## 3 Methodology of Reconstructing the 3D Foot Shape
### Segmentation Foot Image
#### 3.5.1 Dataset for Training  
The CAESAR 3D human model dataset [39] presented in the analysis is unsuitable, because its data are artificially generated, missing the necessary measurements, textures, and extraneous objects usually found in actual photographs. This may affect the accuracy of the segmentation model in real conditions. Therefore, it was decided to create our dataset.  
As a training dataset, we decided to use 1200 feet images. The resolution of each image was 1920 \(\times\) 1080 (pixels). The sample contained 50% female and 50% male feet, with a total of 40 people involved. The dataset contained 600 images of female and male feet (300 of left and 300 of right foot). All participants of the experiments signed informed consent. All personal data were anonymized for research.  
Table 1 summarizes the information, including the minima (min), maxima (max), means (avg), and standard deviations for both feet for each of the dimensions.  
In the process of forming the dataset for NN training, an instruction to follow was given to all volunteers. The instruction is described in \"Dataset formation\" in Section 3.1. Since the methodology is aimed at practical use, data heterogeneity is one of the key factors that positively affect the quality of reconstruction based on real data. Here, the heterogeneity of the data was derived from the different genders of the volunteers: the length of their feet varied from 228 to 321 mm, and the hair cover of the foot varied for each participant. In addition, due to the home environment of video recording, the background and light for each video were unique.  
Each of the participants videotaped their feet at home. This fact allowed us to collect images from different backgrounds. Additionally, it affects the variability of the model under other conditions. Another reason to use video is the condition of the high complexity of determining the optimal number of photos and angles to obtain an acceptable 3D model of the foot.  
The dataset was processed using the following algorithm: extract a series of images from a video file (30 from each video), manually mark each extracted image and form masks (Figure 3), divide the resulting set into training and test samples by an 80/20 proportion, and convert the resulting mask set into a COCO-annotation file.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Measurements**} & \multicolumn{8}{c}{**Men**} & \multicolumn{8}{c}{**Women**} \\ \cline{2-13}  & \multicolumn{4}{c}{**Left Foot**} & \multicolumn{4}{c}{**Right Foot**} & \multicolumn{4}{c}{**Left Foot**} & \multicolumn{4}{c}{**Right Foot**} \\ \cline{2-13}  & **Min** & **Max** & **Avg** & **Std** & **Min** & **Max** & **Avg** & **Std** & **Min** & **Max** & **Avg** & **Std** \\ \hline Length foot (mm) & 253 & 307 & 266.15 & 13.91 & 252 & 307 & 267.07 & 14.05 & 228 & 319 & 255.93 & 23.02 & 232 & 321 & 255 & 23.07 \\ Width foot (mm) & 95 & 128 & 116 & 12.56 & 95 & 129 & 13.29 & 44.53 & 80 & 111 & 94.93 & 9.85 & 80 & 111 & 96.07 & 10.46 \\ Instep girth (mm) & 200 & 265 & 247.43 & 19.91 & 204 & 270 & 248.93 & 17.14 & 210 & 270 & 228.79 & 15.33 & 208 & 277 & 229.43 & 17.27 \\ Ball girth (mm) & 232 & 270 & 250 & 9.27 & 231 & 270 & 249.71 & 9.65 & 199 & 282 & 228.14 & 21.63 & 210 & 279 & 229.36 & 19.30 \\ Heel girth (mm) & 245 & 360 & 322.64 & 31.13 & 243 & 360 & 323.43 & 31.41 & 280 & 360 & 311.57 & 26.51 & 282 & 360 & 309.93 & 25.90 \\ Shin girth (mm) & 203 & 260 & 226.86 & 16.76 & 201 & 261 & 226.86 & 18.22 & 182 & 280 & 218.86 & 27.50 & 181 & 260 & 217.64 & 22.35 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary information. Values of men’s and women’s feet for each of the measurements.