## 2 Materials and Methods
### Radiograph Quantification  
The BMD was quantified using the color pixel-counting (CPC) protocol [63]. Each sub-image was resized to 423 pixels wide by 536 pixels high to ensure the visibility of the entire calcaneus and a fragment of the proximal epiphysis of the second, third, and fourth metatarsal bones. Then, each sub-image was saved as a BMP file. If necessary, the background was manually masked using the HEX color #000000 in Paint.NET v.4.3.2 software, ensuring that the entire non-#000000 pixel area represented the tarsal joint. As a result, automatic segmentation was applied without the need for manual image segmentation. The entire tarsal joint was designated as the region of interest (ROI) for pixel counting. The CPC protocol was applied to the decomposed sub-images using the color histogram method from the extcolors package in Python ([[https://pypi.org/project/extcolors/](https://pypi.org/project/extcolors/)]([https://pypi.org/project/extcolors/](https://pypi.org/project/extcolors/)), accessed on 11 April 2024). Visual similarity was calculated using the CIE76 Formula (1) in the CIELAB color space, and based on this calculation, the colors were grouped. \[\Delta\text{E}^{*}=\surd((\Delta\text{L}^{*})+(\Delta\text{a}^{*})+(\Delta\text{b}^ {*})) \tag{1}\]  
The CIELAB color space, denoted as L*a*b*, comprises three components: L* represents the perceptual lightness, while a* and b* represent the colors of vision in the chromo \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Decomposition** & **S1** & **S2** & **S3** & **S4** & **S5** & **S6** & **S7** & **S8** & **S9** & **S10** \\ \hline Relative & \multirow{2}{*}{1009 \(\pm\) 163} & \multirow{2}{*}{1212 \(\pm\) 111} & \multirow{2}{*}{1407 \(\pm\) 98} & \multirow{2}{*}{1600 \(\pm\) 134} & \multirow{2}{*}{1804 \(\pm\) 112} & \multirow{2}{*}{2011 \(\pm\) 99} & \multirow{2}{*}{2204 \(\pm\) 107} & \multirow{2}{*}{2400 \(\pm\) 133} & \multirow{2}{*}{2607 \(\pm\) 129} & \multirow{2}{*}{2803 \(\pm\) 147} \\ density (HU) & & & & & & & & & & \\ Color & Yellow & Orange & Red & Light & Dark & Dark & & & & \\ HEX code & \#FFFF00 & \#E08000 & \#FF000 & \#E0800C0 & \#E080080 & \#0000 FF & \#080000 & \#808000 & \#00 FF00 & \#A6 CAF0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The values (mean \(\pm\)SD) of relative density measured for the ten steps of the density standard (S1–S10) with an assigned color and HEX code. Figure 2: Exemplary dorsopalmar view radiographs of the tarsal joint decomposited to ten sub-images related to the relative density of the ten steps (S1–S10) of the density standard. (**A**) S1 relative density masked in yellow, (**B**) S2 relative density masked in orange, (**C**) S3 relative density masked in red, (**D**) S4 relative density masked in light purple, (**E**) S5 relative density masked in dark purple, (**F**) S6 relative density masked in dark blue, (**G**) S7 relative density masked in dark green, (**H**) S8 relative density masked in navy green, (**I**) S9 relative density masked in light green, (**J**) S10 relative density masked in light blue, (**K**) S1–S10 relative density masked in white, (**L**) S1–S10 relative density masked in annotated colors with the density standard displayed. plane (red, green, blue, and yellow). A difference of approximately \(\Delta\)E* \(\approx\) 2.3 signifies detectable differences in colors [64]. The quantification results were presented as the number of pixels of each color within the non-#000000 ROI segmented on the sub-image. The total count of non-#000000 pixels was determined on the sub-image where the S1-S10 relative density was masked in white. This count was used for each sub-image to calculate the percentage of color-annotated pixels (%color pixels). The results were depicted as a list detailing the most frequently used colors in the sub-image, along with the corresponding number of pixels for each color.