Accurate landmark localisation is an essential precursor to many 3D face processing algorithms but, as yet, there is a lack of convincing solutions that work well over a wide range of head poses.\ud In this thesis, an investigation to localise facial landmarks from 3D images is presented, without using any assumption concerning facial pose. In particular, this research devises new surface descriptors, which are derived from either unstructured face data, or a radial basis function (RBF) model of the facial surface.\ud A ground–truth of eleven facial landmarks is collected over well–registered facial images in the Face Recognition Grand Challenge (FRGC) database. Then, a range of feature descriptors of varying complexity are investigated to illustrate repeatability and accuracy when computed for the full set of eleven facial landmarks. At this stage, the nose–tip and two inner–eye corners are observed as the most distinctive facial landmarks as a trade–off among repeatability, accuracy, and complexity. Thus, this investigation focuses on the localisation of these three facial landmarks, which is the minimum number of landmarks necessary for pose normalisation.\ud Two new families of descriptors are introduced, namely point–pair and point–triplet descriptors, which require two and three vertices respectively for their computation. Also, two facial landmark localisation methods are investigated; in the first, a binary decision tree is used to implement a cascade filter, in the second, graph matching is implemented via relaxation by elimination. Then, using all of these descriptors and algorithms, a number of systems are designed to localise the nose–tip and two inner–eye corners. Above all, 99.92% of nose–tip landmarks within an accuracy of 12mm is the best localisation performance, which is achieved by one cascade filter system.\ud Finally, landmark localisation performance is reported by using a novel cumulative error curve. Localisation results are gathered by computing errors of estimated landmark locations against respective ground–truth data
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