Q–MAF shape decomposition

Abstract

This paper address the problems of generating a low dimensional representation of the shape variation present in a set of shapes represented by a number of landmark points. First, we will present alternatives to the featured Least-Squares Procrustes alignment based on the L∞-norm and the L1-norm. Second, we will define a new shape decomposition based on the Maximum Autocorrelation Factor (MAF) analysis, and investigate and compare its properties to the Principal Components Analysis (PCA). It is shown that Molgedey-Schuster algorithm for Independent Component Analysis (ICA) is equivalent to the MAF analysis. The shape MAF analysis utilises the natural order of landmark points along shape contours.