curve_to_q {fdasrvf}

Curve to SRVF Space

Description

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)

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.

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.

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.

Examples

q <- curve_to_q(beta[, , 1, 1])$q