Methodologies to build automatic point distribution models for faces represented in images

This paper presents new methods to automatically build Point Distribution Models for faces represented in images. These models consider significant points of faces from several images and study them in order to obtain the mean shape of the object and the main modes of variation. Active Shape Models and Active Appearance Models use the Point Distribution Model to segment the modelled object in new images. In this paper these models, their automatically building and some application examples from objects like faces represented in images are describe. Figure 1. Training image, landmarks and an image labelled with the landmark points (from left to right). In this modelling method, all the training examples are aligned into a standard co-ordinate frame and a Principal Component Analysis is applied to the co-ordinates of the landmark points. This produces the mean position for each landmark, and a description of the main ways in which these points tend to move together. The equation below represents the Point Distribution Model or Shape Model and can be used to generate new shapes: = + s s x x P b , (1) where x represents the n points of the shape: ( ) 0 0 1 1 1 1 , , , , , , T n n x x y x y x y − − = K , ( ) , k k x y the position of point k , x the mean position of the points, ( ) 1 2 s s s st P p p p = K the matrix of the first t modes of variation, si p , corresponding to the most significant eigenvectors in a Principal Component Analysis of the position variables, and