## 2 Analysis of Existing Technology Solutions  
### Developed Products and Applications  
Today, there are several software products that functionally include the reconstruction of 3D models of human feet.  
For instance, 3D Avatar feet [5] is a mobile application developed by Instituto de Biomecanica (IBV), Valencia, Spain. This system enables obtaining a reconstructed 3D foot model based on three images. The system is based on principal component analysis (PCA) [3], and its application on 40 parameters allows the creators to obtain the maximum error of 1.7 mm on length and width rates. At the output, the user receives a summary of more than 20 parameters (length, width, different foot girths) and a 3D model in STL/PLY format. However, a significant disadvantage of the system is the absence of an individual reconstructed lower arch of the 3D model. This fact makes it only applicable for shoe size recommendations and not for orthopedic tailoring.  
FITTIN [6] is a piece of software that was developed by a Russian IT enterprise. The authors of the system offer the user two methods for 3D reconstruction with the help of special sensors and on the basis of a series of images obtained from a smartphone. The FITTMScope device [7] consists of a camera and special probes, which it is assumed are to be used when working with special sensors. Information about the position of each probe is collected in real-time by the built-in mini-video camera with illumination. Indicator probes provide information about cross-sections of the inner surface in each shot, and the data obtained are then converted into a non-linear space or three-dimensional coordinate system, and the initial point cloud is formed into a 3D model. In the case of a series of images to calibrate measurements, the authors suggest using a white sheet of A4 paper or other items such as a coin, a bank card, or a ruler. By taking a circular photo, the system converts the series of images into a lower resolution to simplify the calculations. After that, the contour of the foot is highlighted on the A4 sheet. The extracted unique voxels further form a polygonal mesh (3D model). The noted disadvantage of the product is a large linear error (1.3 mm). This method is well suited for virtual shoe fitting or size recommendations but not for reconstructing the shape of the foot.  
The authors of the DomeScan/IBV [8] solution suggest using a small universal scanner for home use, which weighs less than 5 kg. The developers state that the scanning time for this product is less than 0.1 s, and the 3D reconstruction time is less than one minute. The mathematical methods for reconstruction are based on PCA. In the study [9], the authors conducted experiments and scanned 16 human feet (8 men and 8 women), which resulted in a linear measurement deviation of less than 0.97 mm.  
Volumental [10] is a mobile application for Apple devices. The application is based on the use of a special LiDAR depth sensor, which has been integrated into Apple mobile devices since the iPhone 12 Pro. This solution makes it possible to obtain output information in the form of generated foot size parameters, instep height, foot width, arch height, and a 3D model. The developers state that their solution has already scanned around 22 million feet for more than 2500 online stores. Further, it should be noted that the deviation of the three-dimensional reconstruction method by linear measurements is about 5 mm, which corresponds to half the shoe size, and this is much higher than that of analogs mentioned earlier.  
Analysis of the listed products points to the conclusion that the issue of creating a system for reconstructing the 3D shape of the human foot remains relevant today. Therefore, it is necessary to analyze a set of methods and tools to achieve this goal.