[vector(numeric)] Times (abscisse) of the first trajectories.
Py
[vector(numeric)] Values of the first trajectories.
Qx
[vector(numeric)] Times of the second trajectories.
Qy
[vector(numeric)] Values of the second trajectories.
timeScale
[numeric]: allow to modify the time scale,
increasing or decreasing the cost of the horizontal shift. If timeScale is
very big, then the Frechet's mean is equal to the
euclidienne distance. If timeScale is very slow, then it is equal to
the Dynamic Time Warping.
FrechetSumOrMax
[character]: Like Frechet's distance,
Frechet's mean can
be define using the 'sum' function or the 'max' function. This option
let the user to chose one or the other.
weightPQ
[couple(numeric)]: respective weight of the two trajectories
(for a weighted mean).
Details
Given two curve P and Q
The Frechet distance between P and Q is define as
distFrechet(P,Q)=inf_{a,b} max_{t} d(P(a(t)),Q(b(t))).
The Frechet path is the couple of function (a(t),b(t)) that
realize the equality of the Frechet distance:
distFrechet(P,Q)=max_{t} d(P(a(t)),Q(b(t)))
Frechet mean is the curve define by the
sequence of all the center of the segments define by the Frechet
path [a(t),b(t)]. If P and
Q have respectively weight p and q, the center is the weighted mean of
the segments : $c(t)=(p.a(t)+q.b(t))/(p+q)$.
The Frechet distance, path and means can also be define using a sum instead of a max.