space with large osteophytes and enthesiophytes; severe deformation of cortical bone surface; subchondral bone sclerosis; flat or intense periosteal proliferation; severe intra-articular mineralization \\ \hline \hline \end{tabular}
\end{table}
Table 2: The scale used for grading the radiographic signs of tarsal joint osteoarthritis (OA) summarized based on the descriptions of previously published radiographic signs (2018, 2019, 2020, 2021).  
Figure 1: Exemplary dorsopalmar radiographs of the equine tarsal joint and density standard scored as (**A**) normal, (**B**) mild OA, (**C**) moderate OA, and (**D**) severe OA.