This undertaking employs advanced statistical techniques in higher dimensions to evaluate the fundamental asymmetry of a patient's facial muscle movements. The primary statistical test utilized is Marietan's "T1-test."
An illustration of the utility usage is present in the main.py
file. The application involves three distinct stages of data
transformations, commencing from the raw data situated in the
/data/ directory, culminating in the computation of the final
p-value.
[_xy, _dxdy, _ids, _frames, _x_mean] = stage_1()
_left_ids, _right_ids = stage_2(_xy, _dxdy, _ids, _frames, _x_mean)
L, R = stage_3(_left_ids, _right_ids, _dxdy, _frames)
print("p value is", stats.marietan_test.marietan_T1_test(L,R))The initial phase (refer to stage_1()) entails converting the
raw data into a more usable format, which includes xy, dxdy,
ids, frames, x_mean. In this context, xy represents the
(x,y) coordinates of each id, dxdy indicates the smoothed
vectors corresponding to any given frame and id, ids records
the available ids, frames gathers the available frames, and
x_mean denotes the average x-coordinate value of all the points.
Subsequently, in the second stage (refer to stage_2()), the
primary objective is to establish a correspondence between the
left and right half points of the face. This is accomplished
using the Hungarian algorithm. The outcomes of stage_2 are two
lists, namely _left_ids and _right_ids. The first list contains
the ids of the points on the left-half of the face, while the
second list contains the ids of the points on the right-half of
the face. Specifically, _left_ids[j] represents the point on the
left-half of the face, and its corresponding mirrored point is
_right_ids[j].
In the third stage (refer to stage_3()), we create two
matrices, the Left Matrix L and the Right Matrix R. L
contains ten vectors of the same size, one for each frame. Each
vector corresponds to a particular frame and comprises the
concatenation of all [dx, dy] pairs for all the points on the
left side of the face, as per the order specified by _left_ids.
The Right Matrix R is similar to L, except that all its dx values
are multiplied by -1.
Finally, we use the marietan_T1_test() function to evaluate L
and R and obtain the p_value. If the computed p_value is
less than 0.05, it implies that the face muscle movements are
significantly asymmetrical, based on statistical analysis.