Non-linear point distribution modelling using a multi-layer perceptron

Abstract

Objects of the same class sometimes exhibit variation in shape. This shape variation has previously been modelled by means of point distribution models (PDMs) in which there is a linear relationship between a set of shape parameters and the positions of points on the shape. A polynomial regression generalization of PDMs, which succeeds in capturing certain forms of non-linear shape variability, has also been described. Here we present a new form of PDM, which uses a multi-layer perceptron to carry out non-linear principal component analysis. We compare the performance of the new model with that of the existing models on two classes of variable shape: one exhibits bending, and the other exhibits complete rotation. The linear PDM fails on both classes of shape; the polynomial regression model succeeds for the first class of shapes but fails for the second; the new multi-layer perceptron model performs well for both classes of shape. The new model is the most general formulation for PDMs which has been proposed to date.