This function computes the SRVF of a given curve. The function also outputs
the length of the original curve and the \(L^2\) norm of the SRVF.
Usage
curve_to_q(beta, scale = TRUE)
Value
A list with the following components:
q: A numeric matrix of the same shape as the input matrix beta storing
the (possibly scaled) SRVF of the original curve beta;
len: A numeric value specifying the length of the original curve;
lenq: A numeric value specifying the \(L^2\) norm of the SRVF of the
original curve.
Arguments
beta
A numeric matrix of shape \(L \times M\) specifying a curve on
an \(L\)-dimensional space observed on \(M\) points.
scale
A boolean value specifying whether the output SRVF function
should be scaled to the hypersphere of \(L^2\). When scale is TRUE,
the length of the original curve becomes irrelevant. Defaults to TRUE.
References
Srivastava, A., Klassen, E., Joshi, S., Jermyn, I., (2011). Shape
analysis of elastic curves in Euclidean spaces. IEEE Transactions on
Pattern Analysis and Machine Intelligence, 33(7), 1415-1428.