FindGraph performs a least-squares orthogonal generalized Procrustes analysis
(least-squares orthogonal mapping).
Procrustes analysis is a method of comparing two sets of data. The method is based on matching corresponding points (landmarks) from each of the two data sets.
Procrustes analysis is a rigid shape analysis that uses isomorphic scaling, translation, and rotation to
find the “best” fit between two or more landmarked shapes.
See wikipedia for generalized orthogonal Procrustes analysis,
and 'Procrustes Analysis' by Amy Ross, www.cse.sc.edu.
Landmarks are points that accurately describe a shape.
Corresponding landmarks would be the same landmark on two different shapes.
To define a reference cluster of landmarks with FindGraph we select the data series
and define N marks.
There are different ways to define an experimental cluster of landmarks:
select the points by hand;
take first N points in series;
find best pattern of N points in series.
FindGraph uses scaling, translation, rotation, and additionally stretching/compressing
and shearing transformations.
It applies nonlinear mapping algorithm to find best fit,
i.e. to find a reference cluster of landmarks,
so that the distance of each reference landmark to it's corresponding experimental landmark
Data points can be given greater or less influence over the Procrustes analysis
by assigning a weight to each point.
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