## 2 Materials and Methods
### Feature Extraction and Parameters Assessment  
Once the 2D-KeyPoints had been found in the images, we could switch from image coordinates to spatial coordinates using the cloud point information and obtain, at the end of this matching process, a set of 3D-KeyPoints. These 3D-KeyPoints had to be validated, eliminating any false positives due to objects or other elements in the test environment, adding a consistency check concerning what was previously determined and also correcting any erroneous matching that had possibly occurred in tests involving more than one subject [40]. These post-processing tasks were carried out due to the complexity of the images taken during the test sessions and of the results of verifying whether updates of each subject's KeyPoints positions were consistent with those previously assumed. The checks implemented in this study took into account both the location and the speed of each KeyPoint. Downstream of these elaborations, our system analyzed the kinematics of the 3D KeyPoints to compute some of the features that are currently used by clinicians for MDS-UPDRS items' scoring. Motor impairment in PD is characterized by a reduction in walking speed due to the combination of a shorter stride length and a higher cadence, greater asymmetry of the upper and lower limbs, axial stiffness and a reduction in the excursion of the articular chains of the lower limbs, and postural instability. The setup for testing the gait of the subject consisted of arranging a free space to be walked through in a straight line, both with  
Figure 2: The KeyPoints of the BODY-25 model. and without an obstacle that the subject had to navigate around. The test was conducted with video cameras placed in the frontal and side positions (Figure 3). The tests were carried out following this procedure: in the first walk, the subject started in a standing position and was asked to walk forward, then simply turn around and walk back. In the second walk, the subject started again in a standing position and was asked to walk forward, avoiding and moving around an obstacle clockwise, then turn around and come back, moving around the same obstacle again (this time contra-clockwise). Item 3.10 of MDS-UPDRS aims to evaluate specific characteristics of the subject's gait that are useful for functional impairment assessment: stride amplitude and speed, turning, the height of foot lift and heel strike during walking. Stride length is the distance between successive points of initial contact of the same foot; it adds up the lengths of two steps, for the left and the right leg respectively, which are usually equal if the person is walking in a straight line. To assess left and right step lengths, stride amplitude and speed, the cinematic characteristics of two KeyPoints, No. 21 and No. 24, were considered, corresponding respectively to the left and right heel of the subject performing the test. In addition, the distance between these two KeyPoints was computed. People with Parkinson's disease have difficulty with turning, which is particularly challenging due to the significant number of additional steps and longer time required to turn. To assess turning, the cinematic characteristics of KeyPoint No. 8, corresponding to the middle point of the hips, was considered. Walking in PD is often characterized by short and stiff steps whose height becomes shorter. To assess the height of the foot lift, was possible to consider again the cinematic characteristics of the two KeyPoints corresponding to the left and right heel (No. 21 and No. 24) and analyze the height of the heels from the ground during walking. To minimize errors due to the presence of occlusions (e.g., when the nearest leg covers the farthest one) in the images recorded by the camera at the laterally viewed angle, only the section of the path travelled by the foot closest to the camera (and visible to it) was taken into consideration. For example, for the left foot, the kinematic characteristics of KeyPoint No.