1 Introduction

In the previous chapter, models for describing the (two-dimensional) appearance of faces were discussed. In this chapter, we continue to discuss models of facial images, this time, however, with the focus on three-dimensional models and how they are used for face tracking.

Whether we want to analyze a facial image (face detection, tracking, recognition) or synthesize one (computer graphics, face animation), we need a model for the appearance and/or structure of the human face. Depending on the application, the model can be simple (e.g., just an oval shape) or complex (e.g., thousands of polygons in layers simulating bone and layers of skin and muscles). We usually wish to control appearance, structure, and motion of the model with a small number of parameters, chosen so as to best represent the variability likely to occur in the application.

When analyzing facial images, we try to identify our model with the face in the image, find the model parameters that makes the model describe the image as well as possible, and regard the found model parameters as parameters of the face in the image. For example, if our face model is just an oval shape within a certain size range, we look for such a shape in the image, measure its position and size, and assume that the measured values are measurements of the position and size of the face.

When analyzing a sequence of images (or frames), showing a moving...