Shape Modelling Using Maximum Autocorrelation Factors

This paper addresses the problems of generating a low dimensional representation of the shape variation present in a training set after alignment using Procrustes analysis and projection into shape tangent space. We will extend the use of principal components analysis in the original formulation of Active Shape Models by Timothy Cootes and Christopher Taylor by building new information into the model.

This new information consists of two types of prior knowledge. First, in many situation we will be given an ordering of the shapes of the training set. This situation occurs when the shapes of the training set are in reality a time series, e.g.\$\backslash\$ snapshots of a beating heart during the cardiac cycle or when the shapes are slices of a 3D structure, e.g. the spinal cord.

Second, in almost all applications a natural order of the landmark points along the contour of the shape is introduced. Both these types of knowledge may be used to defined Shape Maximum Autocorrelation Factors. The resulting point distribution models are compared to ordinary principal components analysis using leave-one-out validation.