*4.4. Movement Characterization by Kinematic Parameters*

The analysis and the related characterization of the considered UPDRS tasks make use of kinematic parameters which are mainly estimated from angles between pairs of body segments, involving femur, knee, tibia, spine and head. The body segments are defined by their distal and proximal points, which in our system are assumed to correspond to the joints of the skeleton model of Figure 2. The centroid of each segment is calculated as the midpoint between the proximal and distal extremities. The postural stability is assessed by the body CoM, which is estimated by the weighted average of the body segment centroids. In particular, the kinematic characterization of the LA, AC and Po tasks is based on the evaluation of the angles ANGKNEE and ANGTRUNK. Only for the Po task two further angles are considered: the forward ANGFORHEAD and lateral ANGLATHEAD bending angles of the head respect to spine direction. Specifically, with reference to Figure 5 for the proximal and distal 3D points relevant for the analysis, and to Figure 2a for the 3D skeleton joints involved, we considered:


**Figure 5.** Segments involved in the estimation of the angular measures during lower limbs and postural tasks: (**a**) LA task (**b**) AC task (**c**) Po task. Note that the depth axis of the Kinect device is perpendicular to the subject frontal plane in all the tests, see Section 4.3).

The CoM is estimated during the Phase1 and the Phase2 of the Po task, both to evaluate the postural instability and to evidence the effects of the secondary tasks. A subject specific quasi-static center of mass **C**<sup>b</sup> is evaluated by applying the kinematic method described in [52,53]. As indicated in Equation 1, **C**<sup>b</sup> is obtained by the weighted average of the body segment centroids (**C**i), evaluated from the skeleton model, where the weights wi are provided by standard body segment densities obtained from anthropometric data [54]:

$$\mathbf{C}\_{\mathbf{b}} = \frac{1}{N} \sum\_{i=1}^{N} \mathbf{C}\_{i} \ast \; \mathbf{w}\_{i} \tag{1}$$

The centroids **C**<sup>i</sup> of the following segments made by pairs of skeleton joints are considered (Figure 2a): Head-SpineS, ShouldR-WristR, ShouldL-WristL, SpineS-SpineB, HipR-AnkleR, and HipL-AnkleL. Please note that **C**<sup>b</sup> is a 3D point; but here only the transverse (or horizontal) plane components are evaluated for the analysis of the body sway. Concerning the evaluation of the kinematic parameters, the skeleton joints provided every 1/30 s by the Kinect SDK allow the estimation of the relevant parameters at the same rate. In particular, the angles ANGKNEE, ANGTRUNK, ANGFORHEAD and ANGLATHEAD were evaluated from the inner products of the pairs of unity vectors representing to the body segments involved. The vertical direction *n*ˆ, used to evaluated ANGTRUNK, was estimated by the normal to the floor plane. The 3D orientation of the plane was obtained by segmentation of the Kinect depth map using a RANSAC approach [55], with the upside direction of the Kinect skeleton and the feet location as priors. The angle signals were resampled both to remove the typical jitter of the Kinect sampling frequency, and to fit the sampling frequency of the optoelectronic system (100 Hz). The signals are filtered to reduce noise by a second order low-pass Butterworth filter with a cut-off frequency of 10Hz. Most of the significant kinematic parameters presented in the Results and used as input to the classifiers were obtained by standard signal processing algorithms applied to the sampled signals of the ANGKNEE, ANGTRUNK, ANGFORHEAD and ANGLATHEAD angles. The velocity parameters were evaluated as the derivatives of the spline approximations to the angle signals obtained through Matlab functions (unmkpp, mkpp and ppval). Specifically:

• For the LA task, the ANGKNEE signal is segmented in a sequence of flexion/extension movements (cycles) by finding all the minimum-maximum-minimum sequences in the amplitude of the angle signal. The peak to peak amplitude, the speed and the duration of every flexion/extension movement of the leg is evaluated. Specifically, MKAm is the mean of the peak to peak amplitude

maxima and MKAv is its standard deviation; TDm is the mean of the cycle durations and TDv is its standard deviation; SPm is the mean of the speed maxima. Finally PM is the number of "poor movements", defined as the cycles whose amplitude and duration are both less than 25% of the MKAm and the TDm values. This last parameter tries to catch hesitations and very small amplitude cycles in a sequence of almost relevant cycles.


The Pearson's correlation between the measures of the kinematic parameters provided by our system and those measured by the optoelectronic system was used to assess the body tracking accuracy. Because all the kinematic parameters for LA, AC, Po and PSCOM were obtained from the ANGKNEE, ANGTRUNK, ANGFORHEAD and ANGLATHEAD angles and from the CoM components in the transversal plane, only these last "essential" parameters were considered for the accuracy assessment.

The correspondences between optoelectronic markers (Figure 4 and Table 1) and Kinect joints (Figure 2a) we adopted for the comparison are shown in Table 2. The optoelectronic angular parameters corresponding to the essential ones were obtained by the marker correspondences of Table 2 and by the same procedure we used for the Kinect joints in Section 4.4. The CoM measured by the optoelectronic system was evaluated according to [51].


**Table 2.** Correspondences between body segments for Kinect and optoelectronic systems.

<sup>a</sup> MeanPSI = (LPSI + RPSI)/2.
