Statistical models for the evolution of facial curves

Resumen

This thesis presents statistical models for the study of the evolution of shape. Particularly, it focuses on the evolution of facial curves. Evolution can be modelled viewing time as a linear, continuous variable, i.e., one curve that is gradually changing in a particular situation. Alternatively, it can play the role of evolutionary time, where branching points in the evolution can occur: ancestors diverging into multiple daughters. Two applications are studied: the evolution of the shape of the lips during the performance of an emotion (linear evolution) and the evolution of nose shape within and between ethnic groups (phylogenetic evolution). The facial images available are in the form of three-dimensional point clouds which characterize each facial surface. Each face is represented by around 100,000 points. Anatomical curves are studied to provide a rich characterization of the full anatomical surface. The curves define the boundaries of morphological features of interest, using information of the facial surface curvature. Methods for the identification of facial three-dimensional curves are studied, and an algorithm to track four-dimensional curves (three spatial dimensions plus time) proposed.