Statistical models for the evolution of facial curves

Mariñas del Collado, Irene (2017) Statistical models for the evolution of facial curves. PhD thesis, University of Glasgow.

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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.

The physical characterisation of facial expression involves a set of human facial movements. This thesis considers the shape of the lips as a unique facial feature to characterise emotions. Different approaches are proposed to model the lip shape and its change during the performance of an emotion. A first analysis of the evolving curves is performed using techniques of Procrustes analysis and a model based on B-splines. The thesis then moves to Gaussian Process (GP) models as an alternative approach. Models for k-dimensional curves and k-dimensional evolving curves are proposed. One direct application of the GP models is to study the grouping of different expressions of emotions in a space defined in terms of correlation parameters. To model the evolution of facial curves over many generations, the GP model for evolving k-dimensional curves is extended, using the phylogenetic covariance function, to allow for branching points in the evolution. A case study is conducted on data specially collected from different ethnic groups, where the phylogenetic model is applied to points on two curves defining the shape of the nose.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Keywords: Gaussian processes, shape analysis, facial curves.
Subjects: H Social Sciences > HA Statistics
Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Statistics
Supervisor's Name: Macaulay, Dr. Vincent and Bowman, Professor Adrian
Date of Award: 2017
Depositing User: Dr Irene Mariñas
Unique ID: glathesis:2017-8641
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 19 Dec 2017 16:28
Last Modified: 11 Jan 2018 16:50

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