One of the frameworks used in shape space is to represent the data as landmarks. Each shape is a point set of \(k\) points in \(\mathbf{R}^p\) where each point is a labeled object. We consider general landmarks in \(p=2,3,\ldots\). Note that when \(p > 2\), it is stratified space but we assume singularities do not exist or are omitted. The wrapper takes translation and scaling out from the data to make it preshape (centered, unit-norm). Also, for convenience, orthogonal Procrustes analysis is applied with the first observation being the reference so that all the other data are aligned to that reference. The full orthogonal group O(p), including reflections, is used. This is not an SO(p)-only orientation-preserving analysis. Singular configurations are rejected. Fitted tangent models retain and apply their own training reference.
Arguments
- input
data matrices to be wrapped as
riemdataclass. Following inputs are considered,- array
a \((k\times p\times n)\) array where each slice along 3rd dimension is a \(k\)-ad in \(\mathbf{R}^p\).
- list
a length-\(n\) list whose elements are \(k\)-ads.
- reference
optional reference configuration for alignment. If NULL, the first observation is used.
Value
a named riemdata S3 object containing
- data
a list of preshapes in \(\mathbf{R}^p\).
- size
size of each preshape.
- name
name of the manifold of interests, "landmark"
References
Dryden IL, Mardia KV (2016). Statistical shape analysis with applications in R, Wiley series in probability and statistics, Second edition edition. John Wiley and Sons, Chichester, UK ; Hoboken, NJ. ISBN 978-1-119-07251-5 978-1-119-07250-8.
Examples
## USE 'GORILLA' DATA
data(gorilla)
riemobj = wrap.landmark(gorilla$male)